A hybrid beamforming method, system and storage medium based on storage optimization

Abstract

The application discloses a kind of based on storage optimization's hybrid beam forming method, system and storage medium, its method includes steps: according to the number of radio frequency link, antenna quantity and channel state calculation transmitting end hybrid precoding matrix constraint condition;According to constraint condition, the objective function of transmitting end hybrid precoding matrix optimization is established;According to the relationship of time delay and / or spectral efficiency and / or memory occupancy and quasi-newton method storage capacity calculation optimal storage capacity;According to the optimal storage capacity corresponding finite memory quasi-newton method, the optimal solution of transmitting end hybrid precoding matrix optimization objective function is calculated;According to the optimal solution of transmitting end hybrid precoding matrix optimization objective function, transmitting end hybrid precoding matrix is obtained and is used for hybrid beam forming.The application solves the problem that the system performance of existing hybrid beam forming method is poor and the calculation time delay is high.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a hybrid beamforming method, system and storage medium based on storage optimization. Background Art

[0002] Beamforming technology generates directional beams by controlling the relative phase and amplitude between different array elements. This technology leverages large-scale input and output technologies and millimeter wave technology. Digital beamforming uses radio frequency (RF) links to change the phase and amplitude of array elements. Each antenna is equipped with a separate RF link. RF links can better calibrate amplitude and phase, but they are expensive. A large number of antennas requires a large number of RF links, which increases cost and power consumption. Analog beamforming uses phase shifters (PS) to change the phase of array elements. Phase shifters are less expensive, but they only adjust the signal phase and have poor performance.

[0003] To address the above issues, a hybrid beamforming technology combining digital and analog beamforming is proposed. In hybrid beamforming, only a small number of RF links are required, each of which can be connected to multiple phase shifters, which are then connected to antennas. A small number of RF links are used for digital domain processing to provide spatial multiplexing gain and handle multi-user interference. The spatial degrees of freedom provided by the number of RF links only need to ensure the independent transmission of data streams. A large number of phase shifters are used for high-dimensional analog domain processing to provide spatial diversity gain. Therefore, hybrid beamforming technology can effectively improve the system's spectral efficiency while reducing system hardware cost and energy consumption. However, the system performance achieved by existing hybrid beamforming methods, namely spectrum rate and bit error rate, is significantly lower than that of pure digital beamforming systems. Furthermore, the computational complexity of calculating the hybrid code is high, resulting in high computational latency.

[0004] In order to solve the problems of poor system performance and high computational delay in existing hybrid beamforming methods, a hybrid beamforming method, system and storage medium based on storage optimization are proposed. Summary of the Invention

[0005] The embodiments of the present invention provide a hybrid beamforming method, system, and storage medium based on storage optimization to at least solve the problems of poor system performance and high computational latency in related technologies.

[0006] According to one embodiment of the present invention, a hybrid beamforming method based on storage optimization is provided, comprising:

[0007] Calculate the constraints of the hybrid precoding matrix at the transmitter based on the number of RF chains, the number of antennas, and the channel state;

[0008] Establishing the objective function of the hybrid precoding matrix optimization at the transmitting end according to the constraint conditions;

[0009] Calculating an optimal storage amount based on a relationship between delay and / or spectrum efficiency and / or memory occupancy and a storage capacity of the quasi-Newton method;

[0010] Calculate the optimal solution of the transmit end hybrid precoding matrix optimization objective function using the limited memory quasi-Newton method corresponding to the optimal storage capacity;

[0011] The hybrid precoding matrix at the transmitting end is obtained according to the optimal solution of the optimization objective function of the hybrid precoding matrix at the transmitting end, and hybrid beamforming is performed based on it.

[0012] In an exemplary embodiment, the calculation of the constraints of the transmitting end hybrid precoding matrix according to the number of radio frequency chains, the number of antennas and the channel state includes the steps of:

[0013] The number of RF links at the transmitter is recorded as The number of antennas is N t ;

[0014] The original data stream is represented by s and its dimension is N s ×1, after The digital precoding matrix V B , then through The simulated precoding matrix V RF , get N t ×1 transmission signal x=V RF V B s, the normalized constraint at the transmitter is

[0015] The power constraint condition of the transmitter is calculated based on the Frobenius norm: where Q s is the preset transmitter power constraint constant;

[0016] The constant modulus constraint of the hybrid precoding matrix is ​​expressed as V RF ∈V, where V is the feasible set of analog precoders with constant modulus constraints.

[0017] In an exemplary embodiment, establishing an objective function for optimizing a transmitting end hybrid precoding matrix according to the constraint conditions comprises the steps of:

[0018] Get the optimal digital precoding matrix for digital beamforming, denoted as V opt ;

[0019] The first objective function is constructed based on the Euclidean distance between the optimal digital precoding matrix and the hybrid precoding matrix:

[0020] Take the partial derivative of the first objective function to obtain the least squares solution in It is V RF Moore-Penrose pseudoinverse;

[0021] According to the least squares solution The objective function based on the simulated precoding matrix is ​​constructed using the Frobenius norm: stV RF ∈v.

[0022] In an exemplary embodiment, the step of calculating the optimal storage capacity based on the relationship between the time delay and / or the spectrum efficiency and / or the memory occupancy and the storage capacity of the quasi-Newton method comprises the following steps:

[0023] The functional relationship between latency and storage capacity is calculated based on the relationship between the computational complexity and storage capacity of the finite memory quasi-Newton method;

[0024] The functional relationship between spectral efficiency and storage capacity is calculated based on the spectral efficiency of the finite memory quasi-Newton method with different storage capacities;

[0025] The functional relationship between memory occupancy and storage capacity is calculated based on the finite memory quasi-Newton method for different storage capacities;

[0026] Constructing a storage optimization model based on a functional relationship between latency and storage capacity, and / or a functional relationship between spectrum efficiency and storage capacity, and / or a functional relationship between memory occupancy and storage capacity;

[0027] The storage capacity corresponding to the maximum value of the storage capacity optimization model is the calculated optimal storage capacity.

[0028] In an exemplary embodiment, the method of calculating the functional relationship between the delay and the storage amount based on the relationship between the computational complexity and the storage amount of the finite memory quasi-Newton method comprises the steps of:

[0029] Computing the inherent computational complexity of the limited memory quasi-Newton method; the inherent computational complexity includes the computational complexity of Euclidean gradient, orthogonal projection, retraction, and line search;

[0030] Compute the approximate complexity of the Hessian matrix inverse based on the relationship between storage and updating the Hessian matrix in the limited memory quasi-Newton method;

[0031] The functional relationship between computational complexity and storage capacity is obtained based on the inherent computational complexity of the finite memory quasi-Newton method and the approximate complexity of updating the inverse of the Hessian matrix.

[0032] According to the positive correlation between the computational complexity and delay of the finite memory quasi-Newton method, the functional relationship between delay and storage capacity is calculated.

[0033] In an exemplary embodiment, calculating the optimal solution of the transmit end hybrid precoding matrix optimization objective function according to the limited memory quasi-Newton method corresponding to the optimal storage capacity includes:

[0034] Construct a Riemannian complex circular manifold and initialize the parameters;

[0035] Calculate the cost function and Riemann gradient of the initial point;

[0036] Determine whether a stopping condition is met, and if so, calculate the optimal solution of the transmit end hybrid precoding matrix optimization objective function; otherwise, proceed to the next step; the stopping condition is that the norm of the gradient reaches a preset value;

[0037] The search direction is calculated based on the approximation of the Riemann gradient and the inverse of the Hessian matrix;

[0038] A line search based on the Armijo criterion is used to search in the tangent space and then retract to the manifold to obtain a new solution;

[0039] Calculate the cost function and Riemann gradient of the new solution;

[0040] Determine whether the vector pair meets the storage condition. If so, update the initial value of the Hessian matrix and proceed to the next step; otherwise, do not update the initial value of the Hessian matrix and return to determine whether the stop condition is met;

[0041] Determine whether the current storage capacity is greater than the optimal storage capacity. If so, discard the earliest stored vector, otherwise proceed to the next step;

[0042] Perform vector transfer on all vector pairs in the memory, store the current vector pair, increase the current storage by 1, and then return to determine whether the stop condition is met.

[0043] In an exemplary embodiment, obtaining a transmit hybrid precoding matrix based on an optimal solution of an optimization objective function of the transmit hybrid precoding matrix and performing hybrid beamforming based on the matrix includes the following steps:

[0044] According to the optimal solution of the transmit hybrid precoding matrix optimization objective function, the simulated precoding matrix V is obtained RF ;

[0045] According to the optimal digital precoding matrix V opt and simulated precoding matrix V RF Calculate the digital precoding matrix V B ;

[0046] The signal passes through the digital precoding matrix V B After adjusting the amplitude and phase, it is transmitted through multiple radio frequency links;

[0047] According to the simulated precoding matrix V RFBuild phase shifters and connect to RF links;

[0048] The RF link signal passes through the phase shifter and then forms a hybrid beam through the antenna.

[0049] In an exemplary embodiment, the hybrid beamforming transmission signal is transmitted through the channel H and then received by the receiving antenna, and N is obtained. t ×1 received signal y=HV RF V B s+n, where n is the additive white Gaussian noise vector; at the receiving end, The analog combiner W RF Perform analog domain processing and then After transmission through the RF link Digital combiner W B Perform digital domain processing and finally get N s ×1 signal The analog combiner W RF and digital combiner W B The calculation method of the simulated precoding matrix V according to claim 7 RF and the digital precoding matrix V B The calculation method is the same.

[0050] According to yet another embodiment of the present invention, a computer-readable storage medium is provided, which stores a computer program for electronic data exchange, wherein the computer program enables a computer to execute the above method.

[0051] According to yet another embodiment of the present invention, a hybrid beamforming system based on storage optimization is provided, including:

[0052] processor;

[0053] Memory;

[0054] as well as

[0055] One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the processor, the programs causing the computer to perform the above method.

[0056] The hybrid beamforming method, system, and storage medium based on storage optimization of the present invention have the following advantages:

[0057] (1) The least squares solution of the variables is adopted in the objective function of the hybrid precoding matrix optimization, which reduces the number of variables in the solution from two to one. Compared with the traditional hybrid precoding matrix optimization objective function, it can effectively reduce the search space, the number of calls to the objective function and the number of external iterations, and the calculation delay.

[0058] (2) The present invention uses delay and / or spectrum efficiency and / or memory occupancy to calculate the optimal storage capacity and solves the objective function based on the limited memory quasi-Newton method of the optimal storage capacity. Compared with the traditional limited memory quasi-Newton method with preset storage capacity, the present invention can achieve the optimization among spectrum efficiency, delay and storage capacity according to different requirements, thereby improving the overall performance of the system.

[0059] (3) The present invention adopts a limited memory quasi-Newton method, which only requires the use of multiple first-order derivative information when constructing the search direction. Compared with the traditional quasi-Newton method or gradient descent method, it can effectively reduce the calculation amount and storage amount of the Hessian matrix, thereby reducing the calculation delay and memory usage.

[0060] (4) The objective function solving method adopted by the present invention has a faster search direction and a faster search speed than the traditional conjugate gradient method, which can find the solution faster and effectively reduce the calculation delay while maintaining the advantages of superlinear convergence, improving spectrum efficiency and reducing bit error rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 1 is a basic architecture diagram of a hybrid beamforming system according to an embodiment of the present invention;

[0062] Figure 2 is a flow chart of a hybrid beamforming method based on storage optimization according to an embodiment of the present invention;

[0063] Figure 3 is a method flow chart of step S01 of an embodiment of the present invention;

[0064] Figure 4 is a flowchart of step S02 of an embodiment of the present invention;

[0065] Figure 5 is a method flow chart of step S03 of an embodiment of the present invention;

[0066] Figure 6 is a method flow chart of sub-step S031 of an embodiment of the present invention;

[0067] Figure 7 is a flowchart of step S04 of an embodiment of the present invention;

[0068] Figure 8 is a method flow chart of step S05 of an embodiment of the present invention;

[0069] Figure 9 1 is a bit error rate and signal-to-noise ratio change curve of different hybrid beamforming algorithms according to an embodiment of the present invention;

[0070] Figure 10 1 is a curve showing the variation of different hybrid beamforming delays with signal-to-noise ratios according to an embodiment of the present invention;

[0071] Figure 11 This is a schematic diagram of the structure of a hybrid beamforming system based on storage optimization according to an embodiment of the present invention. DETAILED DESCRIPTION

[0072] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the invention, but are not intended to limit the present invention in any form. It should be noted that those skilled in the art may make several changes and modifications without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0073] In the hybrid beamforming system, the original signal is sent to the channel after being processed by digital beamforming and analog beamforming at the transmitting end. The final signal is obtained after being processed by analog beamforming and digital beamforming at the receiving end. The system architecture diagram of the hybrid beamforming is shown in the figure below. Figure 1 As shown. Among them, the digital beamforming and analog beamforming processing at the transmitting end are subject to power constraints, and the analog beamforming at both the transmitting and receiving ends must meet constant modulus constraints. The hybrid beamforming method is to calculate a more accurate digital beamforming matrix and analog beamforming matrix to approach the optimal pure digital beamforming matrix, but the existing algorithms often have high latency and poor performance. The present invention decouples the problems of the transmitting and receiving ends and solves them separately, substitutes their least squares solutions into the objective function to obtain a new objective function, and uses a limited memory quasi-Newton method with optimized storage to calculate the analog beamforming matrix, thereby reducing complexity while improving spectrum efficiency and lowering bit error rate, solving the problems of poor system performance and high latency of the hybrid beamforming algorithm. The specific steps of the hybrid beamforming method based on storage optimization proposed in the present invention are described in detail below.

[0074] A hybrid beamforming method based on storage optimization according to an embodiment of the present invention is shown in the flowchart as follows: Figure 2 As shown, the steps include:

[0075] Step S01: Calculate the constraints of the hybrid precoding matrix at the transmitting end according to the number of radio frequency links, the number of antennas, and the channel state;

[0076] Step S02: establishing an objective function for optimizing the hybrid precoding matrix at the transmitting end according to the constraint conditions;

[0077] Step S03: Calculate the optimal storage capacity based on the relationship between the time delay and / or spectrum efficiency and / or memory occupancy and the storage capacity of the quasi-Newton method;

[0078] Step S04: Calculate the optimal solution of the transmit end hybrid precoding matrix optimization objective function according to the limited memory quasi-Newton method corresponding to the optimal storage capacity;

[0079] Step S05: Obtain a transmit-end hybrid precoding matrix according to the optimal solution of the transmit-end hybrid precoding matrix optimization objective function and perform hybrid beamforming based on the matrix.

[0080] In an exemplary embodiment, the step S01 calculates the constraints of the transmitting end hybrid precoding matrix according to the number of radio frequency links, the number of antennas and the channel state, and the flow chart is as follows: Figure 3 As shown, the steps include:

[0081] Step S011: Obtain the number of radio frequency links and antennas at the transmitting end; specifically, the number of radio frequency links at the transmitting end is recorded as The number of antennas is N t

[0082] Step S012: represent the digital precoding matrix and analog precoding matrix in hybrid beamforming; specifically, in hybrid beamforming, the original data stream is represented as s, and the dimension is N s ×1, after The digital precoding matrix V B , then through The simulated precoding matrix V RF , get N t ×1 transmission signal x=V RF V B s, the normalized constraint at the transmitter is

[0083] Step S013: Calculate the power constraint of the transmitter according to the Frobenius norm; the power constraint is where Q s is the preset transmitter power constraint constant;

[0084] Step S014: Calculate the constant modulus constraint of the hybrid precoding matrix; the constant modulus constraint is expressed as where ν is the feasible set of analog precoders with constant modulus constraints.

[0085] In this embodiment, the number of RF links at the transmitting end is recorded as The number of antennas is N t ; In hybrid beamforming, the original data stream is represented by s and the dimension is N s ×1, after The digital precoding matrix V B , then through The simulated precoding matrix V RF , get N t ×1 transmission signal x=V RF V B s, the normalized constraint at the transmitter is The power constraint condition of the transmitter is calculated based on the Frobenius norm: where Q s is the preset transmitter power constraint constant; the constant modulus constraint of the hybrid precoding matrix is ​​expressed as V RF ∈ν, where ν is the feasible set of analog precoders with constant modulus constraints.

[0086] In an exemplary embodiment, the step S02 is to establish an objective function for optimizing the hybrid precoding matrix at the transmitting end according to the constraint conditions. The flow chart is as follows: Figure 4 As shown, the steps include:

[0087] Step S021: Obtain the optimal digital precoding matrix for digital beamforming; the optimal digital precoding matrix is ​​denoted as V opt ;

[0088] Step S022: construct a first objective function based on the Euclidean distance between the optimal digital precoding matrix and the hybrid precoding matrix; the first objective function is

[0089] Step S023, find the partial derivative of the first objective function to obtain the least squares solution; the least squares solution is in It is V RF Moore-Penrose pseudoinverse;

[0090] Step S024: construct an objective function based on the simulated precoding matrix according to the least squares solution and the Frobenius norm; the objective function based on the simulated precoding matrix is:

[0091] stV RF ∈V.

[0092] In this embodiment, the optimal digital precoding matrix for digital beamforming is obtained, which is denoted as V opt ; According to the Euclidean distance between the optimal digital precoding matrix and the hybrid precoding matrix, the first objective function is constructed as Take the partial derivative of the first objective function to obtain the least squares solution in It is V RF Moore-Penrose pseudo-inverse; according to the least squares solution The objective function based on the simulated precoding matrix is ​​constructed using the Frobenius norm:

[0093]

[0094] stV RF ∈V (1)

[0095] In an exemplary embodiment, the step S03, calculating the optimal storage capacity according to the relationship between the time delay and / or spectrum efficiency and / or memory occupancy and the storage capacity of the quasi-Newton method, is as shown in the flowchart. Figure 5 As shown, the steps include:

[0096] Step S031, calculating the functional relationship between the time delay and the storage capacity according to the relationship between the computational complexity and the storage capacity of the limited memory quasi-Newton method;

[0097] Step S032, calculating a functional relationship between spectrum efficiency and storage capacity according to the spectrum efficiency of the limited memory quasi-Newton method with different storage capacities;

[0098] Step S033, calculating the functional relationship between memory occupancy and storage capacity according to the limited memory quasi-Newton method for different storage capacities;

[0099] Step S034: constructing a storage optimization model based on the functional relationship between latency and storage capacity, and / or the functional relationship between spectrum efficiency and storage capacity, and / or the functional relationship between memory occupancy and storage capacity;

[0100] Step S035: The storage capacity corresponding to the maximum value of the storage capacity optimization model is the calculated optimal storage capacity.

[0101] In an exemplary embodiment, the step S031 is to calculate the functional relationship between the delay and the storage amount according to the relationship between the computational complexity and the storage amount of the limited memory quasi-Newton method, as shown in the flowchart. Figure 6 As shown, the steps include:

[0102] Step S0311, calculating the inherent computational complexity of the limited memory quasi-Newton method;

[0103] Step S0312: Calculate the approximate complexity of the Hessian matrix inverse based on the relationship between the storage capacity and the updating of the Hessian matrix inverse in the limited memory quasi-Newton method;

[0104] Step S0313: obtaining a functional relationship between computational complexity and storage capacity based on the inherent computational complexity of the finite memory quasi-Newton method and the approximate complexity of updating the inverse Hessian matrix;

[0105] Step S0314: Calculate the functional relationship between the delay and the storage capacity based on the positive correlation between the computational complexity of the limited memory quasi-Newton method and the delay.

[0106] In this embodiment, in the sub-step of step S031, the inherent computational complexity includes the computational complexity of Euclidean gradient, orthogonal projection, retraction and line search. Let N ant =max{N t , N r}, and assume that N RF =N s, then the complexity of calculating the Euclidean gradient is The computational complexity of orthogonal projection is N ant N RF , the computational complexity of the retraction is N ant N RF , the computational complexity of line search is

[0107] The variable x represents the storage capacity. Based on the relationship between the storage capacity and the updating of the Hessian matrix inverse in the finite memory quasi-Newton method, the approximate complexity of the Hessian matrix inverse is calculated as N ant N RF x 2 ;

[0108] Sum the above complexities to get the functional relationship between complexity and storage capacity, denoted as O(x);

[0109] According to the positive correlation between the computational complexity and latency of the finite memory quasi-Newton method, the functional relationship between latency and storage capacity is calculated as T(x) = u1·O(x) u2 +u3, where u1, u2 (u2>0), and u3 are pre-trained calculation coefficients.

[0110] In step S032, the functional relationship between the spectrum efficiency and the storage amount calculated according to the spectrum efficiency of the limited memory quasi-Newton method with different storage amounts is the functional relationship between the spectrum efficiency and the storage amount obtained by training the hybrid-shaped spectrum efficiency obtained by the limited memory quasi-Newton method under different storage amounts, which is recorded as R(x);

[0111] In step S033, the memory occupancy rate and the functional relationship between the memory occupancy rate and the storage capacity are calculated based on the positive correlation between the memory occupancy rate and the storage capacity according to the limited memory quasi-Newton method of different storage capacities, and the functional relationship between the memory occupancy rate and the storage capacity is calculated based on the positive correlation between the memory occupancy rate and the storage capacity, which is recorded as C(x)=u4·x u5 +u6, where u4, u5 (u5>0), and u6 are pre-trained calculation coefficients.

[0112] In a preferred embodiment, in step S034, the storage optimization model constructed according to the functional relationship between delay and storage and / or the functional relationship between spectrum efficiency and storage and / or the functional relationship between memory occupancy and storage is a storage optimization model obtained by weighted sum of the functional relationship between delay and storage and / or the functional relationship between spectrum efficiency and storage and / or the functional relationship between memory occupancy and storage. The storage optimization model is denoted as A(x). Then the storage optimization model

[0113] A(x)=u7·T(x) u8 +u9·R(x) u10 +u11·C(x) u12+u13, where u7, u8, u9, u10, u11, u12, and u13 are pre-trained calculation coefficients. Under the optimization model, lower latency, higher spectral efficiency, and lower memory usage are preferred. Therefore, u7 < 0, u9 > 0, and u11 < 0. Larger values ​​in the memory optimization model result in higher efficiency for the hybrid forming system.

[0114] In another preferred embodiment, in step S034, the storage optimization model constructed according to the functional relationship between delay and storage and / or the functional relationship between spectrum efficiency and storage and / or the functional relationship between memory occupancy and storage is obtained by multiplying the exponential product of the functional relationship between delay and storage and / or the functional relationship between spectrum efficiency and storage and / or the functional relationship between memory occupancy and storage, and the storage optimization model is denoted as A(x). Then the storage optimization model

[0115] A(x)=u14·T(x) u15 ·R(x) u16 C(x) u17 +u18, where u14, u15, u16, u17, and u18 are pre-trained calculation coefficients. Under the optimization model, lower latency, higher spectral efficiency, and lower memory usage are preferred. Therefore, u15 < 0, u16 > 0, and u17 < 0. Larger values ​​in the memory optimization model result in higher efficiency for the hybrid forming system.

[0116] In step S035, the storage capacity corresponding to the maximum value of the storage optimization model is the calculated optimal storage capacity. The maximum value of the storage optimization model A(x) is calculated using methods including, but not limited to, commonly used gradient descent methods and quasi-Newton methods for finding function extremities. The storage capacity x corresponding to the maximum value of A(x) is the optimal storage capacity, denoted as M. In this embodiment, the optimal storage capacity M = 3.

[0117] Hybrid beamforming has different requirements for latency, spectral efficiency, and memory usage in different application scenarios. Therefore, a storage optimization model corresponding to different calculation coefficients obtained through training for the current application scenario can obtain a more optimal storage capacity for limited-memory quasi-Newton method calculations.

[0118] In an exemplary embodiment, the step S04 is to calculate the optimal solution of the transmit end hybrid precoding matrix optimization objective function according to the limited memory quasi-Newton method corresponding to the optimal storage amount, as shown in the flowchart. Figure 7 As shown, the steps include:

[0119] Step S041, constructing a Riemann complex circular manifold and initializing parameters;

[0120] Step S042, calculating the cost function and Riemann gradient of the initial point;

[0121] Step S043: Determine whether the stop condition is met. If so, calculate and obtain the optimal solution of the transmit end hybrid precoding matrix optimization objective function; otherwise, proceed to the next step.

[0122] Step S044: Calculate the search direction based on the approximate Riemann gradient and the inverse of the Hessian matrix;

[0123] Step S045: Search in the tangent space using a line search based on the Armijo criterion, and then retract to the manifold to obtain a new solution;

[0124] Step S046: Calculate the cost function and Riemann gradient of the new solution;

[0125] Step S047: Determine whether the vector pair meets the storage condition. If so, update the initial value of the Hessian matrix and proceed to the next step; otherwise, do not update the initial value of the Hessian matrix and return to step S043;

[0126] Step S048: Determine whether the current storage capacity is greater than the optimal storage capacity. If so, discard the earliest stored vector; otherwise, proceed to the next step.

[0127] Step S049: Perform vector transfer on all vector pairs in the memory, store the current vector pair, increase the current storage capacity by 1, and then return to step S043.

[0128] In this embodiment, after determining the optimal storage capacity M according to the method described in the above embodiment, the limited memory quasi-Newton method is used to solve the objective function of formula (1). The following details the solution of V RF Specific steps.

[0129] In step S041, construct a Riemann complex circular manifold Initialization: number of iterations k = 0, initial point The number in the lower right corner of v0 is the number of iterations k, the storage occupancy: the number of vectors currently stored m = 0, the optimal storage capacity M, and the initial value of the Hessian matrix γ0 = 1 at the beginning of each iteration.

[0130] The analog beamforming design based on the finite memory quasi-Newton method simulates the beamforming matrix V RF Construct a vector v=V RF (:), ​​vector v forms a complex circular manifold in is the total number of matrix elements. Every element on the complex circular manifold belongs to the complex plane with a regular inner product And they are all unit modules, that is where |v i | i＝1...nThe tangent direction at a point v on the complex circular manifold is η, and the set of η constitutes the tangent space Right now

[0131] During the solution process, the analog beamforming matrix needs to satisfy the constant modulus constraint, that is, each element in the obtained analog beamforming matrix must be of unit modulus. All points on satisfy the constant modulus constraint. When solving the objective function on In this space, the search sister also satisfies the constant modulus constraint. The process of updating the solution is to start from an initial solution on the complex circle manifold Start along the tangent space A search direction η in k Search in Find a new point in the tangent space, but this point belongs to the tangent space And does not satisfy the constant modulus constraint, so it is mapped back to The solution that satisfies the constant modulus constraint is obtained.

[0132] In step S042, the cost function and Euclidean gradient of the initial point are calculated, and the Riemannian gradient is obtained from the Euclidean gradient. The Riemannian gradient is the mapping of the Euclidean gradient in the tangent space. The Euclidean gradient and Riemannian gradient of the objective function are derived below.

[0133] When taking derivatives of complex numbers, the relationship between the total differential and the gradient is: in express right The differential of represents the gradient, V RF In matrix form. By tr(A T )=tr(A) and tr(AB)=tr(BA), we can get Therefore, we can get the gradient expression through the derivative of the objective function. Derivative the objective function term by term, as shown below:

[0134]

[0135] According to d(X -1 )=-X -1 f(X)X -1 , we get the following formula:

[0136]

[0137] Therefore, we get

[0138]

[0139] According to the above formula, we can calculate

[0140]

[0141] in After sorting, we get

[0142]

[0143] Therefore, the Euclidean gradient of the objective function is

[0144]

[0145] The complex circular manifold is a Riemann submanifold of the complex plane. For a Riemann submanifold, the Riemann gradient is the orthogonal projection of the Euclidean gradient on the tangent space. Therefore, the Riemann gradient of the objective function (1) is As shown below:

[0146]

[0147] When the objective function is derived, the matrix form is adopted, and the final Riemann gradient is Converted to vector form.

[0148] In step S043, it is determined whether the internal loop stop condition is met. If the stop condition is met, the algorithm is terminated and the optimal solution of the transmit end hybrid precoding matrix optimization objective function is obtained. Otherwise, the process proceeds to step S044.

[0149] The inner loop stops when the norm of the gradient reaches a certain value β.

[0150] In step S044, Calculate the search direction η k When there is no vector stored, the search direction is the negative gradient direction, that is When there is vector storage, the search direction is determined by the approximation of the inverse of the Hessian matrix and the gradient, that is, in To approximate the inverse of the Hessian matrix, the present invention uses the most recent m gradient information The inverse of the Hessian matrix is ​​approximated and the explicit expression of the inverse of the Hessian matrix is ​​avoided through bidirectional recursion. On the Riemannian manifold, the gradient information generated by each iteration is in a different tangent space and cannot be directly combined. Therefore, the gradient information generated by the kth iteration is Vectors in space {s k ,y k}Transfer to the next space In the figure, the vector after transmission is This operation is called vector transfer and is expressed as:

[0151]

[0152]

[0153] When m vector pairs are stored When calculating

[0154]

[0155] in is the initial symmetric positive definite matrix. In this embodiment ρ k =1 / k ,y k >,

[0156] In step S045 , a search is performed in the tangent space along the calculated search direction, and a line search based on the Armijo criterion is used to find the next point in the tangent space, which is then mapped onto the manifold to obtain a new solution.

[0157] Specifically, from point v k Start by searching in the direction η k Choose a step size α k , the next point is v k +α k η k The search direction is given in step S044. In the embodiment of the present invention, the step length is determined by the Armijo criterion. The content of the Armijo criterion is shown in the following formula:

[0158]

[0159]

[0160] Where 0<c<1, is the objective function, v k is the current point, α k is the independent variable, η k For the descending direction, is the Taylor expansion of the function, is the Riemann gradient of the current point.

[0161] Points found using line search in tangent space To project it back from the tangent space to the manifold M n This is called retraction and is expressed as:

[0162]

[0163] ​

[0164] In step S046, calculate the new solution v k+1 The cost function and Riemann gradient Prepare for the next iteration.

[0165] In step S047, it is determined Whether the storage conditions are met. The storage conditions are The value of is greater than the threshold ω. If the storage condition is met, the initial value of the Hessian matrix is ​​updated, that is, Go to the next step; if the storage condition is not met, the initial value of the Hessian matrix is ​​not updated, that is, let r k+1 =r k , return to step S043 (the number of iterations k increases by 1).

[0166] In step S048, it is determined whether the current storage capacity is greater than the optimal storage capacity, that is, before performing the storage operation, it is determined whether the memory is full. If m≥M, it means that the memory is full and the earliest stored vector pair is discarded. Otherwise, it goes directly to the next step.

[0167] In step S049, a storage operation is performed. All vector pairs {s, y} in the memory are vector-transferred and the current Specifically, the history storage vector Transfer to Space obtained Then store the current iteration After increasing the current storage amount m by 1, the process returns to step S043 (the number of iterations k increases by 1).

[0168] In an exemplary embodiment, the step S05 is to obtain the transmitting end hybrid precoding matrix according to the optimal solution of the transmitting end hybrid precoding matrix optimization objective function and perform hybrid beamforming based on it. The flow chart is as follows: Figure 8 Shown, including:

[0169] Step S051: Obtain the simulated precoding matrix V according to the optimal solution of the transmit end hybrid precoding matrix optimization objective function. RF ;

[0170] Step S052: According to the optimal digital precoding matrix V opt and simulated precoding matrix V RF Calculate the digital precoding matrix V B ;

[0171] Step S053: The signal passes through the digital precoding matrix V B After adjusting the amplitude and phase, it is transmitted through multiple radio frequency links;

[0172] Step S054: simulate the precoding matrix V RF Build phase shifters and connect to RF links;

[0173] Step S055: The RF link signal passes through the phase shifter and then forms a hybrid beam through the antenna.

[0174] In this embodiment, the vehicle divides the task into local subtasks and fog node subtasks according to the task type and data volume based on the unloading ratio; and sends the fog node subtasks to the selected fog node.

[0175] In an exemplary embodiment, the hybrid beamforming transmission signal is transmitted through the channel H and then received by the receiving antenna, and N is obtained. t ×1 received signal y=HV RF V B s+n, where n is the additive white Gaussian noise vector; at the receiving end, The analog combiner W RF Perform analog domain processing and then After transmission through the RF link Digital combiner W B Perform digital domain processing and finally get N s ×1 signal The analog combiner W RF The calculation method of the digital combiner WB is the same as that of the analog precoding matrix V described in the above embodiment. RF and the digital precoding matrix V B The calculation method is the same.

[0176] The performance of the hybrid beamforming method provided by the present invention is evaluated through data and simulation experiments. In this embodiment, the spectrum efficiency and delay under different storage amounts are shown in the following table.

[0177] Storage capacity 3 4 5 6 7 Spectral efficiency 2.5129 2.4802 2.4857 2.5176 2.4926 Latency 3.1878 2.5774 2.3386 2.2360 2.6641

[0178] According to the method described in the above embodiment, the optimal storage capacity M=6 is obtained (the specific solution process involves multiple training of calculation coefficients, which will not be described in detail). In the simulation experiment, the number of transmitting and receiving antennas N t =N r =64, data stream N s =2, the number of RF links at the transmitting and receiving ends The internal loop stop threshold is β=10 -6 , the external loop stop threshold is δ=10 -3 , the threshold of storage condition is ω=10 -4m (m is the modulus of the current gradient).

[0179] Figure 9The bit error rate (Ber) of different hybrid beamforming algorithms varies with the signal-to-noise ratio (SNR). In terms of bit error rate, the method of the present invention (represented as LBFGS in the figure) is compared with the full digital SVD method (FD MSE, the best performance V opt The corresponding all-digital hybrid beamforming method), the orthogonal pursuit matching (OMP) method, and the AltMin method are compared. It can be seen that the method of the present invention is far superior to the OMP method.

[0180] Figure 10 The curves of different hybrid beamforming delays changing with signal-to-noise ratios. In terms of delay, compared with the AltMin method, it can be seen that the overall delay of the method of the present invention (represented as LBFGS in the figure) is 32.12% lower than that of the AltMin method. On the one hand, in terms of the number of external iterations and the number of internal iterations, the objective function of this method adopts the least squares solution, and the number of calls to the objective function adopted is less than that of the AltMin method, which reduces the number of external iterations; at the same time, this method uses multiple first-order derivatives to approximate the Hessian matrix to obtain the search direction, so the search direction decreases faster, and the number of internal iterations is much less than that of the AltMin method; on the other hand, because the search direction adopted by this method decreases faster, the single internal cycle time is lower. Therefore, this method is lower than the AltMin method in terms of delay.

[0181] A computer-readable storage medium according to an embodiment of the present invention stores a computer program for electronic data exchange, wherein the computer program enables a computer to execute the method according to any one of the above embodiments.

[0182] A hybrid beamforming system based on storage optimization according to an embodiment of the present invention is shown in the structural diagram. Figure 11 Shown, including:

[0183] processor;

[0184] Memory;

[0185] as well as

[0186] One or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the processor, and the programs enable the computer to execute the method of any one of the above embodiments.

[0187] Of course, those skilled in the art should realize that the above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. As long as they are within the scope of the present invention, any changes or modifications to the above embodiments will fall within the scope of protection of the present invention.

Claims

1. A hybrid beamforming method based on storage optimization, characterized in that: include: Calculate the constraints of the hybrid precoding matrix at the transmitter based on the number of RF chains, the number of antennas, and the channel state; Establishing the objective function of the hybrid precoding matrix optimization at the transmitting end according to the constraint conditions; Calculating an optimal storage amount based on a relationship between delay and / or spectrum efficiency and / or memory occupancy and a storage capacity of the quasi-Newton method; Calculate the optimal solution of the transmit end hybrid precoding matrix optimization objective function using the limited memory quasi-Newton method corresponding to the optimal storage capacity; The hybrid precoding matrix at the transmitting end is obtained according to the optimal solution of the optimization objective function of the hybrid precoding matrix at the transmitting end, and hybrid beamforming is performed based on it.

2. The hybrid beamforming method based on storage optimization according to claim 1, characterized in that The calculation of the constraints of the transmitting end hybrid precoding matrix according to the number of radio frequency links, the number of antennas and the channel state comprises the steps of: The number of RF links at the transmitter is recorded as , the number of antennas is recorded as ; In hybrid beamforming, the original data stream is represented as s , the dimension is ,go through Digital precoding matrix , then through The simulated precoding matrix ,get The transmission signal , the normalized constraint at the transmitter is ; The power constraint condition of the transmitter is calculated based on the Frobenius norm: ,in Q s is the preset transmitter power constraint constant; The constant modulus constraint of the hybrid precoding matrix is ​​expressed as ,in is the feasible set of analog precoders with constant modulus constraints.

3. The hybrid beamforming method based on storage optimization according to claim 2, characterized in that The objective function of optimizing the hybrid precoding matrix at the transmitting end is established according to the constraint conditions, comprising the steps of: Get the optimal digital precoding matrix for digital beamforming, denoted as ; The first objective function is constructed based on the Euclidean distance between the optimal digital precoding matrix and the hybrid precoding matrix: ; Take the partial derivative of the first objective function to obtain the least squares solution ,in yes Moore-Penrose pseudoinverse; According to the least squares solution The objective function based on the simulated precoding matrix is ​​constructed using the Frobenius norm: , .

4. The hybrid beamforming method based on storage optimization according to claim 1, characterized in that The method of calculating the optimal storage capacity based on the relationship between the time delay and / or spectrum efficiency and / or memory occupancy and the storage capacity of the quasi-Newton method comprises the following steps: The functional relationship between latency and storage capacity is calculated based on the relationship between the computational complexity and storage capacity of the finite memory quasi-Newton method; The functional relationship between spectral efficiency and storage capacity is calculated based on the spectral efficiency of the finite memory quasi-Newton method with different storage capacities; The functional relationship between memory occupancy and storage capacity is calculated based on the finite memory quasi-Newton method for different storage capacities; Constructing a storage optimization model based on a functional relationship between latency and storage capacity, and / or a functional relationship between spectrum efficiency and storage capacity, and / or a functional relationship between memory occupancy and storage capacity; The storage capacity corresponding to the maximum value of the storage capacity optimization model is the calculated optimal storage capacity.

5. The hybrid beamforming method based on storage optimization according to claim 4, characterized in that: The method of calculating the functional relationship between the time delay and the storage capacity according to the relationship between the computational complexity and the storage capacity of the finite memory quasi-Newton method comprises the following steps: Computing the inherent computational complexity of the limited memory quasi-Newton method; the inherent computational complexity includes the computational complexity of Euclidean gradient, orthogonal projection, retraction, and line search; Compute the approximate complexity of the Hessian matrix inverse based on the relationship between storage and updating the Hessian matrix in the limited memory quasi-Newton method; The functional relationship between computational complexity and storage capacity is obtained based on the inherent computational complexity of the finite memory quasi-Newton method and the approximate complexity of updating the inverse of the Hessian matrix. According to the positive correlation between the computational complexity and delay of the finite memory quasi-Newton method, the functional relationship between delay and storage capacity is calculated.

6. The hybrid beamforming method based on storage optimization according to claim 1, characterized in that The method of calculating the optimal solution of the transmitting end hybrid precoding matrix optimization objective function according to the limited memory quasi-Newton method corresponding to the optimal storage capacity includes the following steps: Construct a Riemannian complex circular manifold and initialize the parameters; Calculate the cost function and Riemann gradient of the initial point; Determine whether the stopping condition is met, and if so, calculate the optimal solution of the transmit end hybrid precoding matrix optimization objective function; Otherwise, proceed to the next step; the stopping condition is that the norm of the gradient reaches a preset value; The search direction is calculated based on the approximation of the Riemann gradient and the inverse of the Hessian matrix; A line search based on the Armijo criterion is used to search in the tangent space and then retract to the manifold to obtain a new solution; Calculate the cost function and Riemann gradient of the new solution; Determine whether the vector pair meets the storage conditions. If so, update the initial value of the Hessian matrix and proceed to the next step; Otherwise, the initial value of the Hessian matrix is ​​not updated, and the result is returned to determine whether the stopping condition is met; Determine whether the current storage capacity is greater than the optimal storage capacity. If so, discard the earliest stored vector, otherwise proceed to the next step; Perform vector transfer on all vector pairs in the memory, store the current vector pair, increase the current storage by 1, and then return to determine whether the stop condition is met.

7. The hybrid beamforming method based on storage optimization according to claim 6, characterized in that The method of obtaining a transmitting end hybrid precoding matrix based on an optimal solution of an optimization objective function of the transmitting end hybrid precoding matrix and performing hybrid beamforming based on the matrix comprises the following steps: The simulated precoding matrix is ​​obtained based on the optimal solution of the transmitter hybrid precoding matrix optimization objective function ; According to the optimal digital precoding matrix and simulated precoding matrix Calculate the digital precoding matrix ; The signal passes through the digital precoding matrix After adjusting the amplitude and phase, it is transmitted through multiple radio frequency links; According to the simulated precoding matrix Build phase shifters and connect to RF links; The RF link signal passes through the phase shifter and then forms a hybrid beam through the antenna.

8. The hybrid beamforming method based on storage optimization according to claim 6, characterized in that: The transmission signal of hybrid beamforming passes through the channel After transmission, it is received by the receiving antenna and obtained The received signal ,in, N t is the number of transmitting antennas, n is the additive white Gaussian noise vector, and the original data stream is expressed as s , the dimension is N s ×1; at the receiving end N r × Analog combiner Perform analog domain processing and then After transmission through the RF link × N s Digital combiner Perform digital domain processing and finally get signal ,in N r represents the number of receiving antennas and N r = N t , Indicates the number of RF chains at the receiving end; the analog combiner The digital combiner is obtained based on the optimal solution of the target function of the mixed precoding matrix optimization at the receiving end. It is based on the optimal digital precoding matrix and analog combiners Calculated.

9. A computer-readable storage medium storing a computer program for electronic data exchange, wherein: The computer program enables a computer to execute the method according to any one of claims 1 to 8.

10. A hybrid beamforming system based on storage optimization, characterized in that include: processor Memory; as well as One or more programs, wherein the one or more programs are stored in a memory and configured to be executed by the processor, the programs causing the computer to perform the method according to any one of claims 1 to 8.

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