A double-time-scale transmission method and system for a RIS-assisted MIMO system

Abstract

The application discloses a RIS-assisted MIMO system double-time-scale transmission method and system, and the method comprises the following steps: step one, constructing a single-cell uplink RIS-assisted millimeter wave massive MIMO system model; step two, converting the RIS element phase shift vector problem into a multi-armed bandit problem, and finding out a correlation matrix closely related to each time slot phase shift vector; step three, based on an improved orthogonal matching pursuit algorithm, using the information of all time slots before the current time slot to calculate the hour slot matrix of the current time slot, and finally obtaining the correlation matrix of the whole time period; step four, according to the calculated correlation matrix, using a CMAB-based phase shift algorithm to solve the phase shift vector of all time slots; step five, calculating the effective uplink matrix and the combination matrix according to the solved phase shift vector, and further solving the base station received signal. The method can significantly reduce the cost and improve the effective spectrum efficiency.

Description

TECHNICAL FIELD

[0001] The application relates to a double-time-scale transmission method for an RIS-assisted MIMO system and belongs to the technical field of wireless communication. BACKGROUND

[0002] In recent years, an intelligent reflecting surface (RIS)-assisted network has attracted much attention due to its ability to improve network capacity. An intelligent radio environment can use an intelligent reflecting surface (RIS) to programmably manipulate the propagation of incident electromagnetic waves, thereby actively changing the realization of a channel and turning a wireless channel into a controllable system block, which can improve the overall performance of the system through optimization.

[0003] In order to fully utilize the advantages of the intelligent reflecting surface (IRS), various joint beamforming design schemes have been proposed in the prior art. For a single-cell multi-user multiple-input multiple-output (MIMO) or multiple-input multiple-output (MISO) system, an active and passive beamforming joint design scheme is proposed, aiming to minimize the total transmit power or maximize the spectral efficiency. And by analyzing the ergodic capacity, an asymptotically optimal beamforming algorithm for a distributed RIS-assisted massive antenna system is proposed. However, the above technical solutions all assume that the base station (BS) can provide instantaneous channel state information (I-CSI). In order to calculate the instantaneous channel state information (I-CSI) within the channel coherence interval, the pilot overhead will increase with the increase of the number of signal elements and users on the intelligent reflecting surface.

[0004] In order to reduce the pilot overhead, a double-time-scale transmission scheme (TTTS) relying on S-CSI is proposed, which greatly reduces the pilot overhead, including optimal phase shift design based on ergodic spectral efficiency upper bound and statistical channel state information, considering single-user and multi-user cases, designing an efficient algorithm based on statistical channel state information (CSI) to design the phase shift, designing the phase shift and power allocation under a large time scale based on S-CSI, and designing the base station (BS) beamforming under a small time scale. However, I-CSI is not easy to obtain, especially in high-speed cases. When the user moves quickly, the time during which I-CSI remains unchanged is relatively short, and the pilot overhead for calculating I-CSI occupies a large proportion of symbols, thereby reducing the spectral efficiency. SUMMARY

[0005] The technical problem to be solved by the application is the problems of low efficiency and high cost in the prior art for calculating a channel using CSI and transmitting a signal.

[0006] To solve the above technical problems, the application provides a double-time-scale transmission method for an RIS-assisted MIMO system, comprising the following steps:

[0007] Step one, constructing a single-cell uplink RIS-assisted millimeter wave massive MIMO system model;

[0008] Step two, phase shift vector θ of RIS element t Design problem is converted into multi-arm slot machine problem, find out phase shift vector θ of each time slot t The closely related correlation matrix R;

[0009] Step three, based on the improved orthogonal matching pursuit algorithm, using the information of all time slots before the current time slot to calculate the hour slot matrix of the current time slot Finally, the correlation matrix R of the whole time period is obtained;

[0010] Step four, according to the calculated correlation matrix R, using the phase shift algorithm based on CMAB to solve the phase shift vector Θ of all time slots t ;

[0011] Step five, according to the calculated phase shift vector Θ t Calculate the effective uplink matrix And the combination matrix Further solve the base station received signal y(t) = w(t)G(t)diag(θ(t))h(t)s(t), Indicates the channel energy, The transformed effective uplink matrix, Indicates the transpose conjugate matrix of matrix , diag(θ(t)) indicates the diagonal matrix of phase shift matrix θ(t), and G(t) is the channel vector from intelligent reflecting surface RIS to base station BS.

[0012] The aforementioned RIS-assisted MIMO system double-time scale transmission method, in step one, the one single-cell uplink intelligent reflecting surface RIS-assisted millimeter wave massive MIMO system comprises a base station BS, the base station BS communicates with a single-antenna user through an RIS with N cell units, and the base station BS and the RIS are respectively equipped with M=M x ×M y And N=N x ×N y Element uniform planar antenna array, M x , M y Respectively represent the number of elements of the base station side uniform antenna array in the horizontal and vertical directions; N x , N y Respectively represent the number of elements of the RIS side uniform antenna array in the horizontal and vertical directions;

[0013] Let G(t) and h(t) represent the channel vector from intelligent reflecting surface RIS to base station BS and the channel vector from user to RIS in the tth time slot respectively; the geometric millimeter wave channel model is used to describe the channel characteristics, y = [y1, y2, …, y K ]T denotes the received signal; K denotes the number of channels;

[0014] The channel vector G(t) of the smart reflecting surface RIS to the base station BS is denoted as:

[0015]

[0016] where L is the number of paths; is the path gain of the lth path; a M and a N are the steering vectors of the RIS and BS, respectively; denote the horizontal and vertical angles of departure of the lth path at the RIS, respectively; denote the horizontal and vertical angles of arrival of the lth path at the base station, respectively;

[0017] The channel vector h(t) from the user to the RIS is denoted as:

[0018]

[0019] where P is the number of paths, β p is the path gain of the pth path, denote the horizontal and vertical angles of arrival of the pth path at the RIS, respectively;

[0020] θ t denotes the phase shift vector of the RIS in the tth time slot, where the modulus of the nth element θ n,t satisfies |θ n,t |=1, let s(t) be the symbol transmitted by the user, and the combining matrix of the base station in the tth time slot be w(t), assuming that the direct channel between the base station and the user is blocked, then the signal received by the base station in time slot t is:

[0021] y(t) = w(t)G(t)diag(θ(t))h(t)s(t) + n(t) (3)

[0022] where n(t) is the Gaussian noise in the tth time slot;

[0023] After obtaining the phase shift vector θ t , the combining matrix is designed in each time slot, as shown in equation (6), the user transmits a pilot signal s = 1, and the signal received by the base station in the tth time slot is:

[0024]

[0025] where the effective uplink channel matrix becomes n(t) is the noise;

[0026] The effective uplink channel matrix is transformed as:

[0027]

[0028] The combination matrix w(t) is expressed as equation (6):

[0029]

[0030] wherein, represents the channel energy, represents the matrix the transpose conjugate matrix of.

[0031] The aforementioned double-time-scale transmission method of RIS-aided MIMO system, in step two, when designing the time slot phase shift vector θ t , maximizes the channel energy , which is expressed as problem as follows:

[0032]

[0033] θ t represents the phase shift vector of the RIS in the t-th time slot, wherein the n-th element is θ n,t .

[0034] The problem P1 is converted into a multi-armed bandit problem for solving, and the solving process is:

[0035] The phase shift is regarded as an action, and the channel energy is regarded as a reward, which is expressed as follows:

[0036]

[0037] wherein, r(θ t ) represents the reward under the phase shift vector θ t , and E(·) represents the energy;

[0038] Let be the concatenated channel, and equation (9) is simplified as:

[0039]

[0040] wherein, the correlation matrix diag(h(t)) represents the diagonal matrix of the effective uplink channel matrix, is the concatenated channel.

[0041] The aforementioned double-time-scale transmission method of RIS-aided MIMO system, in step three, in the t-th time slot, the signal received by the base station is:

[0042]

[0043] t c,1 and t c,2 denote the start and end time slots in the cth coherence time, assuming the current time slot is located in the cth coherence time, equation (11) is transformed as:

[0044]

[0045] where and Θ c are the received signal and the performed phase shift vector in the cth coherence time, respectively, denotes the concatenated channel in the cth coherence time, denotes the noise in the cth coherence time, and we have

[0046]

[0047] where ∧ n is a diagonal matrix, is a random variable with zero mean, is the noise matrix in the cth coherence time, denotes the transpose conjugate matrix, denotes the concatenated channel matrix in the kth time slot in the cth coherence time;

[0048] According to equation (13), the calculation of the correlation matrix R is expressed as the problem

[0049]

[0050] where, ‖·‖ F denotes the F-norm;

[0051] Let then we have

[0052]

[0053] where, is the K-R product matrix operation, and is the Hadamard matrix operation; Let variable matrix one R G = E(G H (t)G(t)), and variable matrix two R h = E(h * (t)h T (t)), then we have

[0054] R = E(G H (t)G(t)) ⊙ E(h * (t)h T (t)) = RG ⊙R h (16)

[0055] Define intermediate variables denotes the Kronecker product operation, vec(·) is a vectorization operator, and h is a diagonal matrix, m c is the signal of the cth coherence time, M c is the signal matrix of the cth coherence time, then the calculation problem of the intermediate variable is represented as problem

[0056]

[0057] Let A = [A1; A2; …; A c ], m = [m1; m2; …; m c ], then problem P3 is converted into problem

[0058]

[0059] For problem , the intermediate variable is obtained by using the OMP algorithm. Then the diagonal matrix is calculated using the following formula

[0060]

[0061] where unvec(·) is a matrixization operator, denotes the matrixization of the intermediate variable , denotes the matrixization of the intermediate variable and then the converted result is transformed into a transposed conjugate matrix. At the same time, the diagonal matrix is obtained, and is used to solve the change matrix two

[0062] , and denote the discrete Fourier transform (DFT) vector on the RIS side and the transpose of the discrete Fourier transform (DFT) vector on the RIS side, respectively.

[0063] Similarly, given the initial value of the matrix change matrix two , the change matrix one is solved in the manner of solving the change matrix two according to the above formula (17) to formula (20), and then the change matrix one and the change matrix two Until convergence, the final small phase shift matrix is obtained Finally, the correlation matrix R of the entire time period is obtained.

[0064] The aforementioned RIS-assisted MIMO system double-time-scale transmission method, in step four, the phase shift vector of the tth time slot is represented as:

[0065]

[0066] where k is a random variable uniformly distributed in [0, 1], ε and η are two constants; η represents the probability of selecting the optimal phase shift; ε represents the probability of selecting a phase shift with high spectral efficiency in the set S t ; random(S t ) represents randomly selecting an element in the set S t ; f sub represents a random variable selecting a subspace close to the main eigenvalue in the set S t ; θ opt is the phase shift that maximizes the received energy.

[0067] U R represents a combined matrix composed of eigenvectors corresponding to the eigenvalues of the correlation matrix R; the distance between the phase shift vector and the correlation matrix R is represented by chord distance, defined as

[0068]

[0069] where u θ is the eigenvector of θ, i.e. f sub (S t ) is the solution to problem P5,

[0070]

[0071] For problem , first calculate the chord distance of each phase shift in the set S t , then select the phase shift vector with the smallest chord distance as the solution to problem ;

[0072] random(S t ) represents randomly selecting an element in the set S t , θ represents the phase shift, and θ opt is the phase shift that maximizes the received energy, which is the solution to problem :

[0073]

[0074] where θ represents the phase shift, s.t. represents the restriction, i.e., the restriction condition.

[0075] The aforementioned RIS-assisted MIMO system double-time-scale transmission method, in step four, solves the problem based on the phase shift design algorithm of the Riemann conjugate gradient method The steps are as follows, where ∈1 is a convergence threshold:

[0076] Step 1: input the calculated vector matrix and set the starting point coordinate θ0=1 on the complex circle manifold, k=0;

[0077] Step 2: calculate the Riemann gradient gradf(θ (k) ) according to formula (27);

[0078] Step 3: calculate the Riemann conjugate direction d k according to formula (26);

[0079] Step 4: select the step size α k according to the Armijo backtracking line search rule;

[0080] Step 5: update the point θ according to formula (28) by k←+1;

[0081] Step 6: calculate the modulus of the gradient ||gradf(θ (k) )||2, if ||gradf(θ (k) )||2>∈1, repeat

[0082] Step 2-Step 6; until ||gradf(x k )||2≤∈1 is satisfied;

[0083] Step 7: output the phase shift θ opt that maximizes the received energy;

[0084]

[0085] where β k is the Polak-Ribiere parameter, gradf(θ (k) ) is the Riemann gradient of the function f at the point θ (k) on the manifold , and the value is:

[0086]

[0087] where, is the vector transmission operation, and the calculation formula is

[0088]

[0089] The double-time-scale transmission method of the RIS-assisted MIMO system in the foregoing, in step four, obtains the phase shift vector Θ based on the CMAB phase shift algorithm t The steps are as follows, where ∈2 is a convergence threshold:

[0090] Step 1: Let the initial signal y l = 1, the initial position θ l = 1, l = 1, 2, …, t, and initialize the change matrix one of the initial time slot The initial iteration number k = 1; I represents a unit matrix with all elements being 1.

[0091] Step 2: Calculate the signal matrix M of the cth coherence time and the phase shift vector Θ of the cth coherence time according to the formulas c and c ;

[0092] Step 3: Given the change matrix one of the kth time slot, convert it into the solution problem of the intermediate variable of the kth time slot according to formula (19), and solve the intermediate variable of the kth time slot by using the OMP algorithm

[0093] Step 4: Solve the diagonal matrix according to formula (20), and then solve the change matrix two of the kth time slot according to formula

[0094] Step 5: Given the change matrix two of the kth time slot, solve the change matrix one of the kth time slot

[0095] Step 6: Solve the change matrix two and the change matrix one of the k+1th time slot by k←k+1

[0096] Step 7: Calculate the modulus of the gradient respectively, if or repeat Step 3-Step 6; until or is satisfied; record the change matrix two and the change matrix one of the kth time slot

[0097] Step 8: Calculate the formula according to the hour slot matrix Computing the output hourglass matrix

[0098] Step 9: Obtain the designed phase shift vector Θ according to equation (21) t and output.

[0099] The aforementioned RIS-aided MIMO system double-time-scale transmission method, in step five, according to the obtained phase shift vector Θ t Computing the effective uplink matrix and the combination matrix w(t), further solving the base station received signal y(t), the steps are as follows:

[0100] Computing the effective uplink matrix according to equation (29)

[0101]

[0102] Computing the combination matrix w(t) according to equation (6);

[0103]

[0104] wherein, represents the channel energy, represents the transpose conjugate matrix of matrix .

[0105] Computing the base station received signal y(t) according to equation (30):

[0106] y(t) = w(t)G(t)diag(θ(t))h(t)s(t) (30).

[0107] A computer device / equipment / system, comprising a memory, a processor and a computer program stored on the memory, the processor executes the computer program to realize the steps of the above method.

[0108] A computer readable storage medium, having stored thereon a computer program / instruction, which is executed by a processor to realize the steps of the above method.

[0109] A computer program product, comprising a computer program / instruction, which is executed by a processor to realize the steps of the above method.

[0110] The method of the application converts the phase shift design problem into the MAB problem, obtains the phase shift by using the online learning process, does not need CSI, and solves the effective uplink channel matrix according to the phase shift, designs the combination matrix in the small time scale, reduces the interference, and improves the system spectrum efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0111] Figure 1 is a schematic diagram of a double time scale transmission structure provided by Embodiment 1 of the application;

[0112] Figure 2 is a graph of the relationship between the ESE performance and the number of time slots under different schemes of Embodiment 1 of the application;

[0113] Figure 3 is a graph of the relationship between the ESE performance and the signal-to-noise ratio under different schemes of Embodiment 1 of the application;

[0114] Figure 4 is a graph of the relationship between the ESE performance and the number of channel paths under different schemes of Embodiment 1 of the application. DETAILED DESCRIPTION

[0115] In order to make the purpose, technical scheme and advantages of the application more clear, the application is described in detail below with reference to the drawings and specific embodiments.

[0116] Embodiment 1

[0117] This embodiment proposes a double time scale transmission method (TTTs) for a RIS-aided MIMO system based on context MAB for a single-cell uplink RIS-aided millimeter wave massive MIMO system. Unlike other double time scale transmission schemes, the RIS element phase shift is designed based on MAB and does not need CSI.

[0118] In the large time scale of the TTTs scheme, this embodiment converts the RIS element phase shift design problem into the MAB problem, regards the phase shift as an action, regards the channel energy as a reward, and obtains the phase shift by using a learning process. The reward is related to the covariance channel matrix (CCM) of the cascaded channel. In the learning process, the covariance channel matrix (CCM) is learned by using an improved orthogonal matching pursuit algorithm, and an improved greedy algorithm is used to design the phase shift with high spectrum efficiency. In addition, a manifold optimization algorithm is used to obtain the optimal phase shift.

[0119] In the small time scale of the TTTs scheme, a combination is designed according to the effective uplink channel matrix to reduce the interference and improve the spectrum efficiency. The simulation results also verify the good performance of the scheme.

[0120] A double-time-scale transmission method for a RIS-assisted MIMO system, comprising the following steps:

[0121] Step one, construct a single-cell uplink RIS (intelligent reflecting surface) assisted millimeter wave massive MIMO system model, and plan the overall idea of the scheme.

[0122] Step two, the RIS element phase shift vector θ t Convert the design problem into a multi-armed bandit problem, find the phase shift vector θ t The closely related correlation matrix R;

[0123] Step three, based on the improved orthogonal matching pursuit algorithm, use the information of all time slots before the current time slot to calculate the hour slot matrix H(t) of the current time slot Finally, the correlation matrix R of the entire time period is obtained;

[0124] Step four, according to the calculated correlation matrix R, use the CMAB-based phase shift algorithm to solve the phase shift vector Θ t ;

[0125] Step five, according to the calculated phase shift vector Θ t Calculate the effective uplink matrix And the combination matrix Further solve the base station received signal y(t) = w(t)G(t)diag(θ(t))h(t)s(t), Indicates the channel energy, The transformed effective uplink matrix, Indicates the transpose conjugate matrix of matrix , diag(θ(t)) indicates the diagonal matrix of the phase shift matrix θ(t), and G(t) is the channel vector from the intelligent reflecting surface RIS to the base station BS.

[0126] In step one, a single-cell uplink intelligent reflecting surface RIS assisted millimeter wave massive MIMO system is constructed, which includes a base station BS, the base station BS communicates with a single antenna user through an RIS with N cell units, and the base station BS and the intelligent reflecting surface RIS are respectively equipped with M=M x ×M y And N=N x ×N y Element uniform planar antenna (UPA) array, M x , M y Respectively represent the number of elements of the uniform antenna array on the horizontal and vertical directions of the base station side; N x , N y Respectively represent the number of elements of the uniform antenna array on the horizontal and vertical directions of the RIS side;

[0127] Let G(t) and h(t) represent the channel vector from the intelligent reflector RIS to the base station BS and the channel vector from the user to the RIS, respectively, in the t-th time slot; a geometric millimeter-wave channel model is used to describe the channel characteristics, y = [y1, y2, ..., y K ] T Indicates the received signal;

[0128] The channel vector G(t) from the intelligent reflector RIS to the base station BS is expressed as:

[0129]

[0130] Where L is the number of paths; It is the path gain of the l-th path; a M (·) and a N (·) are the steering vectors of RIS and BS, respectively; These represent the horizontal and vertical departure angles of the l-th path on the RIS side, respectively. These represent the horizontal and vertical angles of arrival for the l-th path on the base station side, respectively. This represents a complex Gaussian distribution with a mean of 0, statistically independent real and imaginary parts, and variances of 1 / 2.

[0131] Similarly, the channel vector h(t) from the user to the RIS is expressed as:

[0132]

[0133] Where P is the number of paths. It is the path gain of the p-th node. These represent the horizontal and vertical arrival angles of the p-th path on the RIS side, respectively.

[0134] θ t Let θ represent the phase shift vector of RIS in the t-th time slot, where the n-th element θ n,t The modulus satisfies |θ n,t |=1, let s(t) be the symbol transmitted by the user, and let w(t) be the combination matrix of the base station in the t-th time slot. Assuming that the direct channel between the base station and the user is blocked, the signal received by the base station in time slot t is:

[0135] y(t)=w(t)G(t)diag(θ(t))h(t)s(t)+n(t) (3)

[0136] Where n(t) is the Gaussian noise in the t-th time slot.

[0137] Assume that the statistical channel state information (CSI) remains constant over T coherent time blocks, and the instantaneous CSI remains constant over one coherent time, each coherent time including Tc slots, the phase shift of the RIS changes once in each slot, the structure is as shown in Figure 1

[0138] When the phase shift vector θ t is obtained, the combining matrix is designed in a small time scale (in each slot), as shown in equation (6), the user sends a pilot signal s = 1, and the signal received by the base station in the tth slot is:

[0139]

[0140] where the effective uplink channel matrix becomes n(t) is noise, the elements of which are mean and unit variance zero Gaussian variables, considering equation (4), the effective uplink channel matrix can be estimated by the least square criterion, and the effective uplink channel matrix can be transformed as:

[0141]

[0142] The combining matrix w(t) is expressed as equation (6):

[0143]

[0144] where, represents the channel energy, represents the transpose conjugate matrix of the matrix .

[0145] In step two, the RIS element phase shift vector θ t is designed, and the correlation matrix R closely related to the phase shift vector θ t is found out, the specific content is as follows:

[0146] Firstly, according to the Shannon formula and equation (4), it can be known that the spectral efficiency (ESE) is affected by the channel energy. Therefore, when designing the tth slot phase shift vector θ t , it is necessary to maximize the channel energy to improve the spectral efficiency, which can be expressed as the problem as shown in the following equation:

[0147]

[0148] θ t represents the phase shift vector of the RIS in the tth slot, where the nth element is θ n,t .

[0149] When using the traditional algorithm to solve the problem​ The CSI is needed to solve the problem in the system, and a large amount of pilot overhead is consumed.

[0150] Therefore, in order to reduce the overhead of the system, the problem is converted into a multi-armed bandit problem, and the problem is solved in detail The process is as follows:

[0151] The phase shift is regarded as an action, and the channel energy is regarded as a reward, and the expression is as follows:

[0152]

[0153] Wherein, r(θ t ) represents the reward under the phase shift θ t , and E(·) represents the energy;

[0154] Let be the concatenated channel, and formula (9) can be simplified as:

[0155]

[0156] Wherein, the correlation matrix diag(h(t)) represents the diagonal matrix of the effective uplink channel matrix, is the concatenated channel;

[0157] According to formula (10), the correlation matrix R is very important for selecting the action phase shift vector θ t , and the correlation matrix needs to be calculated to obtain the phase shift vector θ t .

[0158] In step three, the improved orthogonal matching pursuit algorithm is used to calculate the sub-slot matrix of the current time slot by using the information of all time slots before the current time slot , and the sub-slot matrix is used to select the combined arm of the current time slot, and the specific content is as follows:

[0159] In the tth time slot, the signal received by the base station is:

[0160]

[0161] The concatenated channel remains unchanged within a coherence time, and t c,1 and t c,2 represent the starting time slot and the ending time slot in the cth coherence time.

[0162] Assuming that the current time slot is located in the cth coherence time, considering all previous time slots, formula (11) can be transformed as:

[0163]

[0164] in and These are the received signal and the executed phase shift vector during the Cth coherent time interval, respectively. This represents the cascaded channel in the c-th coherent time. To represent the noise in the c-th coherent time, we can obtain...

[0165]

[0166] Among them ∧ n yes diagonal matrix It is a random variable with a mean of zero. It is the noise matrix during the Cth coherent time interval. Denotes the transpose conjugate matrix. This represents the concatenated channel matrix of the k-th time slot in the c-th coherent time;

[0167] The problem of calculating matrix R according to equation (13) is expressed as follows:

[0168]

[0169] in, ‖·‖ F Denotes the F-norm;

[0170] make Then there is

[0171]

[0172] Where ° represents the KR product matrix operation, and ⊙ represents the Hadamard matrix operation;

[0173] Let the variable matrix be R. G =E(G H (t)G(t)) and variable matrix R h =E(h) * (t)h T (t)), then we have

[0174] R = E(G) H (t)G(t))⊙E(h * (t)h T (t))=R G ⊙R h (16)

[0175] Therefore, the problem of calculating matrix R can be transformed into calculating the variable matrix R. G Variable matrix R h Make an estimate.

[0176] D BS and D RIS Let the Discrete Fourier Transform (DFT) vectors on the BS side and RIS side be represented respectively, and we can obtain... h k (t)=D RIS λ h(t) , among which ∧ G(t) ,λ h(t) G(t) and h are respectively k The angular domain representation of (t) can be obtained from the previously constructed channel model. G(t) and corner domain It is sparse, and an alternating iterative optimization algorithm is used to estimate the variable matrix R. G And variable matrix R h The process is as follows:

[0177] Given a variable matrix R G After initializing the values, estimate the variable matrix R. h This is equivalent to solving the variable matrix R. h Effective uplink channel h for each time slot k λ, the angular domain of (t) h(t) The proof is as follows:

[0178]

[0179] make

[0180] Define intermediate variables

[0181] The Kronecker product operation is represented by vec(·), which is a vectorized operator. h Let m be a diagonal matrix. c For the signal at the c-th coherent time, M c For the signal matrix at the c-th coherent time, then the intermediate variables... The computational problem can be expressed as:

[0182]

[0183] Let A = [A1; A2; ...; A c ], m = [m1; m2; ...; m c ], then the problem This can be transformed into a problem.

[0184]

[0185] Regarding the question Solving for intermediate variables using the OMP algorithm Due to the diagonal matrix It is a Hermitian matrix, from which intermediate variables are obtained. The diagonal matrix can then be calculated using the following formula.

[0186]

[0187] Where unvec(·) is the matrix transformation operator. This indicates that intermediate variables Matrixing, This indicates that intermediate variables After matrixing, the transformed result is then converted into a transpose conjugate matrix.

[0188] At the same time, a diagonal matrix is ​​obtained. Then, using Solving the transformation matrix II approximation, and Let represent the Discrete Fourier Transform (DFT) vector on the RIS side and the transpose of the Discrete Fourier Transform (DFT) vector on the RIS side, respectively. Similarly, given a matrix transformation matrix 2... The initial values ​​are obtained by solving the transformation matrix II according to equations (17) to (20) above. Solving the transformation matrix in one way Then, iteratively calculate the change matrix for different time slots. And the change matrix two Until convergence, the small phase shift matrix is ​​finally obtained. Finally, obtain the correlation matrix R for the entire time period.

[0189] In step four, based on the calculated correlation matrix R, the phase shift vector Θ for all time slots is solved using a CMAB-based phase shift algorithm. t ;include:

[0190] The improved ∈-greedy algorithm uses 1-e -ηt The probability of choosing the arm that maximizes spectral efficiency is given by e. -ηt The probability of selecting random phase shifts is denoted by η, where η is a constant. Furthermore, when randomly selecting phase shifts, m random phase shifts are chosen, defined as a set S. t The improvement lies in that, when randomly selecting a phase shift, a phase shift vector with a probability ∈ is selected that is close to the principal eigenvector, so that the random selection action can bring higher spectral efficiency.

[0191] Therefore, the phase shift vector of the t-th time slot is expressed as:

[0192]

[0193] Where k is a random variable uniformly distributed in [0, 1], and ε and η are two constants; η represents the probability of choosing the optimal phase shift; the larger η is, the more actions are chosen to explore; ε represents the probability of choosing the optimal phase shift in set S. t The probability of selecting a phase shift with high spectral efficiency; random(S) t ) represents a randomly selected set S t One of the elements; f sub In set S t By selecting a random variable whose subspace corresponds to the principal eigenvalues, higher spectral efficiency can be achieved. opt It is a phase shift that maximizes the received energy.

[0194] Define λ i In the i-th time slot, f represents sub (S t The largest eigenvalue corresponding to ) is selected, and the eigenvalue is greater than ) The eigenvalues, ρ is a constant, U R The correlation matrix R is represented by the combination matrix consisting of the eigenvectors corresponding to the eigenvalues ​​of the correlation matrix R; the chord distance represents the distance between the phase shift vector and the correlation matrix R, defined as follows:

[0195]

[0196] Where u θ It is the eigenvector of θ, that is f sub (S t ) is the problem The solution,

[0197]

[0198] Regarding the question First calculate set S t The problem involves determining the chord distance for each phase shift, and then selecting the phase shift vector with the smallest chord distance as the solution. The solution can achieve high spectral efficiency.

[0199] random(S t ) represents a randomly selected set S t One of the elements, θ represents the phase shift, θ opt The problem is the phase shift that maximizes the received energy. Solution:

[0200]

[0201] Where θ represents the phase shift, and st represents the constraint, i.e., the limiting condition.

[0202] Regarding the question Solving using complex circle manifold optimization algorithm In detail:

[0203] 1) The unit modulus constraint forms a product of M complex circle manifolds, denoted as The complex circle manifold is an embedded submanifold of , where the unit modulus constraint |θ i | = 1 represents the complex circle manifold;

[0204] 2) The manifold optimization algorithm is iterative, i.e., given a point at the kth iteration, the tangent space at point θ k is defined as where denotes the real part operation, ° denotes the Hadamard product operation, and {·} * denotes the conjugate operation;

[0205] 3) At the current point θ (k) on the manifold , a descent direction is chosen to ensure that the search direction always lies on the manifold and conforms to the geometry of the manifold;

[0206] 4) The search direction d k is defined using the Riemannian Conjugate Gradient (RCG) method as follows:

[0207]

[0208] where β k is the Polak-Ribiere parameter, and gradf(θ (k) ) is the Riemannian gradient of the function f at point θ (k) on the manifold , which is calculated as:

[0209]

[0210] where is the vector transport operation, which is calculated as

[0211]

[0212] Finally, after selecting the descent direction d k , a retraction operation is used to find the next iteration point θ (k+1) on the manifold .

[0213] In step four, the phase shift design algorithm based on the Riemannian Conjugate Gradient method is used to solve the problem The steps are as follows, where ∈1 is the convergence threshold:

[0214] Step1: Input the calculated vector matrix and set the initial point coordinate θ0=1 on the complex torus and k=0;

[0215] Step2: Calculate the Riemannian gradient gradf(θ (k) ) according to formula (27);

[0216] Step3: Calculate the Riemannian conjugate direction d k according to formula (26);

[0217] Step4: Select the step size α k according to the Armijo backtracking line search rule;

[0218] Step5: Update the point θ according to formula (28) by k←k+1;

[0219] Step6: Calculate the modulus of the gradient ||gradf(θ (k) )||2, if ||gradf(θ (k) )||2>∈1, repeat Step2-Step 6; until ||gradf(x k )||2≤∈1;

[0220] Step7: Output the phase shift θ opt that maximizes the received energy.

[0221] In step four, the CMAB-based phase shift algorithm obtains the phase shift vector Θ t The steps are as follows, where ∈2 is the convergence threshold:

[0222] Step1: Let the initial signal y l =1, the initial position θ l =1, l=1,2,…,t, initialize the change matrix one of the initial time slot the change matrix two of the initial time slot the initial iteration number k=1; I represents the unit matrix whose elements are all 1;

[0223] Step2: Calculate the signal matrix M c of the cth coherence time and the phase shift vector Θ c of the cth coherence time according to formulas and ;

[0224] Step3: Given the change matrix one of the kth time slot the initial value, convert it into the solution problem of the intermediate variable of the kth time slot according to formula (19), and solve the intermediate variable of the kth time slot by using the OMP algorithm

[0225] Step4: Solve the diagonal matrix according to formula (20) Then solve the change matrix two of the kth time slot according to formula

[0226] Step5: The same as Step4, given the change matrix two of the kth time slot Initial value, solve the change matrix one of the kth time slot

[0227] Step6: Solve the change matrix two of the k+1th time slot by k←k+1 And the change matrix one

[0228] Step7: Calculate the modulus value of gradient If Or Repeat Step3-Step 6; until Or The change matrix two of the kth time slot is recorded And the change matrix one

[0229] Step8: Calculate the output time slot matrix according to the time slot matrix calculation formula ;

[0230] Step9: Obtain the designed phase shift vector Θ according to formula (21) t And output.

[0231] Step five, according to the calculated phase shift vector Θ t Calculate the effective uplink matrix And the combination matrix w(t), further solve the base station received signal y(t), the steps are as follows:

[0232] Calculate the effective uplink matrix according to formula (29)

[0233]

[0234] Calculate the combination matrix w(t) according to formula (6);

[0235] Calculate the base station received signal y(t) according to formula (30):

[0236] y(t) = w(t)G(t)diag(θ(t))h(t)s(t) (30).

[0237] ​​In the CMAB process, the information of all previous time slots is used to calculate the matrix R, on the basis of which the phase shift is designed, and the corresponding solution scheme is given. The simulation results verify that the proposed TTTS based on CMAB can significantly reduce the overhead and improve the effective spectral efficiency (ESE).

[0238] The method in the embodiments of the application is simulated and verified in combination with specific implementation manners.

[0239] The performance of the proposed scheme is verified by simulation. A millimeter wave with a frequency of 28 GHz is selected, and its wavelength is 10.7 mm. It is calculated that 550 coherent times are contained in the set time T. A channel model is considered in which a BS and a RIS are both equipped with an 8x8 ULA array, and a single-antenna user is served. In the proposed scheme, ε is set to 0.5, ∈1 is set to 0.01, and ∈2 is set to 0.01. The proposed scheme based on CMAB is compared with the LRT-CCM scheme and the Random design scheme. In a time slot, since some symbols are used for transmitting the pilot matrix, the effective spectral efficiency (ESE) of the system in the t time slot is:

[0240]

[0241] where Ts = 100 represents the number of symbols per time slot. τ = 1 represents the number of pilot transmission symbols per time slot.

[0242] Figure 2 The ESE of the CMAB-based scheme in each time slot is shown. The signal-to-noise ratio is 30 dB. C (the number of time slots in a coherent interval) is set to 3 and 6, corresponding to speeds of 3.57 m / s and 1.78 m / s (the time length of a time slot is 0.5 ms). As the number of time slots increases, the ESE of the MAB-based scheme first increases and then converges. The ESE when C = 6 converges faster than when C = 3. This is because the larger C is, the more time slots there are in a coherent time, and the more accurate the CCM calculation is, resulting in a higher ESE.

[0243] Figure 3 The ESE of different schemes under different signal-to-noise ratios is shown. We consider two cases, one of which is P = L = 2 (the number of channel paths), and the other of which is P = L = 4. C is set to 3, corresponding to a speed of about 3.57 m / s. Compared with the LRT-CCM and random schemes, the CMAB-based scheme achieves a higher ESE. The random scheme randomly designs the phase shift, resulting in the lowest spectral efficiency. The LRT-CCM scheme spends many time slots to calculate the CCM, and the phase shift in these time slots is unrelated to the channel, so the spectral efficiency is lower than the proposed scheme. It can also be seen that the ESE of each scheme when P = L = 2 is less than that when P = L = 4.

[0244] Figure 4 The ESE of different schemes under different path numbers is shown. When the SNR is 30 dB, the ESE of the CMAB-based scheme is higher than that of other schemes. The ESE of the CMAB-based scheme increases with the increase of SNR. This is because the channel energy increases with the increase of the path number.

[0245] A computer device / system, comprising a memory, a processor and a computer program stored on the memory, the processor executing the computer program to implement the steps of the above method.

[0246] A computer readable storage medium, having stored thereon a computer program / instruction, which, when executed by a processor, implements the steps of the above method.

[0247] A computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the above method.

[0248] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) containing computer usable program code.

[0249] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as combinations of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in a flow or multiple flows and / or blocks Figure 1 The functions specified in a flow or multiple flows and / or blocks

[0250] These computer program instructions can also be stored in a computer readable memory that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer readable memory produce a manufactured product including instruction devices that implement the functions specified in the flowcharts and / or block diagrams. Figure 1 The functions specified in a flow or multiple flows and / or blocks Figure 1the function specified in the one or more blocks.

[0251] These computer program instructions can also be loaded into computer or other programmable data processing devices, so that a series of operational steps are performed on the computer or other programmable data processing devices to generate computer-implemented processes, so that the instructions executed on the computer or other programmable data processing devices provide processes for implementing the flows Figure 1 the flow or flows and / or blocks Figure 1 the steps of the function specified in the one or more blocks.

[0252] The above description is only the preferred embodiment of the present application, it should be pointed out that for those skilled in the art, without departing from the technical principles of the present application, a number of improvements and modifications can be made, these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A dual-timescale transmission method for a RIS-assisted MIMO system, characterized in that, Includes the following steps: Step 1: Construct a single-cell uplink RIS-assisted millimeter-wave massive MIMO system model; Step 2: Shift the RIS phase vector The design problem is transformed into a multi-armed gambling machine problem, and the relationship between the phase shift vectors of each time slot is determined. Related correlation matrix ; Step 3: Based on the improved orthogonal matching pursuit algorithm, calculate the small slot matrix of the current time slot using information from all time slots preceding the current time slot. Finally, the phase shift vector of the time slot for the entire time period is obtained. Related correlation matrix ; Step 4: Based on the calculated correlation matrix The phase shift vector of all time slots is solved using a CMAB-based phase shift algorithm. ; Step 5: Based on the calculated phase shift vector Calculate the effective uplink matrix and combination matrix Further solve the base station received signal , Indicates channel energy. The effective uplink matrix of the transformation, Representation matrix The transpose conjugate matrix, Represents the phase shift matrix diagonal matrix, Let be the channel vector from RIS to base station BS. This represents the channel vector from the user to the RIS. Symbols transmitted to the user It is the first Gaussian noise in each time slot; In step two, the phase shift vector of the design time slot is... At that time, the channel energy Maximize, expressed as a problem As shown in the following formula: （7）； （8）； Indicates the number of time slots. This indicates the number of elements in the uniform antenna array on the base station side; Indicates the first The phase shift vector of RIS in the nth time slot, where the nth time slot is... element The modulus satisfies | |=1; The problem The problem can be transformed into a multi-armed gambling machine problem for solution. The solution process is as follows: Treating phase shift as an action, channel energy As a reward, the expression is as follows: （9）； in, Represents the phase shift vector The reward below, Indicates energy; make For cascaded channels, equation (9) simplifies to: （10）； Among them, the correlation matrix , This represents the diagonal matrix of the effective uplink channel matrix. This indicates the number of elements in the RIS-side uniform antenna array.

2. The dual-timescale transmission method for a RIS-assisted MIMO system according to claim 1, characterized in that, In step one, the single-cell uplink RIS-assisted millimeter-wave massive MIMO system includes a base station (BS). The base station BS communicates with a single-antenna user through an RIS with 𝑁 cellular units. The base station BS and the RIS are respectively equipped with and Uniform planar antenna array of components , These represent the number of elements in the horizontal and vertical directions of the uniform antenna array on the base station side, respectively. , These represent the number of elements in the horizontal and vertical directions of the uniform antenna array on the RIS side, respectively; make Let represent the channel vector from RIS to base station BS within the t-th time slot; a geometric millimeter-wave channel model is used to describe the channel characteristics. Indicates the received signal; Indicates the number of channels; Channel vector from RIS to base station BS Represented as: （1）； in, It is the number of paths; It is the first Path gain of a path; and These are the guidance vectors for RIS and BS, respectively; Representing the RIS side, respectively The horizontal and vertical starting angles of the path; These represent the base station side's first... The horizontal and vertical angles of arrival for the path; Channel vector from user to RIS Represented as: （2）； in, It is the number of paths. It is the first Path gain, Representing the RIS side, respectively The horizontal and vertical angles of arrival of the path; set up The symbols transmitted by the base station in the first... The combination matrix in each time slot is Assuming the direct channel between the base station and the user is blocked, then in the time slot The signal received by the base station is: ； in, It is the first Gaussian noise in each time slot; When the phase shift vector is obtained Then, a combination matrix is ​​designed in each time slot, as shown in equation (6). The user sends a pilot signal s=1, and the base station sends a pilot signal s=1 in the first time slot. The signal received in each time slot is: （4）； The effective uplink channel matrix becomes It's noise; The effective uplink channel matrix is ​​transformed as follows: （5）； Combination matrix Expressed as formula (6): （6）； in, Indicates channel energy. Representation matrix The transpose conjugate matrix.

3. The dual-timescale transmission method for a RIS-assisted MIMO system according to claim 1, characterized in that, In step three, at the In each time slot, the base station receives the following signals: （11）； and Let c represent the start and end timeslots in the c-th coherent time. Assuming the current timeslot is within the c-th coherent time, equation (11) transforms into: （12）； in and These are the received signal and the executed phase shift vector during the c-th coherent time interval, respectively. This represents the cascaded channel in the c-th coherent time. To represent the noise in the c-th coherent time, we can obtain... , (13); in yes diagonal matrix It is a random variable with a mean of zero. It is the noise matrix during the c-th coherent time interval. Denotes the transpose conjugate matrix. This represents the concatenated channel matrix of the k-th time slot in the c-th coherent time; According to the correlation matrix of equation (13) The calculation is expressed as a problem : （14）； in, , Denotes the F-norm; make Then there is 15）； in, yes Matrix multiplication operations This is a Hadamard matrix operation; let the variable matrix be one. Variable Matrix II Then there is （16）。 4. The dual-timescale transmission method for a RIS-assisted MIMO system according to claim 3, characterized in that, In step four, the improved Greedy algorithm The probability of choosing the arm that maximizes spectral efficiency, while with The probability of choosing a random phase shift, where, It is a constant, and when randomly selecting a phase shift, the selection... A random phase shift is defined as a set. ; Represented by the correlation matrix The combination matrix consisting of the eigenvectors corresponding to the eigenvalues; the phase shift vector and correlation matrix are represented by the chord distance. The distance between them is defined as （22）； in It is a phase shift The eigenvectors, i.e. , It's a problem The solution, （23）； Regarding the question First calculate the set The chord distance for each phase shift is calculated, and then the phase shift vector with the smallest chord distance is selected as the problem. ; Represents a set of random selections One of the elements, The problem is the phase shift that maximizes the received energy. Solution: （24）； （25）； in, Indicates phase shift, This indicates that something is subject to, or is subject to, restrictions.

5. A dual-timescale transmission method for a RIS-assisted MIMO system according to claim 4, characterized in that, In step four, the phase-shift design algorithm based on the Riemann conjugate gradient method is used to solve the problem. The steps are as follows, where It is the convergence threshold: Step 1: Input the calculated vector matrix Set the coordinates of the starting point on the complex circular manifold. , ; Step 2: Calculate the Riemann gradient according to equation (27) ; Step 3: Calculate the Riemann conjugate direction according to equation (26) ; Step 4: Select the step size according to Armijo's backtracking search rules. ; Step 5: From Update the points according to equation (28) ; Step 6: Calculate the gradient The modulus, if Repeat Steps 2-6 until the condition is met. ; Step 7: Output a phase shift that maximizes the received energy. ; （26）； in, For Polak-Ribiere parameters, Is the function 𝑓 on the manifold superior The Riemann gradient of the point has the following value: （27）； in, , It is a vector transfer operation, and the calculation formula is: （28）。 6. The dual-timescale transmission method for a RIS-assisted MIMO system according to claim 5, characterized in that, In step 4, the phase shift vector is obtained using the CMAB-based phase shift algorithm. The steps are as follows, where It is the convergence threshold: Step 1: Set the start signal Starting position Initialize the start time slot one The starting time slot two Number of initial time slot iterations ; Represents the identity matrix where all elements are 1; Indicates the first One time slot; Step 2: According to the formula and Calculate the signal matrix at the c-th coherent time. The phase shift vector at the c-th coherent time ;in, and These are the received signal and the executed phase shift vector during the c-th coherent time interval, respectively. and This represents the start and end time slots in the c-th coherent time period. This represents the signal received by the channel at the start of the c-th coherent time. This represents the signal received by the concatenated channel at the end of the c-th coherent time. This represents the phase shift of the concatenated channel at the start of the c-th coherent time. This represents the phase shift of the concatenated channel at the end of the c-th coherent time. Step 3: and Let the discrete Fourier transform vectors on the BS side and RIS side be respectively, and we can obtain , ,in They are and The angular domain representation, When given a variable matrix After initializing the values, estimate the variable matrix two. This is equivalent to solving the variable matrix two. Effective uplink channel for each time slot corner domain The proof is as follows: ； ； ； （17）； make , Define intermediate variables , ; This represents the Kronecker product operation. For vectorization operators, It is a diagonal matrix. For the signal at the c-th coherent time, For the signal matrix at the c-th coherent time, then the intermediate variables... The computational problem can be expressed as: （18）； make , Then the problem Transform into a problem : （19）； Regarding the question The OMP algorithm is used to solve for intermediate variables. To obtain intermediate variables Then, the diagonal matrix is ​​calculated using the following formula. : （20）； in, For matrix-based operators, This indicates that intermediate variables Matrixing, This indicates that intermediate variables After matrixing, the transformed result is then converted into a transpose conjugate matrix; Given the change matrix of the k-th time slot The initial value is transformed into an intermediate variable in the k-th time slot according to equation (19). The problem is solved, and the intermediate variables in the k-th time slot are solved using the OMP algorithm. ; Step 4: Solve the diagonal matrix according to equation (20). Then according to the formula Solving for the k-th time slot two ; Step 5: Given the k-th time slot two The initial value is determined according to the above formula (17). Equation (20) solves for the transformation matrix II way ; Step 6: From Solve for the (k+1)th time slot. two With the change matrix 1 ; Step 7: Calculate the gradients respectively , The modulus, if or Repeat Steps 3 through 6 until the condition is met. or Up to; record the k-th time slot two With the change matrix 1 ; Step 8: Calculate the hourly slot matrix using the formula. Calculate the output hour slot matrix ; Step 9: Obtain the designed phase shift vector according to equation (21) and output; The phase shift vector of the nth time slot is expressed as: （21）； in, It is a random variable uniformly distributed in [0, 1]. This represents the probability of selecting the optimal phase shift; Indicates in set The probability of selecting a phase shift with high spectral efficiency; Represents a set of random selections One of the elements; Indicates in set Choose a random variable whose subspace corresponds to the principal eigenvalues. It is a phase shift that maximizes the received energy.

7. A dual-timescale transmission method for a RIS-assisted MIMO system according to claim 6, characterized in that, In step five, based on the calculated phase shift vector... Calculate the effective uplink matrix and combination matrix Further solve the base station received signal The steps are as follows: Calculate the effective uplink matrix according to equation (29). : (29)； Calculate the combination matrix according to equation (6). ; （6）； in, Indicates channel energy. Representation matrix The transpose conjugate matrix; Calculate the base station received signal according to equation (30) : (30)。 8. A computer system comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-7.

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