Channel estimation method for active RIS-assisted millimeter wave MIMO system

Abstract

The invention discloses a channel estimation method of an active RIS-assisted millimeter wave MIMO system, which researches the channel estimation problem of the active RIS-assisted millimeter wave MIMO system in a multipath environment, realizes decoupling of a departure angle at UE and cascade channel parameters by designing a specific UE pilot frequency sequence and RIS phase configuration, and improves the channel estimation accuracy. Making it possible to estimate an angle of arrival at the BS, an angle of departure at the UE, and cascade channel parameters, respectively; in order to solve the challenge of estimating the cascade channel parameters, a low-complexity algorithm for decoupling the two-dimensional cascade channel parameters is developed, and the estimation process is converted into multiple times of one-dimensional search by utilizing a greedy algorithm principle, so that the calculation complexity is greatly reduced.

Description

Technical Field

[0001] The present invention belongs to the field of RIS (Reconfigurable Intelligent Surface) - assisted positioning, and specifically relates to a channel estimation method for an active RIS - assisted millimeter - wave MIMO system, which realizes channel estimation of the multi - path base station (BS) - RIS and RIS - user equipment (UE) channels in an active RIS - assisted millimeter - wave MIMO system. Background Art

[0002] Millimeter - wave (mmWave) systems have shown great potential in the field of positioning due to their wide bandwidth, multi - element antenna arrays, and good propagation characteristics. Integrating antenna arrays into user equipment (UE) in a millimeter - wave MIMO system enables the estimation of the direction and position of the user equipment (UE). In addition, the high - resolution characteristics of propagation paths in the millimeter - wave band can make full use of multi - path information, which is helpful for precise positioning and environmental mapping.

[0003] In recent years, the emergence of RIS technology has significantly improved the positioning ability of millimeter - wave systems. RIS can establish additional non - line - of - sight (NLOS) connections, effectively solve the coverage limitation problem in the millimeter - wave band, and the obstacles of the line - of - sight (LOS) path between the base station (BS) and the user equipment (UE). At the same time, the additional geometric measurement information provided by RIS helps to improve the accuracy and robustness of positioning algorithms. However, the introduction of RIS technology also brings challenges to channel estimation. As an intermediate reflection node, RIS will introduce additional cascaded channels, which are deeply coupled with the parameters of the transmitter and the receiver, bringing great difficulties to channel estimation. Existing methods are difficult to effectively solve this problem, especially in multi - path scenarios.

[0004] In addition, when both the line - of - sight (LOS) path between the base station (BS) and the user equipment (UE) and the non - line - of - sight (NLOS) path established by RIS exist, the multiplicative fading phenomenon of passive RIS limits its introduction effect. This is because the signal power of the line - of - sight (LOS) path is much greater than that of the non - line - of - sight (NLOS) path established by passive RIS, resulting in an imbalance in the signal power between the line - of - sight (LOS) path and the non - line - of - sight (NLOS) path, and thus generating the need for active RIS. However, when using active RIS, additional noise is inevitably introduced, bringing higher complexity and greater challenges to channel estimation. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a channel estimation method for an active RIS-assisted millimeter-wave MIMO system, which can realize decoupling and low-complexity estimation of channel parameters in a multipath environment.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a channel estimation method for an active RIS-assisted millimeter wave MIMO system, the method is applied to an uplink active RIS-assisted millimeter wave MIMO system, the millimeter wave MIMO system comprises an active RIS, a base station equipped with an antenna array, and a user equipment equipped with an antenna array, the three-dimensional position and direction of the active RIS and the base station are known, and the three-dimensional position and direction of the user equipment are unknown, and the method is characterized in that it comprises the following steps:

[0007] Step 1: Based on the geometric channel model, obtain the channel matrix from the user equipment to the base station at time t The expression of the channel matrix from active RIS to base station The expression of the channel matrix from user equipment to active RIS The expression of the cascade channel matrix from user equipment to active RIS and then to base station The expression of The expression includes the arrival angle of the base station and the departure angle of the user equipment in each path of the link between the user equipment and the base station.

[0008] The expression of includes the arrival angle of the base station and the departure angle of the active RIS in each path between the active RIS and the base station link. The expression of includes the arrival angle of the active RIS and the departure angle of the user equipment in each path between the user equipment and the active RIS link;

[0009] Step 2: Based on Get the received signal y at the base station at time t t The expression of The initial expression of the received signal matrix Y at the base station at the moment; then make the initial expression of Y The pilot signal transmitted by the user equipment changes within a certain time, while the phase offset of the active RIS remains unchanged. The phase offset of the active RIS changes within a moment, while the pilot signal transmitted by the user equipment remains unchanged. The final expression of the received signal matrix Y at the base station at the moment is,

[0010] Step 3: Use the algorithm based on DOA estimation to solve the final expression of Y, and obtain the estimated values of the angles of arrival of the base station in each path of the active RIS - base station link, and the estimated values of the angles of arrival of the base station in each path of the user equipment - base station link; then replace the estimated value with the true value of the angle of arrival of the base station in the first path of the active RIS - base station link.

[0011] Step 4: Combine the vectors composed of the pilots transmitted by the user equipment within the subsequent moments and the initial expression of Y to obtain the expression of the received signal matrix at the base station within the subsequent moments; then according to the expression, and combined with the estimated values of the angles of arrival of the base station in each path of the active RIS - base station link and the estimated values of the angles of arrival of the base station in each path of the user equipment - base station link, use the least - squares method and one - dimensional search to iteratively obtain the rough estimated values of the departure angles of the active RIS in each path of the active RIS - base station link and the rough estimated values of the arrival angles of the active RIS in each path of the user equipment - active RIS link; then construct a least - squares problem for refining the rough estimated values, use the quasi - Newton algorithm, and take the rough estimated values as the search initial points to solve the least - squares problem, and obtain the fine estimated values of the departure angles of the active RIS in each path of the active RIS - base station link and the fine estimated values of the arrival angles of the active RIS in each path of the user equipment - active RIS link.

[0012] Step 5: Combine the vectors composed of the phase offsets of the active RIS within the previous moments and the initial expression of Y to obtain the expression of the received signal matrix at the base station within the previous moments; then according to the expression, and combined with the estimated values of the angles of arrival of the base station in each path of the active RIS - base station link, obtain the estimated values of the received signal matrices of all paths of the user equipment - base station link within the previous moments; then based on

[0013] and apply one - dimensional search to obtain the rough estimated values of the departure angles of the user equipment in each path of the user equipment - base station link; finally, use the quasi - Newton algorithm, and take the rough estimated values as the search initial points to solve the least - squares problem for refining the rough estimated values, and obtain the fine estimated values of the departure angles of the user equipment in each path of the user equipment - base station link.

[0013] Step 6: According to the received signal matrix at the base station within the previous expression, and use an algorithm based on DOA estimation to obtain the estimated value of the departure angle of the user equipment in each path of the user equipment and the active RIS link.

[0014] The three-dimensional positions of the active RIS, the base station, and the user equipment refer to the positions based on the global coordinate system, where the global coordinate system is a three-dimensional coordinate system established with the center of the antenna array equipped at the base station as the origin O, the normal vector of the antenna array as the Y-axis, and the antenna array located on the XOZ plane; for the active RIS, the base station, and the user equipment, an Euler angle vector o Q and the rotation order of Z-Y-X are used to describe their respective directions in the global coordinate system, and according to o Q obtain the corresponding rotation matrix where Q ∈ {R, B, U}, o Q has a dimension of 3×1, has a dimension of 3×3.

[0015] In step 1, where L UB represents the number of paths in the user equipment and base station link, l = 1, 2,..., L UB , the first path in the user equipment and base station link is the line-of-sight path, and the remaining paths are non-line-of-sight paths, represents the complex channel gain of the l-th path in the user equipment and base station link, represents the angle of arrival of the base station in the l-th path of the user equipment and base station link, represents the departure angle of the user equipment in the l-th path of the user equipment and base station link, represents based on the far-field steering vector of the base station at represents based on the far-field steering vector of the user equipment at (·) H represents the conjugate transpose operation, L RB represents the number of paths in the active RIS and base station link, l1 = 1, 2,..., L RB , the first path in the active RIS and base station link is the line-of-sight path, and the remaining paths are non-line-of-sight paths, represents the complex channel gain of the l1-th path in the active RIS and base station link, represents the angle of arrival of the base station in the l1-th path of the active RIS and base station link, represents the departure angle of the active RIS in the l1-th path of the active RIS and base station link, represents based on the far-field steering vector of the base station at denote based on the far - field steering vector of the active RIS at time UR denote the number of paths in the user equipment - active RIS link, \(l_2 = 1,2,\cdots,L\) UR , the first path in the user equipment - active RIS link is the line - of - sight path, and the remaining paths are non - line - of - sight paths denote the complex channel gain of the \(l_2\) - th path in the user equipment - active RIS link denote the angle of arrival of the active RIS in the \(l_2\) - th path of the user equipment - active RIS link denote the angle of departure of the user equipment in the \(l_2\) - th path of the user equipment - active RIS link denote based on the far - field steering vector of the active RIS at time denote based on the far - field steering vector of the user equipment at time \(diag(\cdot)\) represents finding the diagonal matrix, \(w\) t denote the phase - shift vector of the active RIS at time \(t\) \(p\) represents the gain coefficient of the active RIS, \(e\) represents the natural constant, \(j\) is the imaginary unit, \(N\) R denote the number of active elements included in the active RIS, \(\omega_1\) and correspondingly represent the phase - shift of the first active element of the active RIS and the \(N\) - th R active element's phase - shift denote the channel gain of the cascaded channel from the user equipment to the active RIS and then to the base station (\cdot) T represents the transpose operation and correspondingly represent the elevation angle and azimuth angle of

[0016] denote the three - dimensional coordinates of the corresponding scatterer in the \(l_1\) - th path in the active RIS - base station link in the global coordinate system. When \(l_1 = 1\) it is the three - dimensional coordinates of the base station in the global coordinate system, \(p\) R denote the three - dimensional coordinates of the active RIS in the global coordinate system denote taking the third element of denote taking the second element of denote taking The first element of, ||·|| is the L2 norm operation symbol, and correspondingly represent the elevation angle and azimuth angle of,

[0017] “⊙” is the Hadamard product operation symbol, (·) * represents the conjugate operation.

[0018] Among them, is the Kronecker product operation symbol,

[0019] and correspondingly represent the elevation angle and azimuth angle of, The antenna spacing in the antenna array equipped by the base station, the antenna spacing in the antenna array equipped by the user equipment, and the spacing between active elements in the active RIS are all d, λ represents the wavelength, and correspondingly represent the number of antennas in the horizontal direction and the number of antennas in the vertical direction of the antenna array equipped by the base station; Among them, and correspondingly represent the elevation angle and azimuth angle of,

[0020] and correspondingly represent the number of antennas in the horizontal direction and the number of antennas in the vertical direction of the antenna array equipped by the user equipment; Among them, and correspondingly represent the elevation angle and azimuth angle of,

[0021] and correspondingly represent the number of active elements in the horizontal direction and the number of active elements in the vertical direction of the active RIS; Among them,

[0022]

[0023] Among them, and correspondingly represent the elevation angle and azimuth angle of,

[0024]

[0025] In step 2, where, x t represents the pilot transmitted by the user equipment at time t, represents the thermal noise at the active RIS at time t, obeys a Gaussian distribution with a mean of 0 and a variance of , I represents the identity matrix, represents the thermal noise at the base station at time t, obeys a Gaussian distribution with a mean of 0 and a variance of ; The initial expression of Y is described as: where, The final expression of Y is described as: Y = A B S + Z B , where, A B = [A BU , A BR , S is the coefficient matrix.

[0026] The specific process of step 4 is as follows:

[0027] Step 4.1: Denote the vector formed by the pilots transmitted by the user equipment within the subsequent time instants as where, represents a column vector of all 1s with a dimension of ; Then, combining and the initial expression of Y, the expression of the received signal matrix at the base station within the subsequent time instants is obtained and described as:

[0028] where,

[0029]

[0030] is composed of the last elements of W, is composed of the last R elements of Z ; is composed of the last B elements of Z ;

[0031] Step 4.2: According to 's expression, obtain: where, is the pseudo-inverse operation symbol, Then, based on Step 3, obtain the estimated value B of A and substitute into G B to construct the matrix G R ,

[0032] where, represents the sub-matrix formed by the (L B +1)-th row to the L-th row of G UB , L = L UB + L RB ,

[0033] Step 4.3: Let where, represents 's l1-th column, is a constant,

[0034]

[0035] Step 4.4: Based on Step 4.3, use the least squares method and one-dimensional search to iteratively obtain the rough estimated values of and

[0036] . The specific process is as follows:

[0037] Step 4.4.1: Let k represent the number of iterations, the initial value of k is 1, and the maximum number of iterations is L UR ;

[0038] Step 4.4.2: Approximate at the k-th iteration as Then construct Optimization Problem 1, described as: where, min represents the minimum value function, represents 's representation at the k-th iteration; then use the properties of the Kronecker product to transform Optimization Problem 1 into Optimization Problem 2, described as: where, After that, under the condition of , use the least squares method to solve Optimization Problem 2 to obtain the least squares solution

[0039] Step 4.4.3: Solve using one-dimensional search Obtain a rough estimate of Then substitute into Optimization Problem 1 to obtain Optimization Problem 3, described as: where denotes the estimate of is the least squares solution of obtained by using the least squares method to solve ; then solve Optimization Problem 3 using one-dimensional search to obtain a rough estimate of

[0040] Step 4.4.4: Let where denotes the representation at the (k + 1)-th iteration;

[0041] Step 4.4.5: Let k = k + 1, then return to Step 4.4.2 to continue execution until a rough estimate of and a rough estimate of where the "=" in k = k + 1 is an assignment symbol;

[0042] Step 4.5: Define the first cascaded channel matrix Φ x and the second cascaded channel matrix Φ z , and let where k = 1, 2,..., L UR , denotes the element in the l1-th row and k-th column of Φ x ; denotes the element in the l1-th row and k-th column of Φ z ; then construct the least squares problem for refining the rough estimate, described as: Then use the quasi-Newton algorithm and take Φ x and Φ z as the search initial points to solve the least squares problem to obtain a fine estimate of Furthermore, obtain a fine estimate of and a fine estimate of

[0043] The specific process of Step 5 is as follows:

[0044] Step 5.1: The first The vector composed of the phase offsets of the active RIS at each moment is denoted as where, represents a column vector of all 1s with dimension ; then, combined with and the initial expression of Y, the received signal matrix at the base station in the first moments is obtained, and the expression is described as:

[0045] where,

[0046] represents the received signal matrix of all paths of the user equipment - base station link in the first moments, represents the received signal matrix of all paths of the user equipment - active RIS - base station link in the first moments,

[0047] is composed of the first B elements of Z ,

[0048] is composed of the first elements of X, represents the element in the l1 - th row and l2 - th column of represents the l1 - th column of C R , is composed of the first R elements of Z ;

[0049] Step 5.2: According to the expression of , the estimated value of is obtained where, represents the estimated value of A BR , obtained based on the estimated value of the angle of arrival of the base station in each path of the active RIS - base station link; then, based on When is defined where, N U represents the number of antennas in the antenna array equipped by the user equipment;

[0050] Step 5.3: Let where, represents the l-th column of; then utilize the property to reshape into a matrix where, vec(·) represents the vectorization operation, is a rank-1 matrix; then apply singular value decomposition to to obtain: where, σ represents the maximum eigenvalue, and are both eigenvectors, and are two components obtained by decomposing σ,

[0051] Step 5.4: Apply one-dimensional search to solve and to correspondingly obtain the estimated value of and the estimated value of and further obtain the rough estimated value of where, |·| is the modulus operation symbol; then construct the least squares problem for refining described as: where, then utilize the quasi-Newton algorithm and use as the search initial point to solve the least squares problem for refining to obtain the fine estimated value of

[0052] The specific process of the said Step 6 is: According to the expression of when it is obtained that: where,

[0053] Then by ignoring the noise term, transform into Then define and then utilize the algorithm based on DOA estimation to solve to obtain the estimated value of where, represents the estimated value of A BR obtained from the estimated values of the arrival angles of the base station in each path of the active RIS and base station link.

[0054] Compared with the prior art, the advantages of the present invention are:

[0055] 1) Compared with passive RIS, the method of the present invention introduces active RIS to combat multiplicative fading, thereby making more effective use of the RIS-aided communication system.

[0056] 2) Through specific configuration of the pilot transmitted by the user equipment and the phase offset of the active RIS, decoupling of channel parameters can be achieved in a multipath environment, so that the high-dimensional channel parameter estimation problem can be decomposed into multiple low-dimensional sub-problems.

[0057] 3) A low-complexity algorithm for decoupling 2D cascaded channel parameters is developed to address the challenge of estimating cascaded channel parameters. Using the idea of the greedy algorithm, the estimation process is transformed into multiple one-dimensional searches, greatly reducing the computational complexity. Description of the Drawings

[0058] Figure 1 It is a scenario diagram of an uplink active RIS-aided millimeter-wave MIMO system;

[0059] Figure 2 It is a schematic diagram of the RMSE of the cascaded channel varying with the total power obtained by using the method of the present invention and the existing method respectively. Detailed Embodiments

[0060] The present invention will be further described in detail below in conjunction with the embodiments of the drawings.

[0061] A channel estimation method for an active RIS-aided millimeter-wave MIMO system proposed by the present invention, which is applied to an uplink active RIS-aided millimeter-wave MIMO system, as Figure 1 shown, the millimeter-wave MIMO system includes an active RIS, a base station (BS) equipped with an antenna array, and a user equipment (UE) equipped with an antenna array. The three-dimensional positions and orientations of the active RIS and the base station are known, while the three-dimensional positions and orientations of the user equipment are unknown. The three-dimensional positions of the active RIS, the base station, and the user equipment refer to the positions based on the global coordinate system, and the global coordinate system is a three-dimensional coordinate system established with the center of the antenna array equipped by the base station as the origin O, the normal vector of the antenna array as the Y axis, and the antenna array located on the XOZ plane. For the active RIS, the base station, and the user equipment, an Euler angle vector o Q and the rotation sequence of Z-Y-X are used to describe their respective orientations in the global coordinate system, and the corresponding rotation matrix is obtained according to o Q where Q ∈ {R, B, U}, the dimension of o is 3×1, and the dimension of Q is 3×3. The method includes the following steps: Step 1: Based on the geometric channel model, obtain the channel matrix from the user equipment to the base station at time t

[0062] ​Expression of the channel matrix from the active RIS to the base station Expression of the channel matrix from the user equipment to the active RIS Expression of the cascaded channel matrix from the user equipment to the active RIS and then to the base station Expression, where The expression contains the angle of arrival (AoA) of the base station and the angle of departure (AoD) of the user equipment in each path of the user equipment - base station link

[0063] The expression contains the angle of arrival (AoA) of the base station and the angle of departure (AoD) of the active RIS in each path of the active RIS - base station link The expression contains the angle of arrival (AoA) of the active RIS and the angle of departure (AoD) of the user equipment in each path of the user equipment - active RIS link

[0064] In this embodiment, in step 1

[0065]

[0066] Where, L UB Represents the number of paths in the user equipment - base station link, l = 1, 2,..., L UB , the first path in the user equipment - base station link is the line - of - sight path, and the remaining paths are non - line - of - sight paths Represents the complex channel gain of the l - th path in the user equipment - base station link Represents the angle of arrival (AoA) of the base station in the l - th path of the user equipment - base station link Represents the angle of departure (AoD) of the user equipment in the l - th path of the user equipment - base station link Represents based on The far - field steering vector of the base station at Represents based on The far - field steering vector of the user equipment at, (·) H Represents the conjugate transpose operation, L RB Represents the number of paths in the active RIS - base station link, l1 = 1, 2,..., L RB , the first path in the active RIS - base station link is the line - of - sight path, and the remaining paths are non - line - of - sight paths Represents the complex channel gain of the l1 - th path in the active RIS - base station link Represents the angle of arrival (AoA) of the base station in the l1 - th path of the active RIS - base station link Represents the angle of departure (AoD) of the active RIS in the l1 - th path of the active RIS - base station link Represents based on Far - field steering vector of the base station at time denotes based on Far - field steering vector of the active RIS at time, L UR denotes the number of paths in the user - equipment to active - RIS link, \(l_2 = 1,2,\cdots,L\) UR , the first path in the user - equipment to active - RIS link is the line - of - sight path, and the remaining paths are non - line - of - sight paths denotes the complex channel gain of the \(l_2\) - th path in the user - equipment to active - RIS link denotes the angle of arrival of the active RIS in the \(l_2\) - th path of the user - equipment to active - RIS link denotes the angle of departure of the user - equipment in the \(l_2\) - th path of the user - equipment to active - RIS link denotes based on Far - field steering vector of the active RIS at time denotes based on Far - field steering vector of the user - equipment at time, \(\Omega\) t is a diagonal matrix is a defined symbol, \(\text{diag}(\cdot)\) represents finding the diagonal matrix, \(w\) t denotes the phase - shift vector of the active RIS at time \(t\) \(p\) represents the gain coefficient of the active RIS, \(p\gt1\), the gain coefficient of the passive RIS is 1, \(e\) represents the natural constant, \(e = 2.71\cdots\), \(j\) is the imaginary unit, \(N\) R denotes the number of active elements included in the active RIS, \(\omega_1\) and correspondingly represent the phase - shift of the first active element and the \(N\) - th R active element of the active RIS denotes the channel gain of the cascaded channel from the user - equipment to the active - RIS and then to the base station (\cdot) T denotes the transpose operation and correspondingly denote the elevation angle and azimuth angle of denotes the three - dimensional coordinates of the corresponding scatterer in the global coordinate system in the \(l_1\) - th path of the active - RIS to base - station link. When \(l_1 = 1\) is the three - dimensional coordinates of the base station in the global coordinate system, \(p\) R denotes the three - dimensional coordinates of the active RIS in the global coordinate system denotes taking the third element of denotes taking The second element of means to take The first element of, ||·|| is the L2 norm operation symbol, and the subsequent elevation angle and azimuth angle follow a similar relationship. and correspondingly represent The elevation angle and azimuth angle of " ⊙” is the Hadamard product operation symbol, (·) * represents the conjugate operation.

[0067] In this embodiment, where is the Kronecker product operation symbol, and correspondingly represent The elevation angle and azimuth angle of The antenna spacing in the antenna array equipped by the base station, the antenna spacing in the antenna array equipped by the user equipment, and the spacing between active elements in the active RIS are all d, and λ represents the wavelength. and correspondingly represent the number of antennas in the horizontal direction and the number of antennas in the vertical direction of the antenna array equipped by the base station. The antenna array equipped by the base station contains N B antennas. where and correspondingly represent The elevation angle and azimuth angle of

[0068]

[0069] and correspondingly represent the number of antennas in the horizontal direction and the number of antennas in the vertical direction of the antenna array equipped by the user equipment. The antenna array equipped by the user equipment contains N U antennas. where and correspondingly represent The elevation angle and azimuth angle of

[0070] and correspondingly represent the number of active elements in the horizontal direction and the number of active elements in the vertical direction of the active RIS. The active RIS contains N R active elements. Among them,

[0071] Among them, and correspondingly represent the elevation angle and azimuth angle,

[0072] Step 2: Based on obtain the expression of the received signal y at the base station at time t, and further obtain t the initial expression of the received signal matrix Y at the base station at several moments; then make the pilots transmitted by the user equipment change within the first several moments, while the phase offsets of the active RIS remain unchanged, and make the phase offsets of the active RIS change within the subsequent several moments, while the pilots transmitted by the user equipment remain unchanged, and determine the final expression of the received signal matrix Y at the base station at several moments, where

[0073] In this embodiment, in Step 2, Among them, x t represents the pilot transmitted by the user equipment at time t, and the dimension of x t is N U ×1, the dimension of y t is N B ×1, N U represents the number of antennas included in the antenna array equipped by the user equipment, and N B represents the number of antennas included in the antenna array equipped by the base station, represents the thermal noise at the active RIS at time t, obeys a Gaussian distribution with a mean of 0 and a variance of , I represents the identity matrix, represents the thermal noise at the base station at time t, obeys a Gaussian distribution with a mean of 0 and a variance of ; the initial expression of Y is described as: Among them, the dimension of Y is the dimension of X is the dimension of W is Z RThe dimension of Z B The dimension of Since and are coupled in the time domain, estimating the parameters and simultaneously is a problem of high complexity. Therefore, a specific active RIS phase shift and pilot structure is designed to eliminate the and coupling effect. The pilot transmitted by the user equipment changes within the first moments, while the phase shift of the active RIS remains unchanged, that is After moments, the phase shift of the active RIS changes, while the pilot transmitted by the user equipment remains unchanged, that is The final expression of Y is described as: Y = A B S + Z B , where the dimension of A B is N B ×(L RB + L UB ), A B = [A BU , A BR , the dimension of A BU is N B ×L UB , the dimension of A BR is N B ×L RB , The dimension of S is S is the coefficient matrix.

[0074] Step 3: Use algorithms based on DOA estimation, such as subspace-based algorithms, compressive sensing-based algorithms, etc., to solve the final expression of Y, and obtain the estimated values of the angles of arrival of the base station in each path of the link between the active RIS and the base station, and the estimated values of the angles of arrival of the base station in each path of the link between the user equipment and the base station; then replace the estimated value with the true value of the angle of arrival of the base station in the first path of the link between the active RIS and the base station. Since the true value of the angle of arrival of the base station in the first path (line-of-sight path) of the link between the active RIS and the base station is known, the estimated value is replaced with the true value.

[0075] Step 4: Combine the vector composed of the pilots transmitted by the user equipment within the latter moments and the initial expression of Y to obtain the expression of the received signal matrix at the base station within the latter moments; then according to The expression, combined with the estimated values of the angles of arrival of the base station in each path of the active RIS and base station link, and the estimated values of the angles of arrival of the base station in each path of the user equipment and base station link, uses the least squares method and one-dimensional search to iteratively obtain the rough estimated values of the departure angles of the active RIS in each path of the active RIS and base station link and the rough estimated values of the arrival angles of the active RIS in each path of the user equipment and active RIS link; then constructs a least squares problem for refining the rough estimated values, uses the quasi-Newton algorithm, and takes the rough estimated values as the search initial points to solve the least squares problem, and obtains the fine estimated values of the departure angles of the active RIS in each path of the active RIS and base station link and the fine estimated values of the arrival angles of the active RIS in each path of the user equipment and active RIS link.

[0076] In this embodiment, the specific process of step 4 is as follows:

[0077] Step 4.1: Denote the vector formed by the pilots transmitted by the user equipment within the subsequent time instants as where, is determined according to x t and represents a column vector of all 1s with dimension ; then, combined with and the initial expression of Y, the expression of the received signal matrix at the base station within the subsequent time instants is obtained, described as: where,

[0078]

[0079] is composed of the subsequent elements of W, is composed of the subsequent R elements of Z and is composed of the subsequent B elements of Z and

[0080] Step 4.2: According to the expression of , obtain: where, is the symbol of the pseudo-inverse operation, the i-th row of G B corresponds to the i-th column of A B Observe G B, it can be found that the row elements corresponding to the link between the user equipment and the base station are constant, while the row elements corresponding to the link between the active RIS and the base station change with the change of the phase shift of the active RIS. Therefore, in G B the row elements corresponding to the link between the user equipment and the base station will have a small variance, while the row elements corresponding to the link between the active RIS and the base station will have a large variance. By comparing the variances, the angle of arrival of the base station can be associated with different paths; then based on step 3, the estimated value of A B is obtained and substitute it into G into G B and then construct the matrix G R , where represents the submatrix formed by the (L B +1)-th row to the L-th row of G UB , L = L UB +L RB , The dimension of G R is

[0081] Step 4.3: Let where represents the l1-th column of , is a constant

[0082]

[0083] Step 4.4: Based on Step 4.3, using the least squares method and one-dimensional search, iteratively obtain the rough estimated values of and

[0084] . The specific process is as follows:

[0085] Step 4.4.1: Let k represent the iteration number, the initial value of k is 1, and the maximum iteration number is L UR .

[0086] Step 4.4.2: Approximate at the k-th iteration as Then construct optimization problem one, described as: where min represents the minimum value function, represents at the k-th iteration; then use the properties of the Kronecker product to transform optimization problem one into optimization problem two, described as: where After that, under the condition In the case of, use the least squares method to solve optimization problem two to obtain the least squares solution of ξ

[0087] Step 4.4.3: Apply one-dimensional search to solve Obtain The rough estimate of Then substitute into optimization problem one to obtain optimization problem three, described as: wherein, represents The estimate of, is to use the least squares method to solve Obtained The least squares solution of; then apply one-dimensional search to solve optimization problem three to obtain The rough estimate of

[0088] Step 4.4.4: In order to remove the correlated components of the signal and obtain the updated residual in the k-th iteration, subtract the projection of the signal in the following way, that is, let wherein, represents The representation at the (k + 1)-th iteration.

[0089] Step 4.4.5: Let k = k + 1, then return to step 4.4.2 to continue execution until obtaining The rough estimate of and The rough estimate of wherein, the "=" in k = k + 1 is an assignment symbol.

[0090] Step 4.5: Define the first cascaded channel matrix Φ x and the second cascaded channel matrix Φ z , and let where k = 1, 2,..., L UR , represents the element in the l1-th row and k-th column of Φ x , represents the element in the l1-th row and k-th column of Φ z ; then construct the least squares problem for refining the rough estimate, described as: Then use the quasi-Newton algorithm, and take Φ x and Φ z as the search initial point to solve the least squares problem to obtain The fine estimate of Furthermore, obtain The fine estimate of and Fine estimate value

[0091] Step 5: Combine the vector sum of the phase offsets of the active RIS within the previous moments and the initial expression of Y to obtain the expression of the received signal matrix at the base station for the previous moments; then, according to the expression of and combined with the estimated values of the angles of arrival of the base station in each path of the link between the active RIS and the base station, obtain the estimated value of the received signal matrix for all paths of the link between the user equipment and the base station for the previous moments ; Then, based on and applying one-dimensional search, obtain the rough estimate value of the angle of departure of the user equipment in each path of the link between the user equipment and the base station; finally, use the quasi-Newton algorithm and take the rough estimate value as the search initial point to solve the least squares problem of refining the rough estimate value, and obtain the fine estimate value of the angle of departure of the user equipment in each path of the link between the user equipment and the base station.

[0092] In this embodiment, the specific process of Step 5 is as follows:

[0093] Step 5.1: Denote the vector formed by the phase offsets of the active RIS within the previous moments as where represents a column vector of all 1s with dimension ; then, combine and the initial expression of Y to obtain the expression of the received signal matrix at the base station for the previous moments, which is described as:

[0094] where

[0095] represents the received signal matrix of all paths of the link between the user equipment and the base station for the previous moments, represents the received signal matrix of all paths of the link from the user equipment to the active RIS and then to the base station for the previous moments, is composed of the first B elements of Z moments,

[0096] is composed of the first elements of X, represents The element in the \(l_1\)-th row and \(l_2\)-th column of denotes \(C\) R the \(l_1\)-th column of \(C\), and the dimension of \(C\) is \(N\) R × \(L\) R × \(L\) RB , which is composed of the first R elements of \(Z\). elements of \(Z\).

[0097] Step 5.2: Since and belong to the same space, the estimate of can be obtained by subtracting the projection of \(A\) BR from it. That is, according to the expression of the estimate of is obtained. the estimate of

[0098] where denotes the estimate of \(A\) BR , which is obtained from the estimated values of the angles of arrival of the base station in each path of the active RIS - base station link; and then based on When is defined where \(N\) U denotes the number of antennas in the antenna array equipped by the user equipment.

[0099] Step 5.3: Let where denotes the \(l\)-th column of ; then using the property reshape into a matrix where \(\text{vec}(\cdot)\) represents the vectorization operation, and the dimension of is a rank - 1 matrix; then apply singular value decomposition to to get: where \(\sigma\) represents the largest eigenvalue, and are both eigenvectors, and are the two components obtained by decomposing \(\sigma\),

[0100] Step 5.4: Apply one - dimensional search to solve and to obtain the corresponding Estimated value and Estimated value Furthermore, obtain Coarse estimated value where |·| is the modulus operation symbol; then construct the refinement Least squares problem, described as: where Represents the orthogonal projection matrix onto the Column space; then use the quasi-Newton algorithm and take As the search initial point to solve the refinement Least squares problem to obtain Fine estimated value

[0101] Step 6: According to the previous Received signal matrix at the base station at moments Expression, and use algorithms based on DOA estimation such as subspace-based algorithms, compressive sensing-based algorithms, etc., to obtain the estimated value of the departure angle of the user equipment in each path of the user equipment - active RIS link.

[0102] In this embodiment, the specific process of step 6 is: According to Expression, when Get: where

[0103] Then by ignoring the noise term, transform Into Then define Since G UR Has the same structure as the initial expression of Y, so then algorithms based on DOA estimation such as subspace-based algorithms, compressive sensing-based algorithms, etc. can be used to Solve to obtain Estimated value where Represents the estimated value of A BR Obtained according to the estimated value of the arrival angle of the base station in each path of the active RIS - base station link.

[0104] To further illustrate the feasibility and effectiveness of the method of the present invention, simulation experiments are carried out on the method of the present invention.

[0105] In the simulation experiment, for the uplink active RIS - assisted millimeter - wave MIMO system, set the carrier frequency f c= 28 GHz, the system bandwidth B = 1 MHz; using a random transmit signal X and an active RIS phase shift configuration matrix W; the calculation formula for the amplification factor χ of the active RIS is: where J R represents the power of the active RIS, and J U represents the power of the user equipment, and J U = E{|x t | 2}, E{·} represents taking the mathematical expectation, and the total power J T is J R + J U , and J R = ∈J U , ∈ represents the power allocation coefficient; the complex channel gain of the line-of-sight path in the user equipment - base station link The complex channel gain of the line-of-sight path in the active RIS - base station link The complex channel gain of the line-of-sight path in the user equipment - active RIS link where p U represents the three - dimensional coordinates of the user equipment in the global coordinate system, p B represents the three - dimensional coordinates of the base station in the global coordinate system, p R represents the three - dimensional coordinates of the active RIS in the global coordinate system, ψ UB represents the random phase of the line-of-sight path in the user equipment - base station link, ψ RB represents the random phase of the line-of-sight path in the active RIS - base station link, ψ UR represents the random phase of the line-of-sight path in the user equipment - active RIS link; the complex channel gain of the l - th path (non - line - of - sight path) in the user equipment - base station link where l = 2,..., L UB , κ is the reflection loss, and ψ UB,l represents the random phase of the l - th path (non - line - of - sight path) in the user equipment - base station link, represents the three - dimensional coordinates of the corresponding scatterer in the global coordinate system in the l - th path of the user equipment - base station link; the complex channel gain of the l1 - th path (non - line - of - sight path) in the active RIS - base station link where l1 = 2,..., L RB , represents the random phase of the l1 - th path (non - line - of - sight path) in the active RIS - base station link, represents the three - dimensional coordinates of the corresponding scatterer in the global coordinate system in the l1 - th path of the active RIS - base station link; the complex channel gain of the l2 - th path (non - line - of - sight path) in the user equipment - active RIS link where l2 = 2,..., LUR , represents the random phase of the l2-th path (non-line-of-sight path) in the active RIS link between the user equipment, and represents the three-dimensional coordinates of the corresponding scatterer in the l2-th path in the active RIS link between the user equipment in the global coordinate system. The simulation parameters are listed in Table 1. The number of Monte Carlo runs is 500 times.

[0106] Table 1 Simulation Parameters

[0107]

[0108] Figure 2 The RMSE of the method of the present invention and various existing methods in estimating the cascaded channel parameters is compared, and the relationship between the estimation accuracy and the total power is shown. Figure 2 The existing methods in [reference] mainly include the method based on atomic norm, the orthogonal matching pursuit (OMP) algorithm, and the method based on nuclear norm. The proposed method (coarse estimation) refers to the method formed by omitting the fine estimation process in the method of the present invention (fine estimation). Figure 2 The results shown indicate that as the total signal power increases, the performance of the OMP algorithm, the method based on nuclear norm, and the coarse estimation of the proposed method all tend to saturate to a certain extent. Generally speaking, the coarse estimation of the proposed method shows higher estimation accuracy and lower complexity compared with the OMP algorithm and the method based on nuclear norm. After refinement, the estimation accuracy of the proposed method can be better than the method based on atomic norm, and the fine estimation of the proposed method still has reliable estimation when the total power is -10 dBm, which fully demonstrates that the method of the present invention is significantly superior to the existing methods.

Claims

1. A channel estimation method for an active RIS-assisted millimeter-wave MIMO system, which is applied to an uplink active RIS-assisted millimeter-wave MIMO system. The millimeter-wave MIMO system includes an active RIS, a base station equipped with an antenna array, and a user equipment equipped with an antenna array. The three-dimensional positions and orientations of the active RIS and the base station are known, while the three-dimensional position and orientation of the user equipment are unknown. It is characterized in that The method includes the following steps: Step 1: Based on the geometric channel model, obtain the channel matrix from the user equipment to the base station at time t expression, the channel matrix from the active RIS to the base station expression, the channel matrix from the user equipment to the active RIS expression, and the cascaded channel matrix from the user equipment to the active RIS and then to the base station expression, where the expression contains the angle of arrival of the base station and the angle of departure of the user equipment in each path of the user equipment - base station link the expression contains the angle of arrival of the base station and the angle of departure of the active RIS in each path of the active RIS - base station link the expression contains the angle of arrival of the active RIS and the angle of departure of the user equipment in each path of the user equipment - active RIS link; Step 2: Based on obtain the received signal y at the base station at time t t to further obtain the initial expression of the received signal matrix Y at the base station at several moments; then make the pilots transmitted by the user equipment change within the first several moments while keeping the phase offsets of the active RIS unchanged, and make the phase offsets of the active RIS change within the subsequent several moments while keeping the pilots transmitted by the user equipment unchanged, and determine Step 3: Use an algorithm based on DOA estimation to solve the final expression of Y, obtaining the estimated values of the angles of arrival of the base station in each path of the active RIS - base station link and the estimated values of the angles of arrival of the base station in each path of the user equipment - base station link; then replace the estimated value with the true value of the angle of arrival of the base station in the first path of the active RIS - base station link; Step 4: After combination the vector composed of pilots transmitted by the user equipment within a certain number of time instants and the initial expression of Y, and after obtaining the expression of the received signal matrix at the base station at a certain number of time instants Then, according to the expression of, and combining the estimated values of the angles of arrival of the base station in each path of the active RIS - base station link and the estimated values of the angles of arrival of the base station in each path of the user equipment - base station link, using the least - squares method and one - dimensional search, iteratively obtain the rough estimated values of the angles of departure of the active RIS in each path of the active RIS - base station link and the rough estimated values of the angles of arrival of the active RIS in each path of the user equipment - active RIS link; then construct a least - squares problem for refining the rough estimated values, use the quasi - Newton algorithm, and take the rough estimated values as the search initial points to solve the least - squares problem, and obtain the refined estimated values of the angles of departure of the active RIS in each path of the active RIS - base station link and the refined estimated values of the angles of arrival of the active RIS in each path of the user equipment - active RIS link; Step 5: Combine the vector sum of the phase offsets of the active RIS in the previous moments and the initial expression of Y to obtain the expression of the received signal matrix at the base station in the previous moments; then, according to the expression of and combined with the estimated values of the angles of arrival of the base station in each path of the active RIS - base station link, obtain the estimated values of the received signal matrix of all paths of the user equipment - base station link in the previous moments; Based on this and applying one - dimensional search, obtain the rough estimated values of the angles of departure of the user equipment in each path of the user equipment - base station link; finally, use the quasi - Newton algorithm and take the rough estimated values as the search initial points to solve the least - squares problem of refining the rough estimated values, and obtain the fine estimated values of the angles of departure of the user equipment in each path of the user equipment - base station link. Step 6: According to the expression of the received signal matrix at the base station in the previous moments, and using the algorithm based on DOA estimation, obtain the estimated value of the departure angle of the user equipment in each path of the user equipment - active RIS link.

2. The channel estimation method of an active RIS-assisted millimeter-wave MIMO system according to claim 1, wherein The three-dimensional positions of the active RIS, the base station, and the user equipment refer to the positions based on the global coordinate system, which is a three-dimensional coordinate system established with the center of the antenna array equipped by the base station as the origin O, the normal vector of the antenna array as the Y-axis, and the antenna array located on the XOZ plane; for the active RIS, the base station, and the user equipment, an Euler angle vector o is used Q and the rotation order of Z-Y-X to describe their respective directions in the global coordinate system, and according to o Q to obtain the corresponding rotation matrix where Q ∈ {R, B, U}, o Q has a dimension of 3×1, has a dimension of 3×3.

3. The channel estimation method of an active RIS-assisted millimeter-wave MIMO system according to claim 2, wherein In the said step 1, Among them, L UB represents the number of paths in the link between the user equipment and the base station, where l = 1, 2,..., L UB , the first path in the link between the user equipment and the base station is the line-of-sight path, and the remaining paths are non-line-of-sight paths represents the complex channel gain of the l-th path in the link between the user equipment and the base station represents the angle of arrival of the base station in the l-th path of the link between the user equipment and the base station represents the angle of departure of the user equipment in the l-th path of the link between the user equipment and the base station represents based on the far-field steering vector of the base station at represents based on the far-field steering vector of the user equipment at, (·) H represents the conjugate transpose operation, L RB represents the number of paths in the link between the active RIS and the base station, where l1 = 1, 2,..., L RB , the first path in the link between the active RIS and the base station is the line-of-sight path, and the remaining paths are non-line-of-sight paths represents the complex channel gain of the l1-th path in the link between the active RIS and the base station represents the angle of arrival of the base station in the l1-th path of the link between the active RIS and the base station represents the angle of departure of the active RIS in the l1-th path of the link between the active RIS and the base station represents based on the far-field steering vector of the base station at represents based on the far-field steering vector of the active RIS at, L UR represents the number of paths in the link between the user equipment and the active RIS, where l2 = 1, 2,..., L UR , the first path in the link between the user equipment and the active RIS is the line-of-sight path, and the remaining paths are non-line-of-sight paths represents the complex channel gain of the l2-th path in the link between the user equipment and the active RIS represents the angle of arrival of the active RIS in the l2-th path of the link between the user equipment and the active RIS represents the angle of departure of the user equipment in the l2-th path of the link between the user equipment and the active RIS represents based on the far-field steering vector of the active RIS at represents based on the far-field steering vector of the user equipment at diag(·) represents finding the diagonal matrix, w t represents the phase shift vector of the active RIS at time t Let \(p\) denote the gain coefficient of the active RIS, \(e\) denote the natural constant, \(j\) denote the imaginary unit, and \(N\) R denote the number of active elements included in the active RIS, and \(\omega_1\) and correspondingly denote the phase offsets of the first and the \(N\)th R active elements of the active RIS, denote the channel gain of the cascaded channel from the user equipment to the active RIS and then to the base station, (·) T denote the transpose operation, and correspondingly denote the elevation angle and the azimuth angle of, denote the three-dimensional coordinates of the scatterer corresponding to the \(l_1\)th path in the link between the active RIS and the base station in the global coordinate system. When \(l_1 = 1\), it is the three-dimensional coordinates of the base station in the global coordinate system, and \(p\) R denote the three-dimensional coordinates of the active RIS in the global coordinate system, denote taking the third element of, denote taking the second element of, denote taking the first element of. \(\|\cdot\|\) is the L2 norm operation symbol, and correspondingly denote the elevation angle and the azimuth angle of, "⊙” is the Hadamard product operation symbol, and \((\cdot)\) * denote the conjugate operation.

4. The channel estimation method of an active RIS-assisted millimeter-wave MIMO system according to claim 3, characterized in that Among them, is the Kronecker product operation symbol, and correspondingly represent the elevation angle and azimuth angle, The antenna spacing in the antenna array equipped by the base station, the antenna spacing in the antenna array equipped by the user equipment, and the active element spacing in the active RIS are all d, λ represents the wavelength, and correspondingly represent the number of antennas in the horizontal direction and the number of antennas in the vertical direction of the antenna array equipped by the base station; Among them, and correspondingly represent the elevation angle and azimuth angle, and correspondingly represent the number of antennas in the horizontal direction and the number of antennas in the vertical direction of the antenna array equipped by the user equipment; Among them, and correspondingly represent the elevation angle and azimuth angle, and correspondingly represent the number of active elements in the horizontal direction and the number of active elements in the vertical direction of the active RIS; wherein, Among them, and correspondingly represent the elevation angle and azimuth angle, 5. The channel estimation method for an active RIS-assisted millimeter-wave MIMO system according to claim 3, characterized in that In the said step 2, wherein, x t represents the pilot transmitted by the user equipment at time t, represents the thermal noise at the active RIS at time t, obeys a Gaussian distribution with a mean of 0 and a variance of , I represents the identity matrix, represents the thermal noise at the base station at time t, obeys a Gaussian distribution with a mean of 0 and a variance of ; The initial expression of Y is described as: Among them, The final expression of Y is described as: Y = A B S + Z B , where A B = [A BU , A BR , S is a coefficient matrix.

6. The channel estimation method of an active RIS-assisted millimeter-wave MIMO system according to claim 5, characterized in that The specific process of the said Step 4 is: Step 4.1: Denote the vector composed of the pilots transmitted by the user equipment in the subsequent time instants as where represents a column vector of all 1s with dimension ; then, combining with the initial expression of Y, obtain the expression of the received signal matrix at the base station in the subsequent time instants, described as: Among them, Consisting of the last several elements of W, consisting of the last R several elements of Z, consisting of the last several elements of Z; B consisting of the last several elements of Z. Step 4.2: According to the expression of, obtain: wherein, is the pseudo-inverse operation symbol, Then based on Step 3, obtain the estimated value B of A and substitute into G B and then construct the matrix G R , wherein, represents the sub-matrix formed by the (L B +1)-th row to the L-th row of G UB , L = L UB + L RB , Step 4.3: Let where denotes the l1-th column of is a constant Step 4.4: Based on Step 4.3, using the least squares method and one-dimensional search, iteratively obtain and the rough estimated values, and the specific process is as follows: Step 4.4.1: Let \(k\) represent the iteration number. The initial value of \(k\) is 1, and the maximum number of iterations is \(L\). UR ; Step 4.4.2: At the k-th iteration is approximated as Then, Optimization Problem 1 is constructed and described as: where min represents the minimum value function, represents at the k-th iteration; then, using the properties of the Kronecker product, Optimization Problem 1 is transformed into Optimization Problem 2, which is described as: where After that, under the condition that is satisfied, the least squares method is used to solve Optimization Problem 2 to obtain the least squares solution Step 4.4.3: Solve using one-dimensional search Obtain a rough estimate of Then substitute into Optimization Problem 1 to obtain Optimization Problem 3, described as: where represents the estimated value of is the least squares solution of obtained by solving using the least squares method; then solve Optimization Problem 3 using one-dimensional search to obtain a rough estimate of Step 4.4.4: Let where denotes the representation at the (k + 1)-th iteration; Step 4.4.5: Let k = k + 1, then return to Step 4.4.2 to continue execution until the rough estimated value of is obtained and the rough estimated value of where the "=" in k = k + 1 is an assignment symbol; Step 4.5: Define the first cascaded channel matrix Φ x and the second cascaded channel matrix Φ z , and let where k = 1, 2,..., L UR , denotes the element in the l1-th row and k-th column of Φ x , and denotes the element in the l1-th row and k-th column of Φ z ; then construct the least squares problem for refining the coarse estimate, described as: Then use the quasi-Newton algorithm, and take Φ x and Φ z as the search initial points to solve the least squares problem, and obtain the fine estimate of Furthermore, obtain the fine estimate of and the fine estimate of ​ 7. The channel estimation method for an active RIS-assisted millimeter-wave MIMO system according to claim 6, characterized in that The specific process of the said Step 5 is: Step 5.1: Denote the vector composed of the phase offsets of the active RIS in the previous time instants as where represents a column vector of all 1s with dimension ; then, combining with the initial expression of Y, obtain the expression of the received signal matrix at the base station in the previous time instants, described as: Among them, represents the received signal matrix of all paths of the user equipment and the base station link in the previous moments, represents the received signal matrix of all paths of the user equipment to the active RIS and then to the base station link in the previous moments, which is composed of the first B elements of Z ; which is composed of the first elements of X represents the element in the l1-th row and l2-th column of represents the l1-th column of C R ; which is composed of the first R elements of Z ; Step 5.2: According to 's expression, obtain 's estimated value where, represents the estimated value of A BR , which is obtained based on the estimated value of the angle of arrival of the base station in each path of the active RIS and base station link; and then based on When is defined as where N U represents the number of antennas included in the antenna array equipped by the user equipment; Step 5.3: Let where denotes the l-th column of; then, using the property reshape into a matrix where vec(·) represents the vectorization operation, is a rank-1 matrix; then apply singular value decomposition to to get: where σ represents the largest eigenvalue, and are both eigenvectors, and are the two components obtained by decomposing σ, Step 5.4: Solve by applying one-dimensional search and correspondingly obtain the estimated value of and the estimated value of and then obtain the rough estimated value of where |·| is the modulo operation symbol; then construct the refinement least squares problem, described as: where Then use the quasi-Newton algorithm, and take as the search initial point to solve the refinement least squares problem, and obtain the fine estimated value of 8. The channel estimation method for an active RIS-assisted millimeter-wave MIMO system according to claim 7, characterized in that The specific process of the said Step 6 is: According to the expression of, when is obtained: Among them, Then, by ignoring the noise terms, transform it into Then define After that, use the algorithm based on DOA estimation to solve it and obtain the estimated value of where denotes the estimated value of A BR which is obtained from the estimated value of the angle of arrival of the base station in each path of the active RIS - base station link.

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