RIS-assisted millimeter wave MIMO-NOMA Internet of Vehicles system channel estimation method based on 4D tensor

Abstract

The invention discloses a 4D tensor-based RIS-assisted millimeter wave MIMO-NOMA Internet of Vehicles system channel estimation method, and aims to reduce the influence of serious Doppler frequency shift and sight line path blockage on communication performance, first, a 5G subframe division scheme without changing a standard 5G frame structure is proposed by introducing concepts of aggregation time slot and half time slot, and a 5G subframe division scheme without changing a standard 5G frame structure is provided; modeling of the received signal is facilitated; then, modeling the received signal into a four-order tensor so as to separate channel parameters into four factor matrixes, thereby avoiding parameter coupling; then, the tensor is decomposed in a closed-form solution form; then, carrying out one-dimensional search on a factor matrix obtained by decomposition to extract channel parameters; after channel parameters are obtained, a least square problem is constructed to obtain channel path gains, and solving of a scaling matrix is avoided; finally, experiments verify that the method can accurately estimate the parameters of the channel, and excellent demodulation performance can be realized based on the parameters of the channel.

Description

Technical Field

[0001] The present invention belongs to the field of vehicle networking, and in particular to a RIS (reconfigurable intelligent surface) assisted millimeter wave MIMO-NOMA (multiple-input multiple-output non-orthogonal multiple access) vehicle networking system channel estimation method based on 4D (four-dimensional) tensor. Background Art

[0002] With the explosive growth of the number of wireless devices and the diversification of wireless service demands, the Internet of Everything is gradually becoming a reality, which has greatly promoted the development of various fields, especially the Internet of Vehicles (IoV). At the same time, it has put forward higher requirements for communication technology. The fifth generation (5G) communication system faces many challenges in supporting IoV, especially in terms of data transmission rate, connection density and positioning accuracy. In order to meet the needs of IoV users for ultra-high-speed data transmission, ultra-dense connections and high-precision positioning, the existing 5G communication system needs further technological innovation.

[0003] The combination of millimeter wave (mmWave) and non-orthogonal multiple access (NOMA) technology can bring unprecedented performance improvement to the existing 5G communication system. The large bandwidth of mmWave can provide a data transmission rate of gigabits per second, while NOMA technology can serve multiple users in the same time-frequency resource block, greatly improving the spectrum efficiency. However, due to the short propagation distance and weak penetration ability of mmWave, its inherent coverage is limited, which leads to significant path loss and susceptibility to obstruction along the line-of-sight (LoS) path.

[0004] To overcome these limitations, multiple-input multiple-output (MIMO) technology and reconfigurable intelligent surface (RIS) technology have been proposed. MIMO technology achieves significant beamforming gain by integrating a large number of antennas to compensate for free space loss and penetration loss. RIS technology uses information metamaterials to generate additional signal propagation paths through controllable electromagnetic properties to overcome obstacles on the line-of-sight path and achieve ideal beamforming gain. However, accurate channel state information (CSI) is the key to achieving optimal RIS phase control and obtaining high beamforming gain. In the IoV environment, the high-speed movement of vehicles brings about a significant Doppler shift effect, which requires the IoV system to frequently perform channel estimation to adapt to the rapid changes of the channel. In addition, the existing technology has deficiencies in handling multipath delays in multipath channels, which is particularly evident in broadband millimeter-wave channels. Therefore, developing a method that can accurately estimate the channel of the RIS-assisted millimeter-wave MIMO-NOMA system in fast-moving scenarios is crucial for practical applications in the IoV field.

[0005] At present, although a variety of channel estimation methods for RIS-assisted millimeter-wave MIMO systems have been proposed, these methods often do not fully consider the Doppler shift problem caused by high-speed movement in IoV systems, or ignore the multipath delay of multipath channels. The greater the mobile speed, the more serious the Doppler effect will be, causing the millimeter-wave channel to change rapidly in a short period of time. Therefore, frequent channel estimation is required to overcome the phase distortion caused by Doppler shift, resulting in overloaded pilot signaling overhead. Ignoring the multipath delay of multipath channels, that is, frequency selective fading, will make the system unsuitable for actual broadband millimeter-wave channels. In addition, the existing research results of RIS-assisted millimeter-wave MIMO systems that fully consider the angle of arrival (angle of arrival, AoA), angle of departure (angle of departure, AoD), multipath delay and Doppler shift are still very rare, not to mention the MIMO-NOMA system combined with NOMA technology. Therefore, the channel estimation method of RIS-assisted millimeter-wave MIMO-NOMA vehicle networking system in fast-moving scenarios that comprehensively considers channel parameters such as AoA, AoD, multipath delay and Doppler frequency shift has important theoretical and practical significance. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a RIS-assisted millimeter-wave MIMO-NOMA vehicle networking system channel estimation method based on 4D tensor, which can effectively improve the estimation performance of channel parameters such as AoA, AoD, multipath delay and Doppler frequency shift in fast moving scenarios.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a RIS-assisted millimeter wave MIMO-NOMA vehicle networking system channel estimation method based on 4D tensor, characterized by comprising the following steps:

[0008] Step 1: Establish a RIS-assisted millimeter-wave MIMO-NOMA vehicle networking system. Consider a two-dimensional scenario in which a base station, a RIS, and N U Mobile users, a hybrid analog-digital architecture is deployed in the base station and each mobile user, downlink communication is adopted between the base station and the mobile user, the LoS path between the base station and the mobile user is blocked, the base station provides communication services to all mobile users simultaneously through RIS and uses the same time-frequency resource block, the base station is equipped with N BS Antenna and M BS RIS is fixed in an aerial position and controlled by the base station. R reflection units, each mobile user is equipped with N MS Antenna and M MS RF chain; where N U >1, N U Mobile users share the same time-frequency resource block, M BS <N BS , M MS <N MS , the carrier center frequency of the NOMA system is set to f c , bandwidth is set to f s , the total number of subcarriers is set to N, and N subcarriers are used to transmit N s Serial data stream, K subcarriers are used as pilot subcarriers for channel estimation, 1<K<N;

[0009] Step 2: Establish the channel frequency domain model between the base station and RIS and between RIS and each mobile user, as follows:

[0010] The frequency domain model of the channel between the base station and the RIS: The frequency domain model of the channel between the base station and the RIS on the kth subcarrier is expressed as Where k = 1, 2, ..., N, G BR,krepresents the frequency domain channel between the base station and the RIS on the kth subcarrier, α represents the complex channel gain of the path between the base station and the RIS, and obeys the complex normal Gaussian distribution CN(0,1), e represents a natural constant, j represents the imaginary part, τ BR represents the path delay between the base station and RIS, θ BR represents the AoA of RIS, φ BR represents the AoD of the base station, a R (θ BR ) represents the steering vector associated with RIS, a B (φ BR ) represents the steering vector associated with the base station, (·) H represents the conjugate transpose operation, (·) T Represents a transpose operation;

[0011] Frequency domain model of the channel between RIS and each mobile user: Using the L-path geometry millimeter wave channel model, the time domain model of the channel between RIS and mobile users is expressed as Among them, t represents the time variable, τ represents the delay variable, G RM [t,τ] represents the time domain channel between RIS and mobile users, l = 1, 2, …, L, β l represents the complex channel gain of the lth path between the RIS and the mobile user, and obeys the complex normal Gaussian distribution CN(0,1), represents the Doppler shift of the lth path between the RIS and the mobile user, v represents the movement speed of the mobile user, represents the angle between the AoA of the mobile user on the lth path and the direction of motion, represents the AoA of the mobile user on the lth path, represents the AoD of RIS on the lth path, represents the guidance vector associated with the mobile user on the lth path, represents the steering vector associated with RIS on the lth path, represents the lth path delay between RIS and mobile user, δ(·) is the impulse function;

[0012] In the 5G system, the duration of each radio frame is 10ms, each radio frame consists of 10 subframes, the duration of each subframe is 1ms, each subframe consists of 8 aggregated time slots, each aggregated time slot is defined as 4 time slots, the duration of each time slot is 0.03125ms, the duration of each aggregated time slot is 0.125ms, and a half time slot is defined as half of a time slot, and a half time slot consists of 7 NOMA symbols; assuming that the channel between the RIS and the mobile user remains unchanged in an aggregated time slot, the time domain channel G between the RIS and the mobile user is RM [t,τ] is Fourier transformed to obtain the channel frequency domain model between RIS and mobile users on the kth subcarrier in the mth aggregation time slot: Where m = 1, 2, ..., M, M represents the number of aggregated time slots in a subframe, G RM,k [m] represents the frequency domain channel between the RIS and the mobile user on the kth subcarrier in the mth aggregated timeslot, T s =1 / Δf, Δf represents the subcarrier spacing, Δf=2 μ ×15KHz, μ ranges from 0 to 6, N b represents the number of NOMA symbols in a half-slot, N st Indicates the number of half-slots in an aggregated slot;

[0013] Step 3: The modulated data symbol on the kth subcarrier transmitted to the i-th mobile user is recorded as x i,k , the superimposed signal x on the kth subcarrier transmitted to all mobile users k Expressed as The data stream transmitted on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated slot is denoted as x nb,nst,k,m , The signal y received by all mobile users on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated time slot nb,nst,k,m Represented as y nb,nst,k,m =W H G RM,k [m]diag(Φ nst )G BR,k Fx nb,nst,k,m +W H n nb,nst,k,m (Equation 3.1); then transform equation 3.1 into (Equation 3.2); Then, based on equation 3.2, let Combined with G BR,k The expression and G RM,k The expression for [m] is

[0014]

[0015] Where i = 1, 2, ..., N U , P represents the normalized total transmission power of the base station, γ i represents the power allocation coefficient allocated to the i-th mobile user, nst=1,2,…,N st ,nb=1,2,…,N b , x nb,nst,k,m The dimension is N s ×1,x ns,nb,nst,k,m represents the nsth data stream transmitted on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated slot, ns = 1, 2, ..., N s ,y nb,nst,k,m The dimension is N s ×1, W represents the mixed combination matrix of mobile users, W is randomly generated from a unit circle, each column of which is normalized, and the dimension of W is N MS ×N s , diag(·) means to diagonalize the vector. ξ nr represents the phase shift of the nrth reflection unit of the RIS in the nst half-time slot, ξ nr ∈[0,2π],nr=1,2,…,N R , F represents the hybrid precoding matrix of the base station. F is randomly generated from a unit circle, and each column is normalized. The dimension of F is N BS ×N s , n nb,nst,k,m represents the received noise of all mobile users on the kth subcarrier of the nbth NOMA symbol in the nst half-slot in the mth aggregated slot, n nb,nst,k,m has a mean of 0 and a variance of Additive independent and identically distributed circularly symmetric complex Gaussian white noise, n nb,nst,k,m The dimension is N MS ×1, N MS The identity matrix of order, represents the Kronecker product, (·) * represents the conjugate operation, ⊙ represents the Khatri-Rao product, Z k [m] stands for G BR,k With G RM,k [m] cascade channel, ρ l represents the cascaded channel gain of the path between the base station and RIS and the lth path between RIS and the mobile user, ρ l =αβl ,

[0016] Step 4: Stack the data stream transmitted on the k'th pilot subcarrier of the nst half-time slot in the mth aggregated time slot into The stacked signal Y received by all mobile users on the k'th pilot subcarrier in the nst half-time slot in the mth aggregation time slot nst,k',m , Then make And define the phase shift matrix Based on equation 4.1, the stacked signal Y received by all mobile users on the k'th pilot subcarrier in the mth aggregation time slot is obtained: k',m , Then, combining equation 3.3 and equation 4.2, we can obtain the three-dimensional tensor of the stacked signal received by all mobile users on the K pilot subcarriers in the mth aggregation time slot: Redefine the factor matrix Factor Matrix Factor matrix C = [ρ1g(τ1),…,ρ L g(τ L )]=[c1,…,c L ], based on Equation 4.3, we get the four-dimensional tensor of the received signals of all mobile users Then define the factor matrix D = [d1,…,d L ]and Simplify Equation 4.4 to

[0017] Where k'=1,…,K,X nst,k',m The dimension is N s ×N b , Y nst,k',m The dimension is N s N b ×1, vec(·) indicates vectorized operation, N nst,k',m represents the received noise of all mobile users on the k'th pilot subcarrier in the nst half-slot in the mth aggregated time slot, N nst,k',m The dimension is N MS ×N b , ×1 means modulo 1 multiplication, Y k',m The dimension is N s N b ×N st , The three-dimensional tensor representing the received noise of all mobile users on the k'th pilot subcarrier in the mth aggregated time slot, The dimension is N MS ×N b ×N st , Indicates that all positive slices of a tensor are vectorized. The dimension is N s N b ×N st × K, represents the outer product, g(τ l ) has a dimension of K×1, The 4D tensor representing the received noise of all mobile users on the K pilot subcarriers in the mth aggregated time slot, The dimension is N MS ×N b ×N st ×K, the dimension of A is N s N b ×L,a l is the lth column vector of A, and the dimension of B is N st ×L,b l is the lth column vector of B, the dimension of C is K×L, c l is the lth column vector of C, The dimension is N s N b ×N st ×K×M, d l The dimension is M×1, d l is the lth column vector of D, A five-dimensional tensor representing the received noise of all mobile users, The dimension is N MS ×N b ×N st ×K×M, Each element in has a mean of 0 and a variance of σ 2 The additive independent and identically distributed circularly symmetric complex Gaussian distribution, represents the Kruskal operator;

[0018] Step 5: Decompose by CP The factor matrix A, B, C, D is estimated from make Transform Equation 5.1 into a three-dimensional tensor CP decomposition problem, which can be described as: For Equation 5.2 Performing modulo 1 expansion, we get Define an integer pair (K4, L4) that satisfies K4+L4=M+1, and define a spatial smoothing operator Will The spatial smoothing matrix Expressed as The factor matrix D is a Vandermonde matrix with And when l'=1, diag l'-1 (D) is a unit matrix, we get For Equation 5.5 Perform singular value decomposition and get Combination is full column rank, and L is known, there exists a full rank matrix Make Then get Based on equations 5.9 and 5.10, we get Equation 5.11 is a similarity transformation that satisfies Perform truncated singular value decomposition on equation 5.11 to obtain Q and Λ, and then obtain According to equations 5.6, 5.7, 5.12 and 5.13, we can get Based on equation 5.14, we get the solution The least squares problem of is described as: Solving equation 5.15, we obtain The closed-form solution of Substituting equation 5.12 and equation 5.13 into equation 5.8, we obtain

[0019] Based on Equation 5.17, we get the solution The least squares problem of is described as: Solving equation 5.18, we get The closed-form solution of Based on formula 5.19, we construct a matrix to solve the matrix obtained by permuting and scaling the factor matrix A. The lth column vector of The matrix obtained after the permutation and scaling blur of and B The lth column vector of The least squares Khatri-Rao decomposition problem of is described as: By changing the Perform singular value decomposition and get The diagonal singular value matrix of Left singular matrix and the right singular matrix Then get Will get Corresponding to the estimated values ​​of A, B, C, and D;

[0020] Among them, ||·|| F It means to find the F norm, is a three-dimensional tensor, The dimension is N s N b N st ×K×M, E=B⊙A=[e1,…,e L ],e l is the lth column vector of E, The dimension is MK×N s N b N st , R (1) express The modulo 1 expansion, N (1) express Modulo 1 expansion, l'=1,2,…,L4,J l' The dimension is K4×M, when l'=1 Represents an empty matrix, when l'>1 represents an all-0 vector or all-0 matrix of dimension K4×(l'-1), Represents the K4-order identity matrix, when l'=L4 Represents an empty matrix, when l'<L4 represents an all-0 vector or all-0 matrix of dimension K4×(L4-l'), I K represents the identity matrix of order K, express The spatial smoothing expansion matrix, represents the submatrix consisting of the first K4 rows of D, 1 1×L represents a row vector of all 1s with a dimension of 1×L. When e'=1, diag e'-1 (D) represents the identity matrix, when e'>1, diag e'-1 (D) represents the diagonal matrix consisting of the l'-1th row elements of the matrix D, represents the submatrix consisting of the first L4-1 rows of D, and U represents The left singular matrix of The diagonal singular value matrix of The right singular matrix of The dimension is L×L, U (:,1:L) represents the submatrix consisting of the first L columns of U, express The lth column vector of represents the column vector consisting of the first K4 rows and the eth column of D, V (:,1:L) represents the submatrix consisting of the first L columns of V, Σ (1:L,1:L) represents the submatrix consisting of the first L rows and first L columns of Σ, represents the submatrix consisting of the first K (K4-1) rows and the first L columns of U, represents the submatrix consisting of the 2nd to K4th rows of D, represents the submatrix consisting of the K+1th to KK4th rows and the first L columns of U, represents the submatrix consisting of the first K4-1 rows of D, is a diagonal matrix whose elements consist of the first row elements of the factor matrix D, Superscript represents the pseudo-inverse, Λ represents the The matrix composed of the eigenvalues ​​of , Δ represents an unknown non-singular diagonal scaling fuzzy matrix, Π represents an unknown non-singular diagonal permutation matrix, represents the matrix obtained by permuting and scaling the factor matrix D The submatrix composed of the first K4 rows of express The e-th column vector, Λ (l,l) represents the e-th row and e-th column element of Λ, represents the matrix obtained by permuting and scaling the factor matrix C, express The e-th column vector of Indicated by The column vector consisting of the first K4 rows and the eth column, Q (:,l) represents the lth column vector of Q, Indicated by The submatrix composed of the first L4-1 rows of represents the matrix obtained by permuting and scaling the factor matrix E, express The lth column vector of Represents a row vector of all 1s and The matrix reconstructed from all elements in the first L4-1 rows of express The lth column vector of N s Nb N st The identity matrix of order S (:,l) represents the lth column vector of S, S = Q -T , Indicates that The matrix is ​​transformed into a dimension of N s N b ×N st The matrix of express The first row and first column element of express The first column vector of express The first column vector of

[0021] Step 6: Based on get Estimated value of Through the maximum likelihood estimator, we get τ l Estimated value of The solution of Estimated value of The solution of Estimated value of The solution of Through the one-dimensional search formula 6.2, we can obtain Through the one-dimensional search formula 6.3, we can obtain By one-dimensional search formula 6.4, we can obtain pass get Estimated value of

[0022] Among them, ∠(Λ (l,l) ) represents Λ (l,l) The phase of , |·| is the modulus operator, ||·||2 is the two-norm operator;

[0023] Step 7: Build the solution The least squares problem of is described as: By defining the matrix Γ k',m and vector ζ k',m , Γ k',m The element in the i'th row and j'th column is The solution of Equation 7.1 is expressed as right The average of all elements in is taken as the channel cascade gain vector estimate

[0024] in, is l,k',m The estimated value of l,k',m represents the concatenated channel gain of the path between the base station and the RIS and the lth path between the RIS and the mobile user on the k'th pilot subcarrier in the mth aggregation time slot, i',j'=1,2,…,L, Tr(·) means finding the trace of the matrix, represents the concatenated channel gain on the k'th pilot subcarrier in the mth aggregated time slot, Represents ρ l An estimated value of

[0025] Step 8: Substituting into equation 3.3, we get the estimated value of the cascade channel.

[0026] Compared with the prior art, the advantages of the present invention are:

[0027] 1) By introducing the concepts of aggregated time slots and half time slots, the present invention proposes a 5G subframe division scheme, which further refines the subframe without changing the standard 5G frame structure, so as to model the data transmitted by the pilot subcarriers in the received signal as a 4D tensor, so as to avoid the need for frequent channel estimation to overcome the phase distortion caused by Doppler frequency shift, thereby resulting in overloaded pilot signaling overhead.

[0028] 2) The present invention models the data transmitted by the pilot subcarrier in the received signal as a 4D tensor, which satisfies the canonical polyadic (CP) decomposition form, and can separate AoA, AoD, multipath delay and Doppler shift into four corresponding factor matrices, avoiding parameter coupling. Then, the present invention uses the Vandermonde structure of the factor matrix corresponding to the Doppler shift and the low-rank characteristics of the millimeter wave channel to propose a 4D structured tensor decomposition, decomposing the tensor into four factor matrices through a closed-form solution, avoiding initialization and iteration, and having low computational complexity.

[0029] 3) After obtaining the AoA, AoD, multipath delay and Doppler shift channel parameters through one-dimensional search, the present invention constructs a least squares problem to obtain the cascade channel gain. The problem has a closed-form solution, does not require the solution of the scaling matrix, and has low computational complexity.

[0030] 4) Simulation experimental results show that the method of the present invention has high channel estimation performance and low bit error rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a general implementation block diagram of the method of the present invention;

[0032] Figure 2 This is a model diagram of the RIS-assisted millimeter-wave MIMO-NOMA vehicle networking system;

[0033] Figure 3 A schematic diagram of the 5G subframe division scheme proposed by the method of the present invention;

[0034] Figure 4 The channel parameter (AoA parameter at the mobile user) vector estimated by the existing CP-ALS-QR method and the OMP method and the method of the present invention (4DSTDCE) is Schematic diagram of the curve of the estimated mean square error (MSE) changing with the signal-to-noise ratio (SNR);

[0035] Figure 5 The channel parameter (AoD parameter at RIS) vector estimated by the existing CP-ALS-QR method and OMP method and the method of the present invention (4DSTDCE) is Schematic diagram of the curve of the estimated mean square error (MSE) changing with the signal-to-noise ratio (SNR);

[0036] Figure 6 The channel parameter (channel delay parameter) vector estimated by the existing CP-ALS-QR method and OMP method and the method of the present invention (4DSTDCE) Schematic diagram of the curve of the estimated mean square error (MSE) changing with the signal-to-noise ratio (SNR);

[0037] Figure 7 The channel parameter (Doppler frequency shift parameter of the channel) vector estimated by the existing CP-ALS-QR method and OMP method as well as the method of the present invention (4DSTDCE) is Schematic diagram of the curve of the estimated mean square error (MSE) changing with the signal-to-noise ratio (SNR);

[0038] Figure 8 The channel parameter (cascade channel gain parameter) vector estimated by the existing CP-ALS-QR method and OMP method and the method of the present invention (4DSTDCE) is Schematic diagram of the curve of the estimated mean square error (MSE) changing with the signal-to-noise ratio (SNR);

[0039] Fig. 9 A schematic diagram of a curve showing the variation of the normalized mean square error (NMSE) of the cascaded channel estimated by the existing CP-ALS-QR method, the OMP method and the method of the present invention (4DSTDCE) with the signal-to-noise ratio (SNR);

[0040] Fig.10A schematic diagram of a curve showing the bit error rate (BER) of a signal of mobile user 1 demodulated at mobile user 2 as a function of the signal-to-noise ratio (SNR) by the existing CP-ALS-QR method, the OMP method and the method of the present invention (4DSTDCE);

[0041] Fig.11 The present invention is a schematic diagram of a curve showing the bit error rate (BER) of the mobile user 2 signal demodulated at the mobile user 2 by the existing CP-ALS-QR method, the OMP method and the method of the present invention (4DSTDCE) as a function of the signal-to-noise ratio (SNR). DETAILED DESCRIPTION

[0042] The present invention is further described in detail below with reference to the accompanying drawings.

[0043] The present invention proposes a RIS-assisted millimeter wave MIMO-NOMA vehicle networking system channel estimation method based on 4D tensor in a fast moving scenario, and its overall implementation block diagram is as follows: Figure 1 As shown, it includes the following steps:

[0044] Step 1: Establish a RIS-assisted mmWave MIMO-NOMA connected vehicle system, such as Figure 2 As shown, a two-dimensional scene is considered in the system, in which a base station, a RIS, N U Mobile Station. To facilitate the hardware implementation of the system, a hybrid analog-digital architecture is deployed in the base station and each mobile user. Downlink communication is adopted between the base station and the mobile user. Due to the obstruction of the building, the LoS path between the base station and the mobile user is blocked. The base station uses RIS and uses the same time-frequency resource block to communicate with all mobile users at the same time. Figure 2 Only two mobile users are shown, namely Mobile Station 1 and Mobile Station 2) provide communication services, and the base station is equipped with N BS Antenna and M BS RIS is fixed in an aerial position, such as on the facade of a building, and is controlled by a base station. R Each mobile user is equipped with N reflection units (array elements). MS Antenna and M MS RF chain; where N U >1, N U Mobile users share the same time-frequency resource block. Mobile users can be moving objects such as vehicles or drones. BS <N BS , M MS <N MSIf the hybrid analog-digital architecture is not deployed in the base station and each mobile user, the number of RF chains required is the same as the number of antennas. After the hybrid analog-digital architecture is deployed, only a small number of RF chains are required, thereby reducing the cost. In this embodiment, N is taken U =2, N BS =32, M BS =8, N MS =32, M MS =8, N R =64, the carrier center frequency of the NOMA system is set to f c , bandwidth is set to f s , the total number of subcarriers is set to N, and N subcarriers are used to transmit N s The K subcarriers (the first K subcarriers of the N subcarriers) are used as pilot subcarriers for channel estimation, 1<K<N, and in this embodiment, f c =28GHz, f s =0.32GHz, N=256, N s =4, K=25, all antennas equipped by the base station are arranged to form a uniform linear array (ULA) with a half-wavelength interval, all antennas equipped by each mobile user are arranged to form a uniform linear array with a half-wavelength interval, and all reflective units of the RIS are arranged to form a uniform linear array with a half-wavelength interval.

[0045] Step 2: Establish the channel frequency domain model between the base station and RIS and between RIS and each mobile user, as follows:

[0046] Channel frequency domain model between the base station and RIS: Generally speaking, the base station and RIS are at a higher position, which limits the local scattering. The signal transmission between the base station and RIS is carried out through the LoS path. Therefore, the channel frequency domain model between the base station and RIS on the kth subcarrier is expressed as Where k = 1, 2, ..., N, G BR,k represents the frequency domain channel between the base station and the RIS on the kth subcarrier, α represents the complex channel gain of the path between the base station and the RIS, and obeys the complex normal Gaussian distribution CN(0,1), e represents a natural constant, e=2.71…, j represents the imaginary part, τ BR represents the path delay between the base station and the RIS. In this embodiment, τ BR ∈(0,250)ns,θ BR represents the AoA of RIS, φ BR represents the AoD of the base station. In this embodiment, θ BR ∈(0,π / 2),φ BR ∈(0,π / 2), a R (θ BR) represents the steering vector associated with RIS, a B (φ BR ) represents the steering vector associated with the base station, (·) H represents the conjugate transpose operation, (·) T represents the transposition operation, where the base station and RIS are installed at known fixed positions, so θ BR ,φ BR and τ BR can be considered known.

[0047] Frequency domain model of the channel between RIS and each mobile user: For the channel between RIS and mobile users, the Doppler frequency shift caused by the rapid movement of mobile users will cause the channel between RIS and mobile users to change rapidly. In order to characterize the impact of Doppler frequency shift on the millimeter wave MIMO channel, the present invention adopts the L-diameter geometry millimeter wave channel model. In this embodiment, L=4 is taken, and the time domain model of the channel between RIS and mobile users is expressed as Among them, t represents the time variable, τ represents the delay variable, G RM [t,τ] represents the time domain channel between RIS and mobile users, l = 1, 2, …, L, β l represents the complex channel gain of the lth path between the RIS and the mobile user, and obeys the complex normal Gaussian distribution CN(0,1), represents the Doppler shift of the e-th path between the RIS and the mobile user, v represents the moving speed of the mobile user. In this embodiment, v=100 km / h. represents the angle between the AoA of the mobile user on the e-th path and the direction of motion. In this embodiment, represents the AoA of the mobile user on the e-th path, represents the AoD of RIS on the e-th path. In this embodiment, represents the guidance vector associated with the mobile user on the lth path, represents the steering vector associated with RIS on the lth path, represents the lth path delay between the RIS and the mobile user. In this embodiment, δ(·) is the impulse function.

[0048] In mobile scenarios, the faster the mobile speed, the greater the Doppler shift, resulting in a shorter channel coherence time interval. Due to the large bandwidth and more diversified subcarrier spacing (SCS) definition in the 5G millimeter wave MIMO system, the SCS can be set larger than the sub-6G system, thereby shortening the symbol duration. Therefore, the complex channel gain, AoA, AoD, delay and Doppler shift remain almost unchanged during an aggregated time slot (each aggregated time slot consists of 4 time slots). According to the technical specifications of 5G; NR; Physical channels and modulation, 3GPP TS 38.211version18.2.0Release 18 (5G; New Air Interface; Physical Channels and Modulation, 3GPP organization in the 18.2.0 frozen version of TS38.211 of the 5G technical standard) released by the 3GPP organization, the value Δf of SCS can be set to 2 μ ×15KHz, where the value of μ ranges from 0 to 6. For example, when μ=5, the value of SCS is Δf=480KHz, then the duration of a time slot (consisting of 14 NOMA symbols) is 0.03125ms. In the 5G system, the duration of each radio frame is 10ms and it consists of 10 subframes, where the duration of each subframe is 1ms, and each radio frame consists of 320 time slots. Therefore, based on the technical specifications, the present invention does not change the 5G standard frame structure, but proposes a 5G subframe division scheme by introducing the concepts of aggregated time slots (each aggregated time slot consists of 4 time slots) and half time slots (a half time slot is half of a time slot), further refining the subframes, such as Figure 3 As shown. In the 5G system, the duration of each radio frame (oneframe) is 10ms, each radio frame consists of 10 subframes, the duration of each subframe (one subframe) is 1ms, each subframe is composed of 8 aggregated slots, each aggregated slot is defined as 4 slots, the duration of each slot is 0.03125ms, the duration of each aggregated slot is 0.125ms, and a half slot is defined as half of a slot, and a half slot consists of 7 NOMA symbols; if the moving speed v of the mobile user is 180Km / h, the moving distance of the mobile user is only 0.625cm, which can be completely ignored in far-field communication. Therefore, it can be reasonably assumed that the channel between the RIS and the mobile user remains unchanged in an aggregated slot, then the time domain channel G between the RIS and the mobile user RM [t,τ] is Fourier transformed to obtain the channel frequency domain model between RIS and mobile users on the kth subcarrier in the mth aggregation time slot: Where m = 1, 2, ..., M, M represents the number of aggregated time slots in a subframe, M = 8, G RM,k [m] represents the frequency domain channel between the RIS and the mobile user on the kth subcarrier in the mth aggregated timeslot, T s =1 / Δf, Δf represents the subcarrier spacing, Δf=2 μ ×15KHz, the value range of μ is 0-6, in this embodiment, μ=5, Δf=480KHz, N b represents the number of NOMA symbols in a half-slot, N b =7,N st N represents the number of half-slots in an aggregated slot. st =8.

[0049] Step 3: Based on the proposed 5G subframe division scheme, the received signal is modeled as a four-dimensional tensor. In the NOMA system, the base station uses the same time-frequency resource block to send signals to multiple mobile users at the same time. By combining the orthogonal amplitude modulation (QAM) technology, the NOMA system can achieve a higher transmission rate. The modulated data symbol on the kth subcarrier transmitted to the i-th mobile user is denoted as x i,k , the superimposed signal x on the kth subcarrier transmitted to all mobile users k Expressed as The data stream transmitted on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated slot is denoted as x nb,nst,k,m , The signal y received by all mobile users on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated time slot nb,nst,k,m Represented as y nb,nst,k,m =W H G RM,k [m]diag(Φ nst )G BR,k Fx nb,nst,k,m +W H n nb,nst,k,m (Equation 3.1); then transform equation 3.1 into

[0050] Then, based on Equation 3.2, let Combined with G BR,k The expression and G RM,k The expression for [m] is

[0051]

[0052] Where i = 1, 2, ..., N U, P represents the normalized total transmission power of the base station, the value is 1, γ i represents the power allocation coefficient allocated to the i-th mobile user. In this embodiment, γ1=0.8, γ2=0.2, nst=1, 2, ..., N st ,nb=1,2,…,N b , x nb,nst,k,m The dimension is N s ×1,x ns,nb,nst,k,m represents the nsth data stream transmitted on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated slot, ns = 1, 2, ..., N s ,y nb,nst,k,m The dimension is N s ×1, W represents the mixed combination matrix of mobile users, W is randomly generated from a unit circle, each column of which is normalized, and the dimension of W is N MS ×N s , diag(·) means to diagonalize the vector. ξ nr represents the phase shift of the nrth reflection unit of the RIS in the nst half-time slot, ξ nr ∈[0,2π],nr=1,2,…,N R , F represents the hybrid precoding matrix of the base station. F is randomly generated from a unit circle, and each column is normalized. The dimension of F is N BS ×N s , n nb,nst,k,m represents the received noise of all mobile users on the kth subcarrier of the nbth NOMA symbol in the nst half-slot in the mth aggregated slot, n nb,nst,k,m has a mean of 0 and a variance of Additive independent and identically distributed (iid) circularly symmetric complex Gaussian white noise, n nb,nst,k,m The dimension is N MS ×1, N MS The identity matrix of order, represents the Kronecker product, (·) * represents the conjugate operation, ⊙ represents the Khatri-Rao product, Z k [m] stands for G BR,k With G RM,k [m] cascade channel, ρ l represents the cascaded channel gain of the path between the base station and RIS and the lth path between RIS and the mobile user, ρ l =αβ l ,

[0053] Step 4: Stack the data stream transmitted on the k'th pilot subcarrier of the nst half-time slot in the mth aggregation time slot into X nst,k',m , The stacked signal Y received by all mobile users on the k'th pilot subcarrier in the nst half-time slot in the mth aggregation time slot nst,k',m , It is worth noting that the N transmitted on the pilot subcarrier s The serial data streams are independent and different in one half-slot, but are the same in different half-slots. Therefore, let X = X nst,k',m and And define the phase shift matrix It is worth noting that the phase shift matrix is ​​the same in different aggregation time slots. Based on equation 4.1, the stacked signal Y received by all mobile users on the k'th pilot subcarrier in the mth aggregation time slot is obtained: k',m , Then, combining equation 3.3 and equation 4.2, we can obtain the three-dimensional tensor of the stacked signal received by all mobile users on the K pilot subcarriers in the mth aggregation time slot: ,

[0054] Redefine the factor matrix Factor Matrix Factor matrix C = [ρ1g(τ1),…,ρ L g(τ L )]=[c1,…,c L ], based on Equation 4.3, we get the four-dimensional tensor of the received signals of all mobile users Formula 4.4 satisfies the canonical polyadic (CP) decomposition; then the factor matrix D is defined as [d1,…,d L ]and Simplify Equation 4.4 to

[0055] Where k'=1,…,K,X nst,k',m The dimension is N s ×N b , x 1,nst,k',m represents the data stream transmitted on the k'th pilot subcarrier of the 1st NOMA symbol of the nst half-slot in the mth aggregated slot, Indicates the Nth half-slot in the mth aggregated slot b The data stream transmitted on the k'th pilot subcarrier of a NOMA symbol, Y nst,k',m The dimension is Ns N b ×1, y 1,nst,k',m represents the signal received by all mobile users on the k'th pilot subcarrier of the 1st NOMA symbol of the nst half-slot in the mth aggregated slot, represents the Nth half-slot of all mobile users in the mth aggregated time slot b The signal received on the k'th pilot subcarrier of a NOMA symbol, G BR,k' represents the frequency domain channel between the base station and the RIS on the k'th pilot subcarrier, G RM,k' [m] represents the frequency domain channel between the RIS and the mobile user on the k'th pilot subcarrier in the mth aggregation time slot, vec(·) represents the vectorization operation, N nst,k',m represents the received noise of all mobile users on the k'th pilot subcarrier in the nst half-slot in the mth aggregated time slot, n 1,nst,k',m represents the received noise of all mobile users on the k'th pilot subcarrier of the 1st NOMA symbol of the nst half-slot in the mth aggregated slot, represents the Nth half-slot of all mobile users in the mth aggregated time slot b The received noise on the k'th pilot subcarrier of a NOMA symbol, N nst,k',m The dimension is N MS ×N b , ×1 means modulo 1 multiplication, Y k',m The dimension is N s N b ×N st , The three-dimensional tensor representing the received noise of all mobile users on the k'th pilot subcarrier in the mth aggregated time slot, The dimension is N MS ×N b ×N st , Indicates that all positive slices of a tensor are vectorized, such as a three-dimensional tensor The dimensions are I1×I2×I3, The dimension is I1I2×I3, The dimension is N s N b ×N st × K, represents the outer product, g(τ l) has a dimension of K×1, The 4D tensor representing the received noise of all mobile users on the K pilot subcarriers in the mth aggregated time slot, The dimension is N MS ×N b ×N st ×K, the dimension of A is N s N b ×L,a l is the lth column vector of A, and the dimension of B is N st ×L,b l is the lth column vector of B, the dimension of C is K×L, c l is the lth column vector of C, The dimension is N s N b ×N st ×K×M, d l The dimension is M×1, d l is the lth column vector of D, A five-dimensional tensor representing the received noise of all mobile users, The dimension is N MS ×N b ×N st ×K×M, Each element in has a mean of 0 and a variance of σ 2 The additive independent and identically distributed (iid) circularly symmetric complex Gaussian distribution, Represents the Kruskal operator.

[0056] Step 5: Before estimating the channel parameters, decompose the The factor matrix A, B, C, D is estimated from To solve Equation 5.1, let Transform Equation 5.1 into a three-dimensional tensor CP decomposition problem, which can be described as: For Equation 5.2 Performing modulo 1 expansion, we can get Define an integer pair (K4, L4) that satisfies K4+L4=M+1. In this embodiment, K4=floor(M+1) / 2, L4=M+1-K4, floor(·) means rounding up, and define a spatial smoothing operator Will The spatial smoothing matrix Expressed as Since the factor matrix D is a Vandermonde matrix, we have And when l'=1, diag l'-1 (D) is a unit matrix, from which we can deduce For Equation 5.5 Performing singular value decomposition (SVD), we can get For ease of explanation, the noise term is ignored in the following derivation. is full column rank, and L is known, there exists a full rank matrix Make

[0057] Therefore, it can be deduced that Based on Equation 5.9 and Equation 5.10, we can deduce Equation 5.11 is a similarity transformation that satisfies Perform truncated singular value decomposition on equation 5.11 to obtain Q and Λ, and then obtain According to equations 5.6, 5.7, 5.12 and 5.13, we can deduce Based on equation 5.14, we get the solution The least squares problem of is described as: Solving equation 5.15, we obtain The closed-form solution of Substituting equation 5.12 and equation 5.13 into equation 5.8, we can get Based on Equation 5.17, we get the solution The least squares problem of is described as: Solving equation 5.18, we get The closed-form solution of Based on formula 5.19, we construct a matrix to solve the matrix obtained by permuting and scaling the factor matrix A. The lth column vector of The matrix obtained after the permutation and scaling blur of and B The lth column vector of The least squares Khatri-Rao decomposition problem of is described as: because is a rank-one vector, so we can Perform singular value decomposition and get The diagonal singular value matrix of Left singular matrix and the right singular matrix Then get Will get Corresponding to the estimated values ​​of A, B, C, and D.

[0058] Among them, ||·|| F It means to find the F norm, is a three-dimensional tensor, The dimension is N s N b N st ×K×M, E=B⊙A=[e1,…,e L ],e l is the e-th column vector of E, The dimension is MK×N s N b N st , R (1) express The modulo 1 expansion, N (1) express Modulo 1 expansion, l'=1,2,…,L4,J e' The dimension is K4×M, when l'=1 Represents an empty matrix, when l'>1 represents an all-0 vector or all-0 matrix of dimension K4×(l'-1), Represents the K4-order identity matrix, when l'=L4 Represents an empty matrix, when l'<L4 represents an all-0 vector or all-0 matrix of dimension K4×(L4-l'), I K represents the identity matrix of order K, express The spatial smoothing expansion matrix, represents the submatrix consisting of the first K4 rows of D, 1 1×L represents a row vector of all 1s with a dimension of 1×L. When l'=1, diag l'-1 (D) represents the identity matrix, when l'>1, diag l'-1 (D) represents the diagonal matrix consisting of the l'-1th row elements of the matrix D, represents the submatrix consisting of the first L4-1 rows of D, and U represents The left singular matrix of The diagonal singular value matrix of The right singular matrix of The dimension is L×L, U (:,1:L) represents the submatrix consisting of the first L columns of U, express The lth column vector of represents the column vector consisting of the first K4 rows and the lth column of D, V (:,1:L) represents the submatrix consisting of the first L columns of V, Σ (1:L,1:L) represents the submatrix consisting of the first L rows and first L columns of Σ, represents the submatrix consisting of the first K (K4-1) rows and the first L columns of U, represents the submatrix consisting of the 2nd to K4th rows of D, represents the submatrix consisting of the K+1th to KK4th rows and the first L columns of U, represents the submatrix consisting of the first K4-1 rows of D, is a diagonal matrix whose elements consist of the first row elements of the factor matrix D, Superscript represents the pseudo-inverse, Λ represents the The matrix composed of the eigenvalues ​​of , Δ represents an unknown non-singular diagonal scaling fuzzy matrix, Π represents an unknown non-singular diagonal permutation matrix, Represents Λ (l,l) The Mth power, represents the matrix obtained by permuting and scaling the factor matrix D The submatrix composed of the first K4 rows of express The lth column vector of (l,l) represents the l-th row and l-th column element of Λ, represents the matrix obtained by permuting and scaling the factor matrix C, express The lth column vector of Indicated by The column vector consisting of the first K4 rows and the lth column, Q (:,l) represents the lth column vector of Q, Indicated by The submatrix composed of the first L4-1 rows of represents the matrix obtained by permuting and scaling the factor matrix E, express The lth column vector of Represents a row vector of all 1s and The matrix reconstructed from all elements in the first L4-1 rows of express The e-th column vector of N s N b N st The identity matrix of order S (:,l) represents the lth column vector of S, S = Q -T , Indicates that The matrix is ​​transformed into a dimension of N s Nb ×N st The matrix of express The first row and first column element of express The first column vector of express The first column vector of .

[0059] Step 6: Based on get Estimated value of Through the maximum likelihood estimator, we get τ l Estimated value of The solution of Estimated value of The solution of Estimated value of The solution of By a simple one-dimensional search formula 6.2, we can obtain By a simple one-dimensional search formula 6.3, we can obtain By a simple one-dimensional search formula 6.4, we can obtain pass get Estimated value of

[0060] Among them, ∠(Λ (l,l) ) represents Λ (l,l) The phase of , |·| is the modulus operator, and ||·||2 is the two-norm operator.

[0061] Step 7: Build the solution The least squares problem of is described as: By defining the matrix Γ k',m and vector ζ k',m , Γ k',m The element in the i'th row and j'th column is The solution of Equation 7.1 can be expressed as right The average of all elements in is taken as the channel cascade gain vector estimate

[0062] in, is l,k',m The estimated value of l,k',mrepresents the concatenated channel gain of the path between the base station and the RIS and the lth path between the RIS and the mobile user on the k'th pilot subcarrier in the mth aggregation time slot, i',j'=1,2,…,L, Tr(·) means finding the trace of the matrix, κ j',k',m and κ i',k',m pass To obtain, represents the concatenated channel gain on the k'th pilot subcarrier in the mth aggregated time slot, Represents ρ l The estimated value of .

[0063] Step 8: Substituting into equation 3.3, we get the estimated value of the cascade channel.

[0064] The feasibility, effectiveness and positioning performance of the method of the present invention are verified by simulation experiments as follows.

[0065] The experimental conditions of the RIS-assisted millimeter-wave MIMO-NOMA vehicle networking system are: the number of antennas of the base station is N BS =32, the number of radio frequency chains of the base station M BS =8, Number of antennas for mobile users N MS =32, the number of radio frequency chains of mobile users M MS =8, the number of reflection units of RIS N R =64, carrier center frequency f of NOMA system c =28GHz, bandwidth f s = 0.32GHz, total number of subcarriers N = 256, number of parallel data streams N s =4, number of pilot subcarriers K = 25, number of channel paths between RIS and mobile users L = 4, speed of mobile users v = 100 km / h, subcarrier spacing Δf = 480 KHz, number of NOMA symbols in one half-slot N b =7, the number of half slots in an aggregated slot N st =8, the number of aggregated time slots in a subframe M = 8, the number of mobile users served by the base station using the same time-frequency resource block N U=2, the power allocation coefficient γ1 allocated to the first mobile user is 0.8, and the power allocation coefficient γ2 allocated to the second mobile user is 0.2. The system adopts 4-QAM modulation, and adopts diversity technology to improve transmission reliability, and the maximum ratio combining (MRC) technology to combine the signals received by different antennas. Finally, the zero-forcing serial interference cancellation (ZF-SIC) technology is applied to decode the two mobile users. The performance comparison is with the Cramer-Rao lower bound (CRB), the CP-ALS-QR method proposed in the literature CPdecomposition for tensors via alternating least squares with QR decomposition, and the OMP method proposed in the literature Channellestimation for IRS-assisted millimeter-wave MIMO systems: Sparsity-inspired approaches.

[0066] Figure 4 The channel parameter vector estimated by the existing CP-ALS-QR method, OMP method and the method of the present invention (4DSTDCE) is given. The curve of the estimated mean square error (MSE) as the signal-to-noise ratio (SNR) changes, Figure 5 The channel parameter vector estimated by the existing CP-ALS-QR method, OMP method and the method of the present invention (4DSTDCE) is given. The curve of the estimated mean square error (MSE) as the signal-to-noise ratio (SNR) changes, Figure 6 The channel parameter vector estimated by the existing CP-ALS-QR method, OMP method and the method of the present invention (4DSTDCE) is given. The curve of the estimated mean square error (MSE) as the signal-to-noise ratio (SNR) changes, Figure 7 The channel parameter vector estimated by the existing CP-ALS-QR method, OMP method and the method of the present invention (4DSTDCE) is given. The curve of the estimated mean square error (MSE) as the signal-to-noise ratio (SNR) changes, Figure 8 The channel parameter vector estimated by the existing CP-ALS-QR method, OMP method and the method of the present invention (4DSTDCE) is given. The estimated mean square error (MSE) of changes with the signal-to-noise ratio (SNR). Figures 4 to 8It can be seen that the channel parameter vectors estimated by the method of the present invention are closest to the Cramer-Rao lower bound, which illustrates the superiority of the method of the present invention in channel parameter estimation.

[0067] Fig. 9 The curves of the normalized mean square error (NMSE) of the cascade channel estimated by the existing CP-ALS-QR method, the OMP method and the method of the present invention (4DSTDCE) as a function of the signal-to-noise ratio (SNR) are given. Fig. 9 It can be seen from the figure that the normalized mean square error of the cascade channel estimated by the method of the present invention decreases with the increase of the signal-to-noise ratio, and has the best cascade channel estimation performance.

[0068] In order to further illustrate the superiority of the performance of the method of the present invention, the present invention also Fig.10 The curves of the bit error rate (BER) of the signal of mobile user 1 demodulated at mobile user 2 and the signal-to-noise ratio (SNR) are given in the existing CP-ALS-QR method, the OMP method and the method of the present invention (4DSTDCE), and the Fig.11 The curves of the bit error rate (BER) of the mobile user 2 signal demodulated at the mobile user 2 by the existing CP-ALS-QR method, the OMP method and the method of the present invention (4DSTDCE) are given as a function of the signal-to-noise ratio (SNR). Fig.10 and Fig.11 It can be seen that the method of the present invention has the lowest bit error rate at both mobile user 1 and mobile user 2 compared with the existing method.

Claims

1. A RIS-assisted millimeter-wave MIMO-NOMA vehicle networking system channel estimation method based on 4D tensor, characterized in that The following steps are involved: Step 1: Establish a RIS-assisted millimeter-wave MIMO-NOMA vehicle networking system. Consider a two-dimensional scenario in which a base station, a RIS, and N U Mobile users, a hybrid analog-digital architecture is deployed in the base station and each mobile user, downlink communication is adopted between the base station and the mobile user, the LoS path between the base station and the mobile user is blocked, the base station provides communication services to all mobile users simultaneously through RIS and uses the same time-frequency resource block, the base station is equipped with N BS Antenna and M BS RIS is fixed in an aerial position and controlled by the base station. R Each mobile user is equipped with N reflection units. MS Antenna and M MS RF chain; where N U >1, N U Mobile users share the same time-frequency resource block, M BS <N BS , M MS <N MS , the carrier center frequency of the NOMA system is set to f c , bandwidth is set to f s , the total number of subcarriers is set to N, and N subcarriers are used to transmit N s Serial data stream, K subcarriers are used as pilot subcarriers for channel estimation, 1<K<N; Step 2: Establish the channel frequency domain model between the base station and RIS and between RIS and each mobile user, as follows: The frequency domain model of the channel between the base station and the RIS: The frequency domain model of the channel between the base station and the RIS on the kth subcarrier is expressed as Where k = 1, 2, ..., N, G BR,k represents the frequency domain channel between the base station and the RIS on the kth subcarrier, α represents the complex channel gain of the path between the base station and the RIS, and obeys the complex normal Gaussian distribution CN(0,1), e represents a natural constant, j represents the imaginary part, τ BR represents the path delay between the base station and RIS, θ BR represents the AoA of RIS, φ BR represents the AoD of the base station, a R (θ BR ) represents the steering vector associated with RIS, a B (φ BR ) represents the steering vector associated with the base station, (·) H represents the conjugate transpose operation, (·) T Represents a transpose operation; Frequency domain model of the channel between RIS and each mobile user: Using the L-path geometry millimeter wave channel model, the time domain model of the channel between RIS and mobile users is expressed as Among them, t represents the time variable, τ represents the delay variable, G RM [t,τ] represents the time domain channel between RIS and mobile users, l = 1, 2, …, L, β e represents the complex channel gain of the e-th path between the RIS and the mobile user, and obeys the complex normal Gaussian distribution CN(0,1), represents the Doppler shift of the e-th path between the RIS and the mobile user, v represents the movement speed of the mobile user, represents the angle between the AoA of the mobile user on the e-th path and the direction of motion, represents the AoA of the mobile user on the lth path, represents the AoD of RIS on the lth path, represents the guidance vector associated with the mobile user on the lth path, represents the steering vector associated with RIS on the lth path, represents the e-th path delay between RIS and the mobile user, δ(·) is the impulse function; In the 5G system, the duration of each radio frame is 10ms, each radio frame consists of 10 subframes, the duration of each subframe is 1ms, each subframe consists of 8 aggregated time slots, each aggregated time slot is defined as 4 time slots, the duration of each time slot is 0.03125ms, the duration of each aggregated time slot is 0.125ms, and a half time slot is defined as half of a time slot, and a half time slot consists of 7 NOMA symbols; assuming that the channel between the RIS and the mobile user remains unchanged in an aggregated time slot, the time domain channel G between the RIS and the mobile user is RM [t,τ] is Fourier transformed to obtain the channel frequency domain model between RIS and mobile users on the kth subcarrier in the mth aggregation time slot: Where m = 1, 2, ..., M, M represents the number of aggregated time slots in a subframe, G RM,k [m] represents the frequency domain channel between the RIS and the mobile user on the kth subcarrier in the mth aggregated timeslot, T s =1 / Δf, Δf represents the subcarrier spacing, Δf=2 μ ×15KHz, μ ranges from 0 to 6, N b represents the number of NOMA symbols in a half-slot, N st Indicates the number of half-slots in an aggregated slot; Step 3: The modulated data symbol on the kth subcarrier transmitted to the i-th mobile user is recorded as x i,k , the superimposed signal x on the kth subcarrier transmitted to all mobile users k Expressed as The data stream transmitted on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated slot is denoted as x nb,nst,k,m , The signal y received by all mobile users on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated time slot nb,nst,k,m Represented as y nb,nst,k,m =W H G RM,k [m]diag(Φ nst )G BR,k Fx nb,nst,k,m +W H n nb,nst,k,m (Equation 3.1); then transform equation 3.1 into Then, based on Equation 3.2, let Combined with G BR,k The expression and G RM,k The expression for [m] is Where i = 1, 2, ..., N U , P represents the normalized total transmission power of the base station, γ i represents the power allocation coefficient allocated to the i-th mobile user, nst=1,2,…,N st ,nb=1,2,…,N b , x nb,nst,k,m The dimension is N s ×1,x ns,nb,nst,k,m represents the nsth data stream transmitted on the kth subcarrier of the nbth NOMA symbol in the nstth half-slot in the mth aggregated slot, ns = 1, 2, ..., N s ,y nb,nst,k,m The dimension is N s ×1, W represents the mixed combination matrix of mobile users, W is randomly generated from a unit circle, each column of which is normalized, and the dimension of W is N MS ×N s , diag(·) means to diagonalize the vector. ξ nr represents the phase shift of the nrth reflection unit of the RIS in the nst half-time slot, ξ nr ∈[0,2π],nr=1,2,…,N R , F represents the hybrid precoding matrix of the base station. F is randomly generated from a unit circle, and each column is normalized. The dimension of F is N BS ×N s , n nb,nst,k,m represents the received noise of all mobile users on the kth subcarrier of the nbth NOMA symbol in the nst half-slot in the mth aggregated slot, n nb,nst,k,m has a mean of 0 and a variance of Additive independent and identically distributed circularly symmetric complex Gaussian white noise, n nb,nst,k,m The dimension is N MS ×1, N MS The identity matrix of order, represents the Kronecker product, (·) * represents the conjugate operation, ⊙ represents the Khatri-Rao product, Z k [m] stands for G BR,k With G RM,k [m] cascade channel, ρ l represents the cascaded channel gain of the path between the base station and RIS and the lth path between RIS and the mobile user, ρ l =αβ l , Step 4: Stack the data stream transmitted on the k'th pilot subcarrier of the nst half-time slot in the mth aggregation time slot into X nst,k',m , The stacked signal Y received by all mobile users on the k'th pilot subcarrier in the nst half-time slot in the mth aggregation time slot nst,k',m , Then let X = X nst,k',m and And define the phase shift matrix Based on equation 4.1, the stacked signal Y received by all mobile users on the k'th pilot subcarrier in the mth aggregation time slot is obtained: k',m , Then, combining equation 3.3 and equation 4.2, we can obtain the three-dimensional tensor of the stacked signal received by all mobile users on the K pilot subcarriers in the mth aggregation time slot: (Formula 4.3); Redefine the factor matrix Factor Matrix Factor matrix C = [ρ1g(τ1),…,ρ L g(τ L )]=[c1,…,c L ], based on Equation 4.3, we get the four-dimensional tensor of the received signals of all mobile users Then define the factor matrix D = [d1,…,d L ]and Simplify Equation 4.4 to Where k'=1,…,K,X nst,k',m The dimension is N s ×N b , Y nst,k',m The dimension is N s N b ×1, vec(·) indicates vectorized operation, N nst,k',m represents the received noise of all mobile users on the k'th pilot subcarrier in the nst half-slot in the mth aggregated time slot, N nst,k',m The dimension is N MS ×N b , ×1 means modulo 1 multiplication, Y k',m The dimension is N s N b ×N st , The three-dimensional tensor representing the received noise of all mobile users on the k'th pilot subcarrier in the mth aggregated time slot, The dimension is N MS ×N b ×N st , Indicates that all positive slices of a tensor are vectorized. The dimension is N s N b ×N st × K, represents the outer product, g(τ l ) has a dimension of K×1, The 4D tensor representing the received noise of all mobile users on the K pilot subcarriers in the mth aggregated time slot, The dimension is N MS ×N b ×N st ×K, the dimension of A is N s N b ×L,a l is the lth column vector of A, and the dimension of B is N st ×L,b l is the lth column vector of B, the dimension of C is K×L, c l is the lth column vector of C, The dimension is N s N b ×N st ×K×M, d l The dimension is M×1, d l is the lth column vector of D, A five-dimensional tensor representing the received noise of all mobile users, The dimension is N MS ×N b ×N st ×K×M, Each element in has a mean of 0 and a variance of σ 2 The additive independent and identically distributed circularly symmetric complex Gaussian distribution of is, [[·]] represents the Kruskal operator; Step 5: Decompose by CP The factor matrix A, B, C, D is estimated from make Transform Equation 5.1 into a three-dimensional tensor CP decomposition problem, which can be described as: For Equation 5.2 Performing modulo 1 expansion, we get Define an integer pair (K4, L4) that satisfies K4+L4=M+1, and define a spatial smoothing operator Will The spatial smoothing matrix Expressed as The factor matrix D is a Vandermonde matrix with And when l'=1, diag l'-1 (D) is a unit matrix, we get For Equation 5.5 Perform singular value decomposition and get Combination is full column rank, and L is known, there exists a full rank matrix Make Then get Based on equations 5.9 and 5.10, we get Equation 5.11 is a similarity transformation that satisfies Perform truncated singular value decomposition on equation 5.11 to obtain Q and Λ, and then obtain According to equations 5.6, 5.7, 5.12 and 5.13, we can get Based on equation 5.14, we get the solution The least squares problem of is described as: 5.15); Solving equation 5.15, we get The closed-form solution of Substituting equation 5.12 and equation 5.13 into equation 5.8, we obtain Based on Equation 5.17, we get the solution The least squares problem of is described as: Solving equation 5.18, we get The closed-form solution of Based on formula 5.19, we construct a matrix to solve the matrix obtained by permuting and scaling the factor matrix A. The lth column vector of The matrix obtained after the permutation and scaling blur of and B The lth column vector of The least squares Khatri-Rao decomposition problem of is described as: By changing the Perform singular value decomposition and get The diagonal singular value matrix of Left singular matrix and the right singular matrix Then get Will get Corresponding to the estimated values ​​of A, B, C, and D; Among them, ||·|| F Indicates the F-norm. is a three-dimensional tensor, The dimension is N s N b N st ×K×M, E=B⊙A=[e1,…,e L ],e l is the e-th column vector of E, The dimension is MK×N s N b N st , R (1) express The modulo 1 expansion, N (1) express Modulo 1 expansion, e'=1,2,…,L4,J e' The dimension is K4×M, when e'=1 Represents an empty matrix, when e'>1 represents an all-0 vector or all-0 matrix of dimension K4×(e'-1), Represents the K4-order identity matrix, when l'=L4 Represents an empty matrix, when l'<L4 represents an all-0 vector or all-0 matrix of dimension K4×(L4-l'), I K represents the identity matrix of order K, express The spatial smoothing expansion matrix, represents the submatrix consisting of the first K4 rows of D, 1 1×L represents a row vector of all 1s with a dimension of 1×L. When l'=1, diag l'-1 (D) represents the identity matrix, when l'>1, diag l'-1 (D) represents the diagonal matrix consisting of the l'-1th row elements of the matrix D, represents the submatrix consisting of the first L4-1 rows of D, and U represents The left singular matrix of The diagonal singular value matrix of The right singular matrix of The dimension is L×L, U (:,1:L) represents the submatrix consisting of the first L columns of U, express The lth column vector of represents the column vector consisting of the first K4 rows and the lth column of D, V (:,1:L) represents the submatrix consisting of the first L columns of V, Σ (1:L,1:L) represents the submatrix consisting of the first L rows and first L columns of Σ, represents the submatrix consisting of the first K (K4-1) rows and the first L columns of U, represents the submatrix consisting of the 2nd to K4th rows of D, represents the submatrix consisting of the K+1th to KK4th rows and the first L columns of U, represents the submatrix consisting of the first K4-1 rows of D, is a diagonal matrix whose elements consist of the first row elements of the factor matrix D, Superscript represents the pseudo-inverse, Λ represents the The matrix composed of the eigenvalues ​​of , Δ represents an unknown non-singular diagonal scaling fuzzy matrix, Π represents an unknown non-singular diagonal permutation matrix, represents the matrix obtained by permuting and scaling the factor matrix D The submatrix composed of the first K4 rows of express The lth column vector of (l,l) represents the l-th row and l-th column element of Λ, represents the matrix obtained by permuting and scaling the factor matrix C, express The e-th column vector of Indicated by The column vector consisting of the first K4 rows and the eth column, Q (:,e) represents the lth column vector of Q, Indicated by The submatrix composed of the first L4-1 rows of represents the matrix obtained by permuting and scaling the factor matrix E, express The e-th column vector of Represents a row vector of all 1s and The matrix reconstructed from all elements in the first L4-1 rows of express The e-th column vector of N s N b N st The identity matrix of order S (:,l) represents the lth column vector of S, S = Q -T , Indicates that The matrix is ​​transformed into a dimension of N s N b ×N st The matrix of express The first row and first column element of express The first column vector of express The first column vector of Step 6: Based on get Estimated value of (Equation 6.1); Through the maximum likelihood estimator, we get τ e Estimated value of The solution of (Formula 6.2), Estimated value of The solution of Estimated value of The solution of Through the one-dimensional search formula 6.2, we can obtain Through the one-dimensional search formula 6.3, we can obtain By one-dimensional search formula 6.4, we can obtain pass get Estimated value of Among them, ∠(Λ (l,l) ) represents Λ (l,l) The phase of , |·| is the modulus operator, ||·||2 is the two-norm operator; Step 7: Build the solution The least squares problem of is described as: By defining the matrix Γ k',m and vector ζ k',m , Γ k',m The element in the i'th row and j'th column is The solution of Equation 7.1 is expressed as right The average of all elements in is taken as the channel cascade gain vector estimate in, is l,k',m The estimated value of l,k',m represents the concatenated channel gain of the path between the base station and the RIS and the lth path between the RIS and the mobile user on the k'th pilot subcarrier in the mth aggregation time slot, Tr(·) means finding the trace of the matrix. represents the concatenated channel gain on the k'th pilot subcarrier in the mth aggregated time slot, Represents ρ l An estimated value of Step 8: Substituting into equation 3.3, we get the estimated value of the cascade channel.

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