Irs aided cascaded mimo double-sparse channel state information estimation method

Abstract

The present application relates to IRS auxiliary cascade MIMO double sparse channel state information estimation method, method includes the following steps: S1, obtain the expression of the angle oversampling cascade channel, then the expression is vectorized again;S2, establish state space model;S3, initialize filter parameter;S4, obtain the observation vector of current pilot symbol;S5, by kalman filtering method calculates one step prediction and estimation angle gain value;S6, initialize the parameter of kalman filtering with norm constraint;S7, with norm constraint kalman filtering method one step prediction and estimation angle gain value;S8, judge whether the absolute value of the difference of two adjacent estimation value is less than the threshold value, and carry out iterative calculation;S9, update the symbol to the next symbol of current symbol, repeat S4-S8, and obtain the instantaneous cascade channel after the filter reaches steady state.Compared with the prior art, the present application has the advantages of strong applicability, no prior information and the like.

Description

Technical Field

[0001] This invention relates to the technical field of wireless channel state information estimation, and in particular to an IRS-assisted cascaded MIMO dual sparse channel state information estimation method. Background Technology

[0002] Intelligent reflective surfaces (IRS) are metasurfaces with numerous passive reflective elements. They can alter the phase of incident signals, thereby modulating the wireless transmission environment and improving spectral efficiency, and enhancing wireless coverage when direct links are obstructed. Obtaining auxiliary cascaded channel state information (CSI) is an essential component of performance improvement in wireless transmission systems incorporating IRS.

[0003] Since wireless channels in the millimeter-wave and terahertz bands typically have only a few diffusion paths, each hop of the IRS-assisted concatenated channel is a doubly sparse channel in both the angle and delay domains. Some research has been conducted on estimating millimeter-wave and terahertz band concatenated channels using sparse signal representation and recovery within the framework of compressed sensing theory.

[0004] Considering the high dimensionality and sparsity of cascaded channels, and combining parallel factorization models, researchers have proposed a series of alternating sparse channel estimation algorithms. The compressed sensing (CS) algorithms used fall into two main categories. The first category consists of sparse reconstruction algorithms, represented by the Orthogonal Matching Pursuit (OMP) algorithm, when sparsity is known. These include the Double Alternating OMP (BAOMP) algorithm and the Double Alternating Regularized OMP (BAROMP) algorithm. The second category consists of sparse reconstruction algorithms, represented by the Sparseness Adaptive Matching Pursuit (SAMP) algorithm, when sparsity is unknown. These algorithms estimate sparsity and fill supports by setting step sizes and appropriate termination conditions. These greedy sparse recovery algorithms typically utilize only a single measurement (observation) vector on the pilot tone, resulting in limited sparse recovery capabilities. Their performance in cascaded channel acquisition needs further improvement. Furthermore, the alternating sparse recovery method based on tensor decomposition still has drawbacks. Due to the non-uniqueness of tensor decomposition, it cannot be guaranteed that the sparse positions of the two channel segments are the same as the sparse positions of the original channel after decomposition, which limits the application of recovery algorithms that require known sparsity.

[0005] In summary, existing sparse channel estimation algorithms have poor recovery performance and require sparse prior information when the dictionary matrix is ​​highly correlated and the channel rank is severely deficient, thus their applicability is limited. Summary of the Invention

[0006] The purpose of this invention is to provide an IRS-assisted cascaded MIMO dual sparse channel state information estimation method to overcome the problem of limited applicability caused by the need for prior information.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A method for estimating the state information of dual sparse channels in IRS-assisted cascaded MIMO, comprising the following steps:

[0009] S1, For configuration N T The communication transmitter of the root transmitting antenna, with N I IRS and configuration of each reflective element N R A cascaded transmission system consisting of communication receivers with root receiving antennas constructs a receiving angle domain dictionary matrix D for channel H1 between the communication transmitter and the IRS. 1R and the transmitted angle domain dictionary matrix D 1T Simultaneously, for channel H2 between the communication receiver and the IRS, a receiving angle domain dictionary matrix D is constructed. 2R and the transmitted angle domain dictionary matrix D 2T Based on the above dictionary matrix, the expression for the cascaded channel after angle oversampling is obtained, and then the expression is vectorized. The vectorized expression includes the cascaded angle gain vector h to be determined.

[0010] S2. Establish a state-space model h(n) for any nth symbol corresponding to the cascaded angle gain vector of S1;

[0011] S3. Initialize the cascaded angle gain vector h to h(0), initialize the estimation error variance of the cascaded angle gain vector h to P(0), set the covariance matrix Q of the update noise in the state space model, and set the observation noise variance R according to the signal-to-noise ratio.

[0012] S4. Obtain the pilot tone observation matrix Y(s) through the diagonal pilot X(s) with guard interval zero-forcing block of the s-th symbol, and vectorize it to obtain the current observation vector y(s). The observation vector y(s) corresponds one-to-one with the symbol number s.

[0013] S5. For the current observation vector, calculate the one-step prediction h(s|s-1) of the angle gain vector using the Kalman filter method, calculate the one-step prediction estimation variance P(s|s-1) based on the covariance matrix Q, calculate the filter gain K(s) based on the observation noise variance R, obtain the current estimate h(s) based on the filter gain and the one-step prediction of the angle gain vector, and obtain the current estimation error variance P(s) based on the filter gain and the one-step prediction estimation variance.

[0014] The initial values ​​used in the first calculation using the Kalman filter method in S5 are the initial h(0) and P(0) of S3. The initial values ​​for other calculations are the cascaded angle gain vector and estimated variance of the current s-th symbol in S8.

[0015] S6. Construct a pseudo-measurement equation for the l1 norm, set the error variance of the l1 norm, and use the current estimated value h(s) as the initial value h for the l1 norm iterative correction. l (0), taking the current estimation error variance P(s) as the initial estimation error variance P for iteration. l (0);

[0016] S7. Calculate the one-step prediction h using the Kalman filter method. l (τ|τ-1), calculate the variance P of the one-step prediction estimation error. l (τ|τ-1), then calculate the iterative filter gain k. l (τ), calculate the current estimated value h l (τ) and the current estimation error variance P l (τ), where τ is the number of iterations;

[0017] The initial value used in S7 when the Kalman filter method was first applied for calculation was the same as the initial value h from S6. l (0) and the initial estimation error variance P l (0);

[0018] S8. Determine the estimated values ​​h of two adjacent values. l (τ) and h l If the absolute value of the difference in the l1 norm of (τ-1) is less than the threshold, the iteration stops; otherwise, it is determined whether the maximum number of iterations has been reached. If so, the iteration stops; otherwise, S7 continues to iterate.

[0019] In S8, after stopping the iteration, h, which has already undergone l1 norm iterative correction, is... l (τ) is used as the cascaded angle gain vector for the current s-th symbol, and P at the time of stopping iteration is... l (τ) represents the variance of the estimation error for the current s-th symbol;

[0020] S9. Update the symbol to the next symbol of the current symbol s. Repeat S4 to S8. After the filtering reaches a steady state, obtain the angle support and the corresponding angle gain in the sparse angle gain vector. Obtain the instantaneous matrix-vectorized channel according to the angle domain dictionary. Obtain the instantaneous cascaded channel H(s) through matrix transformation.

[0021] Furthermore, the vectorized expression for S1 is:

[0022]

[0023] Where H represents the cascaded channel after angle oversampling, g(s) represents the phase shift vector of the IRS at the s-th symbol, and A R，I and A I，TThese are the angle gain matrices between the communication receiver and the IRS in the dictionary-guided vector direction, and the angle gain matrices between the IRS and the communication transmitter, respectively. ⊙ and ⊙ represent the Kronecker product and Khatri-Rao product, respectively, with the symbols (·)* and (·). T and(·) H These represent conjugate, transpose, and conjugate transpose, respectively. Let be the cascaded angular gain vector to be determined.

[0024] Furthermore, the one-step prediction h(s|s-1) and the one-step prediction estimation variance P(s|s-1) of the angle gain vector of S5 are:

[0025] h(s|s-1)=ψh(s-1)

[0026] P(s|s-1)=ψP(s-1)+(1-ψ 2 )Q

[0027] Where ψ is the maximum Doppler frequency shift f in the state-space model. D Given the parameters, P(s-1) is the variance of the estimation error corresponding to the previous symbol, and Q is the covariance matrix of the updated noise.

[0028] Furthermore, the filter gain K(s) is:

[0029] K(s)=P(s|s-1)A H (s)(A(s)P(s|s-1)A H (s)+R) -1

[0030] Where R is the variance of the observation noise. X(s) is the diagonal pilot symbol with guard interval zero-forcing block, (·) * ,(·) T and(·) H These represent conjugate, transpose, and conjugate transpose, respectively.

[0031] The current estimated value h(s) and the current estimation error variance P(s) are:

[0032] h(s)=h(s|s-1)+K(s)(y(s)-A(s)h(s|s-1))

[0033] P(s)=P(s|s-1)-K(s)A(s)P(s|s-1)

[0034] Where h(s|s-1) is the one-step prediction of the angle gain vector, and P(s|s-1) is the variance of the one-step prediction estimation error.

[0035] Furthermore, the pseudo-measurement equation for S6 is:

[0036] 0=||h(s)||1-η(τ)∈

[0037] Where η is the adaptive factor, ∈ is a random number with a fixed variance, and τ is the number of iterations.

[0038] Furthermore, the adaptive factor is:

[0039] η(τ)=1-η(0)exp(-μτ / T)

[0040] Where η(0) and μ are shape parameters, T is a fixed positive constant, and τ is the number of iterations.

[0041] Furthermore, S7's one-step prediction η l (τ|τ-1) and the variance of the one-step prediction estimation error P l (τ|τ-1) is:

[0042] h l (τ|τ-1)=h l (τ-1)

[0043] P l (τ|τ-1)=P l (τ-1)

[0044] Among them, h l (τ-1) is the estimated value at the previous iteration number, P l (τ-1) represents the variance of the estimation error at the previous iteration number;

[0045] Iterative filter gain k l (τ) is:

[0046] k l (τ)=P l (τ|τ-1)c H (τ)(c(τ)P l (τ|τ-1)c H (τ)+r(τ)) -1

[0047] Where c(τ) is the Jacobian matrix composed of subgradient vectors, and r(τ) = η 2 (τ)r ∈ Let r be the measurement variance of the l1 norm. ∈ Let η be the fixed variance of the random number ∈, and η be the adaptive factor.

[0048] Furthermore, the current estimate h l (τ) and the current estimation error variance P l (τ) is:

[0049] h l (τ)=h l (τ|τ-1)+k l (τ)(0-c(τ)h l (τ|τ-1))

[0050] P l (τ)=P l (τ|τ-1)-k l (τ)c(τ)P l (τ|τ-1)

[0051] Where, k l (τ) represents the iterative filter gain.

[0052] Furthermore, the condition for determining whether filtering has reached a steady state is:

[0053] The judgment is made by determining whether the absolute difference of the sum of the main diagonal elements of the estimated error variance obtained from S8 of two adjacent symbols is less than a threshold. If it is, a steady state has been reached; otherwise, a steady state has not been reached.

[0054] Furthermore, the received angle domain dictionary matrix D 1R and the transmitted angle domain dictionary matrix D 1T They are respectively:

[0055]

[0056]

[0057] Received angle domain dictionary matrix D 2R and the transmitted angle domain dictionary matrix D 2T They are respectively:

[0058]

[0059]

[0060] Among them, a 1r，j and a 1t，j j = 0, ..., β1-1 are the steering vectors of channel H1 at the angular grid points, a 2r，j and a 2t，j ,j=0,...,β2-1 is the steering vector of channel H2 at the angle grid points.

[0061] Compared with the prior art, the present invention has the following beneficial effects:

[0062] This invention utilizes an angle-domain oversampling dictionary and diagonal pilots with guard interval zero-forcing blocks. Through pilot tone observation of the sequence and the time-domain correlation of the sparse angle gain vector, it reconstructs the static or dynamic sparse angle gain vector and the corresponding angle support and angle gain vector using a norm-constrained Kalman filtering method. Accurate channel state information can be obtained with relatively little pilot overhead. This invention has no restrictions on the angle-domain oversampling dictionary and can obtain angle support in both static and dynamic channel scenarios, enhancing its applicability. Furthermore, it does not require any prior information about the sparsity of the sparse angle gain vector. It offers high accuracy in estimating angle gain and support for static channels and can estimate angle support and track angle gain for dynamic channels. Attached Figure Description

[0063] Figure 1 This is a flowchart of the present invention;

[0064] Figure 2 This is a schematic diagram illustrating an application scenario of the present invention, wherein... Figure 2 (a) is a transmission scenario from a fixed-location communication transmitter (e.g., user) to an IRS and then to a fixed-location communication receiver (e.g., base station). Figure 2 (b) Application scenarios from mobile communication transmitters (e.g., vehicles) to IRS and then to fixed communication receivers (e.g., base stations);

[0065] Figure 3 This is a schematic diagram of the sparse structure of the angle domain angle gain matrix of the present invention;

[0066] Figure 4 This is a schematic diagram of the diagonal pilot pattern with a guard interval zero-forcing block according to the present invention;

[0067] Figure 5 For the present invention in static scene 1 (N) I The curve showing the variation of the normalized mean square error (NMSE) of the angle gain with the signal-to-noise ratio (SNR) under 4, 4×4 MIMO (L1=2, L2=3);

[0068] Figure 6 For the present invention in static scene 1 (N) I Tracking curves for channel complex fading amplitude under 4, 4×4 MIMO (L1=2, L2=3);

[0069] Figure 7 For the present invention in static scene 1 (N) I The estimation of angle support and angle gain under 4, 4×4 MIMO (L1=2, L2=3);

[0070] Figure 8 For the present invention in static scene 1 (N) IUnder MIMO conditions (L1 = 2, L2 = 3) and SNR = 10 dB, the curve showing the change of normalized mean square error (NMSE) with the number of pilot tone observation vectors.

[0071] Figure 9 For the present invention in dynamic scene 1 (N) I Under the conditions of 4, 4×4 MIMO, L1=2, L2=3, when SNR=10dB and the number of pilot tone observation vectors is 20, the curve of normalized mean square error (NMSE) as a function of ψ;

[0072] Figure 10 For the present invention in dynamic scene 1 (N) I =4, 4×4 MIMO, L1=2, L2=3), tracking curve for a non-zero angle gain h1 when SNR=10dB, pilot tone observation vector number is 20 and ψ=0.9;

[0073] Figure 11 For the present invention in dynamic scene 1 (N) I Under 4, 4×4 MIMO (L1=2, L2=3), at SNR=10dB and ψ=0.9, the curve showing the change of the l1 norm of the estimated angle gain vector with the number of pilot tone observation vectors;

[0074] Figure 12 For the present invention in static scene 2 (N) I The curve showing the variation of normalized mean square error (NMSE) of angle gain with SNR under 4, 4×4 MIMO (L1=1, L2=1);

[0075] Figure 13 For the present invention in static scene 2 (N) I Tracking curves for channel complex fading amplitude under 4, 4×4 MIMO (L1=1, L2=1);

[0076] Figure 14 For the present invention in static scene 2 (N) I The estimation of angle support and angle gain under 4, 4×4 MIMO (L1=1, L2=1);

[0077] Figure 15 For the present invention in static scene 2 (N) I Under MIMO (4×4 dimensional, L1=1, L2=1) conditions, the curve of normalized mean square error (NMSE) as a function of the number of pilot tone observation vectors when SNR=10dB;

[0078] Figure 16 For the present invention in dynamic scene 2 (N) IUnder the conditions of 4, 4×4 MIMO, L1=1, L2=1, when SNR=10dB and the number of pilot tone observation vectors is 20, the curve of normalized mean square error (NMSE) as a function of ψ;

[0079] Figure 17 For the present invention in dynamic scene 2 (N) I =4, 4×4 MIMO, L1=1, L2=1), tracking curve for a non-zero angle gain h1 when SNR=10dB, pilot tone observation vector number is 20 and ψ=0.9;

[0080] Figure 18 For the present invention in dynamic scene 2 (N) I Under 4, 4×4 MIMO (L1=1, L2=1), at SNR=10dB and ψ=0.9, the curve showing the change of the l1 norm of the estimated angle gain vector with the number of pilot tone observation vectors; Detailed Implementation

[0081] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0082] Definitions:

[0083] Intelligent Reflective Surfaces – IRS;

[0084] Multiple Input Multiple Output (MIMO).

[0085] This invention proposes an IRS-assisted cascaded MIMO dual sparse channel state information estimation method, the flowchart of which is as follows: Figure 1 As shown. Application scenarios of this invention include, for example... Figure 2 The scenarios shown include the transmission scenario from a fixed-location communication transmitter (e.g., a user) to an IRS and then to a fixed-location communication receiver (e.g., a base station), as shown in (a), and the application scenario from a mobile communication transmitter (e.g., a vehicle) to an IRS and then to a fixed communication receiver (e.g., a base station), as shown in (b). It may also include downlink application scenarios similar to those shown in (a) and (b). In (a) and (b), the MIMO channel H1(s) between the multiple antennas of the communication transmitter and the IRS element can be a time-invariant static channel or a time-varying dynamic channel, and the MIMO channel H2(s) from the IRS element to the communication receiver antenna is a time-invariant channel.

[0086] The IRS-assisted cascaded MIMO dual sparse channel model of this invention refers to a directional array channel model in the millimeter-wave or terahertz band. The antenna arrays at the communication transmitter and receiver can be either planar or linear arrays. The IRS element array is generally a planar array, but can be a linear array in special cases. Without loss of generality, each hop of the two-hop channel is assumed to be a millimeter-wave planar array antenna channel. The angular domain parameters of the channel are related to the number of paths, the departure angle and arrival angle of the path beam, and the corresponding steering vector, and can be expressed as:

[0087]

[0088]

[0089] In equations (1) and (2), L1 and L2 represent the number of paths in the two channels. and The path angle gain is represented by δ(·), which is the pulse shaping filter response. and These are path delays, and as well as These represent the azimuth and elevation angles of the signal incident (superscript r) and emitted (superscript t) respectively, and the steering vector a r and a t It can be uniformly written as:

[0090]

[0091] In the formula, 0≤m <N y , 0≤n <N z is the index number of the planar array element on the y-axis and z-axis, k = 2π / λ, λ is the wavelength, d is the antenna spacing, d = 0.5λ, (·) T This indicates transpose.

[0092] When angle parameter and as well as and With the corresponding angle gain and Even if the number of paths L1 and L2 are known, a millimeter-wave channel model with angular domain sparsity can be determined. Delay domain sparsity refers to the separability of multipath responses in the delay domain. To separate each path response beat, a diagonal pilot pattern with guard intervals and zero-forcing blocks can be used. By inserting zero-forcing guard intervals, the multi-beat response is separated into the sum of multiple single-beat responses, thus avoiding inter-symbol interference. The delay domain sparsity characteristic in the dual-sparseness of millimeter-wave or terahertz wave channels is hidden, and this hidden sparsity can be used to design pilot patterns.

[0093] When the beam direction is unknown, i.e., the steering vector, which depends on the departure angle and arrival angle, is unknown, a spatial angle grid is needed to divide the spatial angles and detect the response. The channel H1 between the communication transmitter and the IRS is divided into β1 angle grids. Each grid corresponds to a pair of azimuth and elevation angles of the transmitter and a pair of azimuth and elevation angles of the receiver. The steering vector on each grid can be obtained by using equation (3). Then, the dictionary matrix of channel H1 oversampled in the angle domain is obtained, including the dictionary matrix when the IRS is the receiver. dictionary matrix of the communication sender Similarly, the channel H2 between the communication receiver and the IRS is divided into β2 angular grids, with each grid corresponding to a pair of azimuth and elevation angles for the transmitter and a pair for the receiver, resulting in a dictionary matrix of H2 oversampled in the angular domain, including the dictionary matrix of the communication receiver. Dictionary matrix when IRS is the sender

[0094] Let the angle gains corresponding to these angle domain dictionaries be sparse matrices. and Using the angle domain dictionary, the cascaded channel can be written as:

[0095]

[0096] In the formula, g(s) is N in the symbol s. I A × 1-dimensional IRS phase shift vector, diag(·) denotes the vector diagonalization operator, A R，I and A I，T Let be the sparse angular gain matrices between the communication receiver and the IRS element, and between the IRS element and the communication transmitter, respectively, corresponding to the dictionary matrix. H This indicates the conjugate transpose.

[0097] According to the Kronecker product (using the symbol) The properties of the Khatri-Rao product (denoted by the symbol ⊙) and the Khatri-Rao product (denoted by the symbol ⊙) can be expressed as follows:

[0098]

[0099] In the formula, vec(·) represents the operator that vectorizes the matrix column by column, and (·)* represents the conjugate operation; Let be the sparse angular gain vector to be determined, and denoted as .

[0100] When considering the mobility of the communication transmitter or receiver, h can be modeled as a state-space model:

[0101]

[0102] In the formula, ψ is the time-domain correlation coefficient of the angle gain vector, which is given by the Jakes channel model ψ = J0(2πf D T s ) is determined, where J0(·) represents the zeroth-order Bessel function of the first kind, f D T represents the maximum Doppler frequency shift of the mobile party relative to the IRS in communication. s Given the symbol period, when both the communication transmitter and receiver are stationary relative to the IRS, ψ = 1, the state-space model of the angle gain vector degenerates into the time-invariant channel model h(s) = h(s-1), where v(s-1) is the update noise.

[0103] In this state-space model, the zero elements in h always remain zero regardless of the sign. When ψ = 1, it is a static sparse channel model, and when ψ < 1, it is a dynamic sparse channel model.

[0104] This invention reconstructs static or dynamic sparse angle gain vectors using a sequence of pilot tone observations within a Kalman filtering framework, employing an angle-domain oversampling dictionary and diagonal pilots with guard interval zero-forcing blocks. Utilizing the temporal correlation of the structured angle gain vectors, it accurately estimates the angle support and angle gain vectors using a time-series recursive method, obtaining accurate channel state information with minimal pilot overhead. The main idea of ​​this invention is to enhance applicability and reduce pilot overhead, while simultaneously reducing the computational complexity of angle-domain channel state information estimation. For the two segments of a MIMO cascaded channel, an unrestricted angle grid dictionary is used to construct a cascaded angle dictionary matrix. Within the Kalman filtering framework, the angle support and angle gain are estimated using sequential pilot tone measurements and a Kalman filter with l1-norm constraints. Its advantages include: it has no restrictions on the angle dictionary and can obtain the support of the angle domain in both static and dynamic channel scenarios, thus enhancing the applicability of the invention; it does not require any prior information about sparsity and can accurately obtain structured sparse channels with a small number of pilot tone observations; it has high accuracy in estimating angle gain in static environments and can obtain relatively accurate angle support in dynamic environments.

[0105] The method of the present invention includes the following steps:

[0106] A. Configure N T The communication transmitter of the root transmitting antenna, with N I IRS and configuration of each reflective element N R A cascaded transmission system consisting of communication receivers with root receiving antennas constructs a receive angle domain dictionary matrix for channel H1 between the communication transmitter and the IRS. and the transmit angle domain dictionary matrix Construct a receive angle domain dictionary matrix for channel H2 between the communication receiver and the IRS. and the transmit angle domain dictionary matrix Where β1 and β2 are the total number of angular grids dividing the H1 and H2 channels in the angular domain, respectively, and a 1r，j and a 1t，j j = 0, ..., β1-1 are the steering vectors of channel H1 at the angular grid points, a 2r，j and a 2t，j ,j=0,...,β2-1 is the steering vector of channel H2 at the angular grid points; the phase shift vector g(s) of the IRS in the s-th symbol represents the N between the communication transmitter and the communication receiver. R ×N T The concatenated channel H = H2diag(g(s))H1, after angular oversampling, is expressed as: Then vectorize the channel in matrix form as follows: Where the subscripts T, I, and R represent the communication transmitter, IRS, and communication receiver, respectively; vec(·) denotes the matrix vectorization operator; diag(·) denotes the vector diagonalization operator; and A R，I and A I，T These are the angle gain matrices between the communication receiver and the IRS in the dictionary-guided vector direction, and the angle gain matrices between the IRS and the communication transmitter, respectively. ⊙ and ⊙ represent the Kronecker product and Khatri-Rao product, respectively, with the symbol (·). * ,(·) T and(·) H These represent conjugate, transpose, and conjugate transpose, respectively. for The cascaded angular gain vector to be determined.

[0107] The communication receiver and transmitter in step A can be either fixed in location or have one end moving and the other fixed. There are no restrictions on the number of MIMO transceiver antennas or IRS elements. The number of oversampling angle grids can be set to 2 to 4 times the number of transceiver array antennas. When the number of transceiver antennas is large, it can be set to 1 times the number of transceiver array antennas, i.e., β1 = N. T and β2=N R For planar array and linear array MIMO antennas, the angle grid division can be based on uniform sampling according to the angle resolution, or it can be random sampling. If a large angle gain is not obtained on a certain angle dictionary, the angle grid can be further subdivided on the coarse grid to obtain the channel state information in the angle domain.

[0108] B. Establish a state-space model for the angle gain vector h. Where s represents the symbol index, and ψ is determined by the maximum Doppler frequency shift f D It is determined that v(s-1) is the update noise, and the zero elements in h remain zero regardless of the sign.

[0109] In step B, the ψ in the state-space model of the angle gain vector is derived from the Jakes channel model ψ = J0(2πf D T s ) is determined, where J0(·) represents the zeroth-order Bessel function of the first kind, f D T represents the maximum Doppler frequency shift of the mobile party relative to the IRS in communication. s For the symbol period, when both the communication transmitter and receiver are stationary relative to the IRS, ψ = 1, the state-space model of the angle gain vector degenerates into the time-invariant channel model h(s) = h(s-1).

[0110] C. Initialize the angle gain vector h as h(0), initialize the estimation error variance of h as P(0), set the covariance matrix Q of the update noise v(s-1), and set the observation noise variance R according to the signal-to-noise ratio.

[0111] D. Obtain N using the diagonal pilot X(s) of the zero-forcing block with guard interval of the s-th symbol. R ×N T The pilot tone observation matrix Y(s) = H(s)X(s) + W(s), where W(s) is the observation noise matrix, and the vectorized observation equation y(s) = A(s)h(s) + w(s) is obtained, where y(s) = vec(Y(s)) is N. R N T ×1-dimensional observation vector w(s) = vec(W(s)) is N R N T ×1 dimensional observation noise vector.

[0112] E. The one-step prediction of the angle gain vector calculated by the Kalman filter method is h(s|s-1)=ψh(s-1), and the variance of the one-step prediction estimate is P(s|s-1)=ψP(s-1)+(1-ψ 2 Q, calculate the gain as K(s) = P(s|s-1)A H (s)(A(s)P(s|s-1)A H (s)+R) -1 The current estimated value is calculated as h(s) = h(s|s-1) + K(s)(y(s) - A(s)h(s|s-1)), and the current estimated error variance is calculated as P(s) = P(s|s-1) - K(s)A(s)P(s|s-1).

[0113] F. Construct the pseudo-measurement equation of the l1 norm as 0 = ||h(s)||1 - η(τ)∈, where η(τ) is an adaptive factor that monotonically increases with the number of iterations τ. When τ approaches infinity, η(τ) approaches 1, and ∈ is a random number with a fixed variance. Let the variance of ∈ be r. ∈ The error variance of the l1 norm is set as r = η. 2 (τ)r ∈ The current estimated value h(s) is used as the initial value h for the l1 norm iterative correction. l (0), taking the current estimation error variance P(s) as the initial estimation error variance P l (0).

[0114] The l1 norm pseudo-measurement equation in step F is a variance-adaptive pseudo-measurement equation. It introduces an adaptive factor η(τ) to accelerate the convergence of the l1 norm, and the convergence process can be adjusted by an exponentially growing η(τ) = 1 - η(0)exp(-μτ / T), where η(0) and μ are shape parameters, and T is a fixed positive constant.

[0115] G. Calculate the one-step prediction h using the Kalman filter method. l (τ|τ-1)=h l (τ-1), calculate the variance of the one-step prediction estimation error as P. l (τ|τ-1)=P l (τ-1), at the current estimated value h l Calculate the subgradient of the l1 norm on (τ):

[0116]

[0117] get The subgradient vector c(τ) is the Jacobian matrix that linearizes the nonlinear l1-norm pseudo-measurement equation. Then, the iterative filter gain k is calculated. l (τ)=P l (τ|τ-1)c H (τ)(c(τ)P l (τ|τ-1)c H (τ)+r(τ)) -1 Calculate the current estimated value as h l (τ)=h l (τ|τ-1)+k l (τ)(0-c(τ)h l (τ|τ-1)), calculate the current estimation error variance as P l (τ)=P l (τ|τ-1)-k l (τ)c(τ)P l (τ|τ-1).

[0118] The subgradient of the l1 norm in step G is the subgradient of the l1 norm of the complex angle gain vector. When the angle gain is real, the subgradient of the l1 norm with respect to non-zero elements is a sign function, and the subgradient with respect to zero elements is a random value in (-1, 1); the one-step prediction h in step G... l (τ|τ-1)=h l (τ-1) and the variance of the one-step prediction estimation error P l (τ|τ-1)=P l (τ) is only an assignment operation and does not involve any computation.

[0119] H. Determine whether the absolute value of the difference between the l1 norms of two consecutive estimates is less than a small positive number, i.e., whether it satisfies |||h l (τ)||1-||h l (τ-1)||1|<ζ, where |·| represents the absolute value and ζ is a small positive number. If this condition is met, the iteration stops; otherwise, it is checked whether the maximum number of iterations τ has been reached. max If the condition is met, the iteration stops; otherwise, proceed to step G to continue iteration. After stopping the iteration, the h value that has undergone l1 norm iteration correction is... l (τ) is the current h(s), and P is... l (τ) is the current P(s).

[0120] The condition that the absolute value of the difference between two consecutive l1 norms of the estimates in step H is less than a small positive number is a termination condition for the iteration. To ensure the reliability of the algorithm, the maximum number of iterations τ can be set. max The l1 norm correction iteration process stops when one of the two termination conditions is met.

[0121] I. Update the symbol to the next symbol after the current symbol s. Repeat steps D, E, F, G, and H to estimate and track h(s). After filtering reaches a steady state, obtain the angle support in the sparse angle gain vector h(s), i.e., the positions of the non-zero elements in the vector and the corresponding complex angle gain. Obtain the instantaneous angle gain from the angle dictionary. The instantaneous cascaded channel H(s) is then obtained through matrixing.

[0122] Once the filtering in step I reaches a steady state, it can be determined by whether the absolute difference between the sum of the main diagonal elements of the estimation error variances P(s) and P(s-1) of two adjacent symbols is small.

[0123] Below, N R =N I =N T When L1 = 4 and L2 = 3, see attached. Figure 3The method of the present invention will be described using the example shown.

[0124] In N R =N I =N T When L1 = 4 and L2 = 3, a sparse structure of the angle gain matrix corresponding to the angle dictionary with an array size of 1 is provided. Any row or column of this structure is either all 0 or has only one non-zero value. This sparse structure can also be other structures. The method of this invention does not restrict the sparse structure.

[0125] As attached Figure 4 The diagram shows a diagonal pilot pattern with a guard interval and a zero-forcing block, which inserts N after each pilot time slot. g -1 zero-filled time slots, the duration of which is longer than the time slot length corresponding to the longest delayed path beat, in order to overcome inter-symbol interference and convert the multi-beat response of the channel into the sum of multiple single-beat responses.

[0126] When implementing the IRS-assisted cascaded MIMO dual sparse channel state information estimation method of the present invention at the communication receiver, when N R =N I =N T When L1 = 4 and L2 = 2 and L3, the specific implementation steps are as follows:

[0127] Step 1: Construct a 4×4 dimensional dictionary matrix D, which is one times the array size, from a planar array of angles using random angle sampling. 1R and D 1T and D 2R and D 2T Where β1 = 4 and β2 = 4;

[0128] Step 2: After determining ψ based on the Doppler frequency shift, obtain the state-space model of the angle gain vector h;

[0129] Step 3: Initialize h(0) as a 256×1 dimensional complex random vector, and initialize its estimation error variance as P(0) = 100I. 256 , where I 256 Let Q = I, representing a 256×256 dimensional identity matrix, and let Q = I, representing the covariance matrix of the updated noise v(s). 256 Determine the observation noise variance based on the signal-to-noise ratio (SNR). Where I 16 Represents a 16×16 dimensional identity matrix;

[0130] Step 4: Diagonalize the pilot signal using a zero-forcing block with a guard interval to obtain a 4×4 dimensional observation matrix Y(s) and quantize it into a 16×1 dimensional vector y(s);

[0131] Step 5: Calculate h(s|s-1), P(s|s-1), K(s), h(s), and P(s) using the conventional Kalman filter method;

[0132] Step 6: Construct the pseudo-measurement equation of the l1 norm as 0 = ||h||1 - η(τ)∈, and in the parameter settings of the adaptive factor η(τ), set η(0) = 0.9, μ = 0.02, T = 10, and set the variance r of ∈. ∈ =40000, set the measurement variance of the l1 norm as r = η 2 (τ)r ∈ Set h l (0) and P l (0);

[0133] Step 7: Calculate the subgradient of the l1 norm on the current estimate to obtain a 1×256 subgradient vector c, then perform l1 norm correction, and calculate h sequentially. l (τ|τ-1), P l (τ|τ-1),k l (τ), h l (τ) and P l (τ);

[0134] Step 8: Determine if the absolute value of the difference between two consecutive l1 norm values ​​is less than 10. -3 If the value is less than 20, stop the iteration. If it is not less than 20, check if the maximum number of iterations (20) has been reached. If it has, stop the iteration. After stopping the iteration, adjust the h value that has been corrected using the l1 norm. l (τ) is used as the current h(s), and P is used as the current h(s). l (τ) is used as the current P(s), and then the recursive update process from the next observation vector is entered in steps four to eight.

[0135] Step 9: After the filtering reaches a steady state, the angle support and corresponding complex angle gain in the sparse angle gain vector h(s) are obtained. The instantaneous 16×1 dimensional vec(H(s)) and 4×4 dimensional cascaded channel H(s) are obtained from the angle dictionary.

[0136] In this embodiment, a millimeter-wave cascaded channel S1 is used. In a similar embodiment: N R =N I =N T In L1=4, L1=1, and L2=1, a millimeter-wave cascaded channel S2 is used. The azimuth and elevation angles used in their angle dictionaries, as well as the corresponding angle gains, are shown in Tables 1 and 2, respectively. An instantaneous 4×4 MIMO cascaded channel can be generated according to equations (1), (2), and (3).

[0137] Table 1N I=4, L1=2, L2=3 4×4 MIMO cascaded channel

[0138]

[0139] Table 1N I =4, L1=1, L2=1 4×4 MIMO cascaded channel

[0140]

[0141] In dynamic scenarios, the angle parameters of the two scenarios S1 and S2 in the embodiment remain unchanged, and the initial values ​​of the true angle gain are still shown in Tables 1 and 2. The dynamic angle gain is updated with each symbol according to the state-space model. In the embodiment, the phase shifts of the four IRS elements in four consecutive symbols are set to {1, 1, 1, 1}, {1, j, -1, j}, {1, -1, 1, -1}, and {1, -j, -1, j}, and these four sets of phase shifts are repeated as the symbol s increases.

[0142] As attached Figure 5 The figure shows a comparison curve of the normalized mean square error (NMSE) of the method of this invention (denoted as SKF), the sparse filtering method without adaptive factors (denoted as GKF), optimal least squares (denoted as Oracle LS), and OMP under the static scenario S1 channel parameter settings. NMSE is defined as:

[0143]

[0144] In the formula, Let h(S) represent the estimated angle gain vector at the last pilot symbol, h(S) represent the true angle gain vector value, and L represent the number of simulations. It can be seen that the method proposed in this invention has the best NMSE performance. OMP and Oracle LS have lost their ability to estimate angle supports and have very poor performance; GKF also has a low NMSE.

[0145] As attached Figure 6 The figure shows the estimation tracking curve of the angle gain h1 for one of the non-zero values ​​by the method of the present invention. It can be seen that the SKF method of the present invention is significantly better than the general GKF method in terms of estimation process and estimation accuracy.

[0146] As attached Figure 7 The figure shows the estimation results of the angle support and angle gain magnitude of the six non-zero angle gains by the method of the present invention. Compared with the GKF method, the method of the present invention has a lower error.

[0147] As attached Figure 8The figure shows the curve of the NMSE varying with the number of pilot tone observation vectors in the static scenario S1 and SNR = 10dB. It can be seen that when the number of pilot tone observation vectors is the same, the method of the present invention can achieve better NMSE performance.

[0148] As shown in the appendix Figure 9 The figure shows the curve of the NMSE varying with ψ when SNR = 10dB and the number of pilot tone observation vectors is 20. It can be seen that the NMSE is larger when ψ is small. As ψ increases up to 1, the NMSE curve decreases. The method SKF of the present invention has better NMSE performance in the dynamic scenario S1.

[0149] As shown in the appendix Figure 10 The figure shows the dynamic tracking error curve of a non - zero angular gain h1 when SNB = 10dB, the number of pilot tone observation vectors is 20, and ψ = 0.9; in the simulation, the initial value of the channel is the value in Table 1(a). It can be seen that the method of the present invention has a good dynamic tracking effect and can track the dynamic sparse channel to a great extent.

[0150] As shown in the appendix Figure 11 The figure shows the curve of the l1 - norm of the estimated angular gain vector varying with the number of pilot tone observation vectors when SNR = 10dB and ψ = 0.9. It can be seen that the method of the present invention can make the l1 - norm reach a steady state with fewer pilot tone observation vectors and can obtain an estimated result closer to the true l1 - norm.

[0151] As shown in the appendix Figures 12 to 18 The figure shows the performance curve when the channel parameter is S2. Through similar analysis to that in the appendix Figure 5-11 it can be concluded that the method of the present invention has excellent performance in estimating the IRS - assisted cascaded MIMO double - sparse channel state information.

[0152] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention from the concept of the present invention through logical analysis, reasoning or limited experiments on the basis of the existing technology should be within the protection scope determined by the claims.

Claims

1. A method for estimating the state information of a dual sparse channel in an IRS-assisted cascaded MIMO system, characterized in that, The method includes the following steps: S1, For configuration N T The communication transmitter of the root transmitting antenna, with N I IRS and configuration of each reflective element N R A cascaded transmission system consisting of communication receivers with root receiving antennas constructs a receiving angle domain dictionary matrix D for channel H1 between the communication transmitter and the IRS. 1R and the transmitted angle domain dictionary matrix D 1T Simultaneously, for channel H2 between the communication receiver and the IRS, a receiving angle domain dictionary matrix D is constructed. 2R and the transmitted angle domain dictionary matrix D 2T Based on the above dictionary matrix, the expression for the cascaded channel after angle oversampling is obtained, and then the expression is vectorized. The vectorized expression includes the cascaded angle gain vector h to be determined. S2. Establish a state-space model h(n) for any nth symbol corresponding to the cascaded angle gain vector of S1; S3. Initialize the cascaded angle gain vector h to h(0), initialize the estimation error variance of the cascaded angle gain vector h to P(0), set the covariance matrix Q of the update noise in the state space model, and set the observation noise variance R according to the signal-to-noise ratio. S4. Obtain the pilot tone observation matrix Y(s) through the diagonal pilot X(s) with guard interval zero-forcing block of the s-th symbol, and vectorize it to obtain the current observation vector y(s). The observation vector y(s) corresponds one-to-one with the symbol number s. S5. For the current observation vector, calculate the one-step prediction h(s|s-1) of the angle gain vector using the Kalman filter method, calculate the one-step prediction estimation variance P(s|s-1) based on the covariance matrix Q, calculate the filter gain K(s) based on the observation noise variance R, obtain the current estimate h(s) based on the filter gain and the one-step prediction of the angle gain vector, and obtain the current estimation error variance P(s) based on the filter gain and the one-step prediction estimation variance. The initial values ​​used in the first calculation using the Kalman filter method in S5 are the initial h(0) and P(0) of S3. The initial values ​​for other calculations are the cascaded angle gain vector and estimated variance of the current s-th symbol in S8. S6. Construct a pseudo-measurement equation for the l1 norm, set the error variance of the l1 norm, and use the current estimated value h(s) as the initial value h for the l1 norm iterative correction. l (0), taking the current estimation error variance P(s) as the initial estimation error variance P for iteration. l (0); S7. Calculate the one-step prediction h using the Kalman filter method. l (τ|τ-1), calculate the variance P of the one-step prediction estimation error. l (τ|τ-1), then calculate the iterative filter gain k. l (τ), calculate the current estimated value h l (τ) and the current estimation error variance P l (τ), where τ is the number of iterations; The initial value used in S7 when the Kalman filter method was first applied for calculation was the same as the initial value h from S6. l (0) and the initial estimation error variance P l (0); S8. Determine the estimated values ​​h of two adjacent values. l (τ) and h l If the absolute value of the difference in the l1 norm of (τ-1) is less than the threshold, the iteration stops; otherwise, it is determined whether the maximum number of iterations has been reached. If so, the iteration stops; otherwise, S7 continues to iterate. In S8, after stopping the iteration, h, which has already undergone l1 norm iterative correction, is... l (τ) is used as the cascaded angle gain vector for the current s-th symbol, and P at the time of stopping iteration is... l (τ) represents the variance of the estimation error for the current s-th symbol; S9. Update the symbol to the next symbol of the current symbol s. Repeat S4 to S8. After the filtering reaches a steady state, obtain the angle support and the corresponding angle gain in the sparse angle gain vector. Obtain the instantaneous matrix-vectorized channel according to the angle domain dictionary. Obtain the instantaneous cascaded channel H(s) through matrix transformation.

2. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 1, characterized in that, The vectorized expression for S1 is: Where H represents the cascaded channel after angle oversampling, g(s) represents the phase shift vector of the IRS at the s-th symbol, and A R，I and A I，T These are the angle gain matrices between the communication receiver and the IRS in the dictionary-guided vector direction, and the angle gain matrices between the IRS and the communication transmitter, respectively. ⊙ and ⊙ represent the Kronecker product and Khatri-Rao product, respectively, with the symbol (·). * ,(·) T and(·) H These represent conjugate, transpose, and conjugate transpose, respectively. Let be the cascaded angular gain vector to be determined.

3. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 2, characterized in that, The one-step prediction h(s|s-1) and the one-step prediction variance P(s|s-1) of the angle gain vector of S5 are: h(s|s-1)=ψh(s-1) P(s|s-1)=ψP(s-1)+(1-ψ 2 )Q Where ψ is the maximum Doppler frequency shift f in the state-space model. D Given the parameters, P(s-1) is the variance of the estimation error corresponding to the previous symbol, and Q is the covariance matrix of the updated noise.

4. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 2, characterized in that, The filter gain K(s) is: K(s)=P(s|s-1)A H (s)(A(s)P(s|s-1)A H (s)+R) -1 Where R is the variance of the observation noise. X(s) is the diagonal pilot symbol with guard interval zero-forcing block, (·) * ,(·) T and(·) H These represent conjugate, transpose, and conjugate transpose, respectively. The current estimated value h(s) and the current estimation error variance P(s) are: h(s)=h(s|s-1)+K(s)(y(s)-A(s)h(s|s-1)) P(s)=P(s|s-1)-K(s)A(s)P(s|s-1) Where h(s|s-1) is the one-step prediction of the angle gain vector, and P(s|s-1) is the variance of the one-step prediction estimation error.

5. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 1, characterized in that, The pseudo-measurement equation for S6 is: 0=||h(s)||1-η(τ)∈ Where η is the adaptive factor, ∈ is a random number with a fixed variance, and τ is the number of iterations.

6. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 5, characterized in that, The adaptive factor is: η(τ)=1-η(0)exp(-μτ / T) Where η(0) and μ are shape parameters, T is a fixed positive constant, and τ is the number of iterations.

7. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 1, characterized in that, S7's one-step prediction h l (τ|τ-1) and the variance of the one-step prediction estimation error P l (τ|τ-1) is: h l (τ|τ-1)=h l (t-1) P l (τ|τ-1)=P l (t-1) Among them, h l (τ-1) is the estimated value at the previous iteration number, P l (τ-1) represents the variance of the estimation error at the previous iteration number; Iterative filter gain k l (τ) is: k l (τ)=P l (τ|τ-1)c H (τ)(c(τ)P l (τ|τ-1)c H (τ)+r(τ)) -1 Where c(τ) is the Jacobian matrix composed of subgradient vectors, and r(τ) = η 2 (τ)r ∈ Let r be the measurement variance of the l1 norm. ∈ Let η be the fixed variance of the random number ∈, and η be the adaptive factor.

8. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 7, characterized in that, Current estimated value h l (τ) and the current estimation error variance P l (τ) is: h l (τ)=h l (τ|τ-1)+k l (τ)(0-c(τ)h l (τ|τ-1)) P l (τ)=P l (τ|τ-1)-k l (τ)c(τ)P l (τ|τ-1) Where, k l (τ) represents the iterative filter gain.

9. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 1, characterized in that, The condition for determining whether filtering has reached a steady state is: The judgment is made by determining whether the absolute difference of the sum of the main diagonal elements of the estimated error variance obtained from S8 of two adjacent symbols is less than a threshold. If it is, a steady state has been reached; otherwise, a steady state has not been reached.

10. The method for estimating the state information of an IRS-assisted cascaded MIMO dual sparse channel according to claim 1, characterized in that, Received angle domain dictionary matrix D 1R and the transmitted angle domain dictionary matrix D 1T They are respectively: Received angle domain dictionary matrix D 2R and the transmitted angle domain dictionary matrix D 2T They are respectively: Among them, a 1r，j and a 1t，j j = 0, ..., β1-1 are the steering vectors of channel H1 at the angular grid points, a 2r，j and a 2t，j ,j=0,...,β2-1 is the steering vector of channel H2 at the angle grid points.

Images