CN113162664A - Beam forming pre-coding system and method - Google Patents
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Abstract
The embodiment of the invention provides a beam forming pre-coding system and a beam forming pre-coding method, wherein the system comprises a regularization zero forcing module, a singular value decomposition module and a Lagrangian dual module, and can acquire a pre-coding signal matrix of a receiving end in a wireless communication system; determining a beam vector direction for regularization interference nulling according to the size of a matrix corresponding to an input signal; generating a beam forming pre-coding matrix, and analyzing the weight of the main lobe and the side lobe on a target user layer by utilizing the weight value of the beam direction; according to the preset constraint condition of an actual communication system in a multi-user cell, the precoding signal matrix is optimized in an original problem in a Lagrange dual module, and an equivalent function capable of replacing the original signal condition is generated to serve as the generated beam forming precoding signal. By applying the scheme provided by the embodiment of the invention, the utilization rate of network resources can be improved, the pre-coding calculation efficiency can be improved, and the calculation complexity can be reduced.
Description
Technical Field
The present invention relates to the field of wireless communications, and in particular, to a beamforming precoding system method and method. Precoding strategies are one of the key techniques for deciding communication quality in wireless communication networks. The vector direction of the beam forming main lobe is improved in a wireless communication transmission network, and the target users in a multi-user cell are aimed at, so that the precoding performance of the wireless communication network can be effectively improved, and the resource utilization rate is improved.
Background
The beamforming technology can reduce the interference problem in the wireless communication system, enhance the interference suppression effect in the communication network, and is an important signal processing mode in a large-scale MIMO system. In the actual communication system scenario of the multi-user cell at present, a large-scale antenna array is deployed in a limited physical space, which may cause the correlation between each antenna array element to increase, thereby weakening the system gain effect brought by the large-scale MIMO technology. At the same time, the large number of antennas makes synchronization between the antenna elements very difficult. Therefore, a large-scale antenna array needs to be reasonably designed, correlation and coupling degree between each antenna array element are reduced, and antennas need to be processed and calibrated according to characteristics of the antenna array. The beamforming technology is gradually becoming one of the key technologies for precoding in the 5G mobile communication system.
The large-scale antenna array is arranged on the base station side, so that the base station is extremely difficult to process a high-dimensionality random matrix within limited time, and meanwhile, the time for the base station to process signals is prolonged, and the normal operation of a low-delay mobile communication system is influenced. When all data streams in the system are transmitted on the same time, frequency and space, if a large number of users are served simultaneously by a base station deploying a massive antenna array, the massive MIMO system inevitably has severe multiple inter-data-stream interference (ISI) and interference between Multiple Users (MUI). ISI and MUI can cause severe degradation of system performance. In practical MIMO systems, ISI and MUI cannot be completely eliminated, and not all conventional, mature signal processing and interference management techniques can migrate to massive MIMO systems in view of complexity issues. The independent signal data matrix decomposition mode effectively improves the utilization rate of network resources, simultaneously improves the precoding rate of a wireless communication network, and reduces the technical complexity of a large-size antenna matrix of a multi-user cell. Has important research value for the field of wireless communication.
In the large-scale MIMO system precoding technology, the regularization zero forcing technology is a key technology for solving the problem of precoding of users of a multi-cell user system, and is also a technology which is commonly used in the current wireless communication system. At present, the different ways of interference suppression can be mainly divided into the following: the method comprises the following steps of precoding technology based on a zero forcing algorithm, precoding technology based on block diagonalization, precoding technology based on singular value decomposition, precoding technology based on Newman series and the like, wherein the algorithms solve the precoding problem of a multi-cell wireless communication system to a certain extent, but the vector control of beam forming is not well guaranteed. In recent years, the proposed regularization zero forcing algorithm ensures higher precoding transmission quality.
In order to improve the precoding quality of a wireless communication system, ensure high-quality transmission of signals and reduce the computational complexity of a large-size matrix, the patent provides a beam forming precoding system method, which is characterized in that a transmitted transmitting end signal is sequentially distributed to a regularization interference zero forcing module, a singular value decomposition module and a Lagrange dual module, and an optimized matrix meeting constraint conditions is formed by carrying out direction weighting processing on different beam vectors. The precoding quality of the system can be improved by utilizing a layered processing mechanism, and the utilization rate of network resources is improved.
The beamforming pre-coding method based on RZF-singular value-Lagrange aims at improving spectrum transmission efficiency, reducing time delay, reducing network blocking rate and avoiding large-size calculation complexity while ensuring the pre-coding with high transmission quality.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: under the independent same-distribution Rayleigh channel, with the increasing number of transmitting antennas, the channels among multiple users in a large-scale MIMO system tend to be orthogonal to each other. At this time, the performance of the system is only related to the large-scale fading of the channel and is not related to the small-scale fading. The random nature of the wireless physical channel is reduced so that interference between multiple cells can be eliminated by simple linear precoding and a receiver. The invention provides a beamforming pre-coding algorithm based on RZF-singular value-Lagrange, which can reduce time delay, reduce network blocking rate, improve network resource utilization rate and improve spectrum transmission efficiency.
The embodiment of the invention aims to provide a beam forming precoding system method so as to improve the precoding performance of a wireless communication system. The specific technical scheme is as follows:
in one aspect of the present invention, a beamforming pre-coding algorithm based on RZF-singular value-lagrangian is provided, where the algorithm system includes: a regularized interference zero forcing module, a singular value decomposition module, and a lagrange dual module, wherein,
1. the regularized zero forcing module is arranged at a transmitting end of a multi-user cell wireless communication system, a pre-coded signal reaches the regularized zero forcing module and is used for pre-coding signal data of a receiving end in the wireless communication system, the signal of the transmitting end is designed into a proper beam vector direction by using an orthogonal matrix antenna array, main lobe data is aligned to a target user signal, a side lobe is aligned to a zero-value part in the data signal, the inter-user interference generated in a downlink is eliminated, antenna arrays in partial directions can weaken each other until disappear, the mutual interaction of antenna array waves is enhanced, a transmitting end signal exists in an electromagnetic wave form, the direction of a beam is changed by the antenna arrays along with the position change of the receiving end and the transmitting end, a beam direction correlation factor is simulated according to simulated beam information selected by a scheduling user, and the user pilot frequency is reasonably distributed according to the simulated beam information, by utilizing a heuristic pilot frequency distribution method and a pilot frequency distribution method based on user grouping, the beam index and the reference signal power of a user can be obtained in an actual communication system, and the regularized zero-forcing pre-coding matrix is sent to the singular value decomposition module;
2. the singular value decomposition module is used for screening out redundant signals contained in the interference information, mapping the precoding matrix to a low-dimensional matrix space coordinate system, converting the input signals into a singular value decomposition form, enabling the output matrix to be represented by a characteristic value and a singular matrix of the singular value matrix, performing singular value decomposition on a compression result of regularized precoding, and enabling the singular value to be regarded as a representative value of the matrix and representing the information of the precoding matrix by the singular value. The magnitude of the singular value determines how much information it represents. The method is characterized in that a plurality of maximum singular values are removed, data can be basically restored, a user scheduling constraint factor is designed to limit scheduling of a downlink edge user suffering from serious cross interference through processing cross interference characteristics in a dynamic TDD scene, serious base station-to-base station interference is realized, a large-dimensional base station-to-base station interference channel is decomposed into a plurality of interference sub-channels through singular value decomposition, an allocation scheme is designed to enable the interference sub-channels to be respectively handed to an uplink base station and a downlink base station for processing, and the space freedom of a base station antenna in a large-scale MIMO system of a multi-user cell is utilized to eliminate the cross interference. The matrix after singular value decomposition processing is sent to the Lagrangian dual module;
3. the Lagrange dual module is used for physical condition constraint generated in actual communication system transmission, in order to avoid inversion of a large-size pre-coding matrix of a beam forming matrix in an actual constraint scene, optimization processing is carried out on a cost function, the matrix obtained by the singular value decomposition module is used for strengthening dual and KKT conditions, a non-constraint problem is redefined through a Lagrange method, the non-constraint problem is equivalent to the original constraint optimization problem, and therefore the constraint problem is not constrained. The method has the advantages that the original problem is converted into the convex optimization problem, the solution of the original problem is obtained by solving the dual problem under the condition that the strong dual is established, the establishment of the strong dual can be directly assumed in the support vector machine, and at least one absolute feasible point exists. And solving the original problem by the dual problem, wherein the optimal value of the original problem is not less than that of the dual problem, and taking a Lagrangian dual optimization result obtained by equalizing the optimal value of the original problem with the optimal value of the dual problem as a precoding result matrix.
In the method, step 1 is to perform the directional adjustment of the beam vector at the regularized interference zero forcing module according to the position of the antenna array, and perform the regularized beamforming pre-coding. The method comprises the following specific steps:
3.1, optionally, the interference zero forcing mechanism is used for a high-complexity signal input matrix involved in a multi-antenna technology, and when reaching a regular zero forcing step in a precoding module, the input signal matrix with a larger size is transmitted to an RZF for interference zero forcing processing, the RZF acts on an electromagnetic wave antenna array, the direction of a signal is positioned at a fixed position, a beam array in the direction is generated, and a channel in a wireless communication system is separated into a plurality of parallel channels for processing. The main lobe of the wave beam vector is aligned to a target user signal to be transmitted, a null and a side lobe are aligned to an interference signal part, relative positions and amplitudes of two receiving and transmitting ends are controlled through a plurality of antenna array sources, so that the antenna array transmits along a required direction as much as possible, interference of multi-cell and multi-user signals on space and time is inhibited, and signals which are separated in space are designed. Scheduling a signal vector of a target user to be orthogonal to a channel of an interference user, carrying out zero setting processing on interference signals in a transmitting end and a receiving end in a multi-user cell, respectively giving a certain weight value to a main lobe and a side lobe, carrying out weighting selection processing, and transmitting the part of signals to the beam vector orthogonalization mechanism module;
and 3.2, the beam vector orthogonalization mechanism is used for combining a group of phase delays or time delays with fixed weights, reasonably designing large-scale antenna vectors by utilizing the matrix correlation of the large-scale antenna array, reducing the coupling degree of array elements among the large-scale antenna vectors, and orthogonalizing the position beams of the sensor and the signal beams of the target user. The scanning property of the analog beam is utilized to act the analog beam codebook information set at the base station on a target user in the communication system and transmit the analog beam codebook information set in different time slots. And carrying out targeted optimization on a pre-coded transmitting signal, decomposing a large-dimension interference channel from a base station to the base station into a plurality of interference sub-channels, designing a distribution scheme, and respectively handing the interference sub-channels by an uplink base station and a downlink base station, so that a target user uses the power of the signal received by measurement to select a part with strong power as a feedback of using signal information data and the base station in the process of interference nulling by a plurality of antennas. Simulating beam direction relevance factor by using user fairness and a heuristic pilot frequency distribution scheme, reasonably distributing user pilot frequency according to the beam direction relevance factor, and performing orthogonal selection on weighted signals to obtain a precoding matrix processed by a regularized zero forcing module;
in the method, step 2, an input signal is converted into a singular value decomposition form, singular value decomposition is carried out on a compression result of regularization precoding, a large-dimension interference channel from a base station to a base station is decomposed into a plurality of interference sub-channels by utilizing the singular value decomposition, and an allocation scheme is designed to respectively deliver the interference sub-channels to an uplink base station and a downlink base station for processing. The method comprises the following specific steps:
4.1, optionally, the real-symmetric matrix mechanism is configured to perform interference information zero forcing on input signal matrix data at the base station side after an input signal is subjected to interference zero forcing, screen out a part of redundant signals, and reduce complexity of a beamforming matrix actually processed. And representing the precoding matrix into a diagonal matrix corresponding to the eigenvalue dimension by utilizing the real symmetry property of the precoding matrix. Mapping the pre-coded signals to a low-dimensional space, and decomposing a pre-coded matrix into an orthogonal matrix and an expression mode of a characteristic value under a common real symmetric matrix scene;
4.2, the non-real symmetric matrix in the actual scene is used for carrying out importance sequential arrangement distribution on the vector singular value representation in the number input by the multi-cell user communication system in the communication system and the situation that the precoding signal is the non-real symmetric matrix in the actual scene, carrying out singular value decomposition on the beam forming matrix, carrying out evolution processing on the characteristic value of the regular precoding matrix, and complementing the characteristic vector of the dimension reduction signal mapped to the bit space. And the best decomposition result is adopted according to the received power of the reference signal, the direction of the vector signal and the range of singular value decomposition are divided according to the beam service area of the whole user cell, the signal is concentrated to act on the target user area, and the signal decomposition with energy contribution rate is carried out on the system. The size of the matrix eigenvalue represents the number of input signals covering the base station side, partial data with small transmission effect on user signals in a cell are abandoned, eigenvalue decomposition processing is carried out on a singular value matrix, the matrix after the singular value decomposition processing is represented by a left wife system matrix and a right wife system matrix and the precoding matrix eigenvalue, and the matrix eigenvalue is converted into a dimensionality reduction signal matrix for screening out redundancy.
In the method, step 3, the large-size pre-coding matrix of the beam forming matrix is inverted, the cost function is processed in an optimization mode, and the matrix obtained by the singular value decomposition module is used for strengthening even and KKT conditions. The method comprises the following specific steps:
5.1, optionally, the original problem mechanism is used for processing the decomposition result of singular values, adding a certain constraint value to the singular value by using an optimization mode in a machine learning algorithm, performing constraint conditions on a cost function to process the transmission power limit of a base station side transmission end, the total number of users capable of being intervened in a cell and the radiation range of a cell base station, performing generalized Lagrange parameter maximization according to the actual scene constraint conditions, performing optimization processing on an input signal matrix with large scale size according to Shannon limit precoding in a communication system, performing decomposition processing on the Lagrange problem by using a dual function, converting the original optimization problem into a maximum value solving problem and a minimum value solving problem, defining the optimal value of the original problem, performing infinite processing on a partial derivative on an introduced parameter, sending the optimization result under the constraint condition to a strong and weak dual mechanism module;
and 5.2, the strong and weak dual mechanism module is used for solving the initial signal matrix of large size, setting a lower bound on the constraint condition by using a Lagrangian dual function, representing the maximum and minimum problem of the generalized Lagrangian function as a constraint optimization problem, and fusing the constraint conditions together to obtain an unconstrained optimization target. And (3) establishing a lower bound function under the weak dual property, strictly restricting under the strong dual condition to meet the convex optimization corresponding condition, and strictly satisfying the zero value point existing in the condition to the restriction condition under the actual multi-user cell scene in 5.1. The dual problem is not equal to the optimal solution of the original function, but meets certain condition keys, when the constraint condition tends to be strong dual, the constraint condition needs to be strictly considered, and the dual function is set to be equivalent to the problem of limiting the number of target users and the problem of power of a transmitting end of the base station;
and 5.3, the KKT condition mechanism is used for meeting the optimization problem of the Lagrangian function under the strict dual premise, bringing the beam constraint problem in the original input pre-coded signal and the zero point in the Lagrangian dual function into the KKT condition, converting the minimization related to the independent variable of the original problem into the maximization related to the parameters of the dual problem, and finding the maximum lower bound function and dual complementary condition for the inequality. And (4) performing constraint transformation by using a feasible region and an extreme point of a dual function of beam forming, and performing gradient constraint limitation in a feasible region range and a tangent range. And simplifying the constraint condition to obtain a feasible domain, and limiting the constraint condition limiting feasible solution of the situation-based discussion processing to obtain a precoding result in an actual scene.
In yet another aspect of the present invention, a machine learning cascade optimization model is further provided, which, when running in a pre-coding module, implements the beamforming vectors provided by the embodiments of the present invention.
The beamforming pre-coding system method provided by the embodiment of the invention can obtain pre-coding input signals at the base station side, wherein the obtained pre-coding signals are used for being sent to an indication regularization zero forcing instruction; generating interference suppression zero forcing processing, and utilizing a singular value decomposition module for performing dimension reduction screening processing on an indicated large-size input matrix; and performing optimization constraint processing on the optimization function according to the generated cost function and the corresponding constraint condition and the Lagrangian dual module for indication. By applying the scheme provided by the embodiment of the invention, a machine learning dimensionality reduction mechanism can be adopted according to the shortage of precoding input signal resources in the system, and algorithm decomposition is carried out according to the precoding beam forming vector direction and the usefulness analysis of input signals, so that the wireless communication precoding is perfected. And the problems of improving the utilization rate of network resources, improving the pre-coding calculation efficiency, reducing the calculation complexity and the like are obviously improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a structural diagram of an RZF-singular value-lagrangian algorithm-based system according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of an interference suppression zero-forcing method according to an embodiment of the present invention;
FIG. 3 is a schematic flowchart of a singular value decomposition dimension reduction mechanism according to an embodiment of the present invention;
fig. 4 is a schematic flow chart of a lagrangian dual mechanism according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without any creative efforts shall fall within the protection scope of the present invention.
Referring to fig. 1, a structural diagram of a system based on RZF-singular value-lagrangian algorithm according to an embodiment of the present invention is shown, where the system includes: a regularized interference zero forcing module 100, a singular value decomposition module 200, and a lagrange dual module 300, wherein,
a regularization interference zero forcing module 100, which is used to process the input of the base station side transmission signal, pre-code the signal data source, reduce the generated interference signal in the channel to the lowest value, design the beam vector of the signal at the transmitting end by the orthogonal matrix antenna array, eliminate the interference between users generated in the downlink, and transmit the signal with the improved beam forming vector direction to the singular value decomposition module 200, compress the information of the pre-code matrix signal inputted, filter the interference information irrelevant to the target user in the pre-code matrix data, perform the low-dimensional mapping process on the whole matrix vector, screen out the redundant signal contained in the interference information, convert the input signal into the form of singular value decomposition, make the output matrix can be represented by the eigenvalue and singular matrix of the matrix, send the pre-code matrix after mapping to the lagrange duality module 300 by the singular value decomposition module, and performing original problem analysis processing on the low-dimensional mapped matrix signal transmission, performing optimization mode processing on a cost function, performing strong dual and KKT conditions on the matrix obtained by the singular value decomposition module, and taking the obtained Lagrangian dual optimization result as a precoding result matrix.
The precoding matrix generally refers to input data signals transmitted by a transmitting end on a base station side, the correlation among large-scale antenna arrays is deployed in a physical space in a communication system, the gain effect of the system is weakened, the antenna array elements in a large number of antennas are difficult to synchronize, the large-scale antenna arrays are reasonably designed, the correlation and the coupling degree among the antenna array elements are reduced, the antennas are processed and calibrated according to the characteristics of the antenna arrays, and the larger the size of the precoding matrix is, the more the data quantity transmitted in unit time is, and correspondingly, the larger the data quantity of the finger signals transmitted by the transmitting end is.
The singular value decomposition module 200 is configured to screen out redundant signals included in the interference information, map the precoding matrix to a low-dimensional matrix space coordinate system, convert the input signal into a singular value decomposition form, so that the output matrix may be represented by a singular value matrix and a characteristic value of the singular value matrix, perform singular value decomposition on a compression result of the regularized precoding, where a singular value may be regarded as a representative value of a matrix, and represent information of the precoding matrix by the singular value. The magnitude of the singular value determines how much information it represents. The method is characterized in that a plurality of maximum singular values are removed, data can be basically restored, a user scheduling constraint factor is designed to limit scheduling of a downlink edge user suffering from serious cross interference through processing cross interference characteristics in a dynamic TDD scene, serious base station-to-base station interference is realized, a large-dimensional base station-to-base station interference channel is decomposed into a plurality of interference sub-channels through singular value decomposition, an allocation scheme is designed to enable the interference sub-channels to be respectively handed to an uplink base station and a downlink base station for processing, and the space freedom of a base station antenna in a large-scale MIMO system of a multi-user cell is utilized to eliminate the cross interference. And sends the matrix after singular value decomposition to the lagrangian dual module 300.
In one implementation, the range of signals radiated by the transmitting end base station in the wireless communication system may be limited to a radius of 800 meters, and the transmission power of the base station may be 100 w.
The lagrangian dual module 300 is configured to receive signal matrices sent by the regularized interference zero forcing module 100 and the singular value decomposition module 200, constrain physical conditions generated in actual communication system transmission, perform optimization processing on a cost function on a matrix obtained from the singular value decomposition mechanism 200 to avoid inversion of a large-size pre-coding matrix of a beamforming matrix in an actual constraint scene, make the matrix obtained by the singular value decomposition module be a strong dual and KKT condition, and redefine a unconstrained problem through a lagrangian method, where the unconstrained problem is equivalent to an original constrained optimization problem, so that the constrained problem is unconstrained. The method has the advantages that the original problem is converted into the convex optimization problem, the solution of the original problem is obtained by solving the dual problem under the condition that the strong dual is established, the establishment of the strong dual can be directly assumed in the support vector machine, and at least one absolute feasible point exists. And solving the original problem by the dual problem, wherein the optimal value of the original problem is not less than that of the dual problem, and taking a Lagrangian dual optimization result obtained by equalizing the optimal value of the original problem with the optimal value of the dual problem as a precoding result matrix.
The precoding matrix can be distinguished from different sizes to carry out dimension reduction mapping, so that the beam vector size analysis needs to be carried out after the obtained regularized zero-forcing precoding matrix, and the dimension reduction mapping can be carried out on the precoding matrix if redundant data which are useless for the target user signal of the output signal are screened out because the duality optimization processing needs to be carried out on the output signal.
Referring to fig. 2, which shows a schematic structural diagram of an interference suppression zero-forcing method 100 according to an embodiment of the present invention, the interference suppression zero-forcing system 100 may include: a transmission signal weighting processing mechanism 201, an antenna channel orthogonal processing mechanism 202, a precoding matrix parameter measurement mechanism 203, a beam matrix pseudo-inverse mechanism 204, a beam vector weighting processing mechanism 205, an interference zero forcing mechanism 206, wherein,
the transmit signal weighting processing 201 is configured to perform weighting processing on the vector direction main lobe information and the side lobe information of the antenna array by using a digital signal transmission finger pre-coding module in the wireless communication system, and send the weighted data signal to the antenna channel orthogonal processing 202.
The antenna channel orthogonal processing mechanism 202 is configured to utilize correlation between array elements to reasonably design a large-scale antenna array, reduce correlation and coupling between the antenna array elements, process and calibrate an antenna according to characteristics of the antenna array, and send an orthogonally processed matrix to the precoding matrix parameter measurement mechanism 203.
In one implementation, the number of subcarriers is 600, the system bandwidth is 20MHz, the transmit power of each transmit antenna is 100mw, and the number of iterations is 5.
The precoding matrix parameter measurement mechanism 203 is used for performing parameter orthogonalization processing on cell interference parameters in a channel model, performing array design on useless signals and parameters in a channel, and sending a measurement mechanism result to the beam matrix pseudo-inverse mechanism 204.
And the beam matrix pseudo-inverse mechanism 204 is used for generating a precoding matrix channel model pseudo-inverse related to the target user, converting the transmission model under constraint, and sending a result obtained by solving the pseudo-inverse to the beam vector weighting processing mechanism 205.
The beam vector weighting mechanism 205 is used to strictly limit the time overhead of channel estimation in TDD mode. And solving the beam forming space direction weighting for completing the pre-coding in a limited time, obtaining a high-precision target user corresponding vector, and sending a beam vector pre-coding signal to the interference zero forcing mechanism 206.
And an interference zero forcing mechanism 206, configured to convert the user matrices in the cell into pilot sequences orthogonal to each other, eliminate useless signals of pilot pollution and pilot multiplexing in the system, set interference to zero, and generate a regularized interference suppression precoding matrix.
Referring to fig. 3, which shows a flowchart of a singular value decomposition dimension reduction mechanism provided in an embodiment of the present invention, the singular value decomposition module 200 may include: a low-dimensional space mapping mechanism 301, a non-real symmetric matrix mechanism 302, a real symmetric matrix mechanism 303, a singular value decomposition mechanism 304, a singular value representation arrangement mechanism 305, a singular value matrix representation mechanism 306, wherein,
the low-dimensional space mapping mechanism 301 is configured to receive a pre-coding matrix from the interference suppression zero forcing output, obtain a signal with redundant data information filtered out, perform mapping processing on a high-dimensional signal generated by the large-size antenna array, and send the result to the non-real symmetric matrix mechanism 302 and the real symmetric matrix mechanism 303.
The non-real symmetric matrix mechanism 302 is configured to perform singular value decomposition on a beamforming pre-coding matrix in a multi-user cell in an actual scene, convert a pre-coding result of the matrix into a singular matrix form of a non-square matrix, convert a cell communication signal into an expression mode of singular values and eigenvalues, and transmit a matrix signal to the singular value decomposition mechanism 304.
And the real symmetric matrix mechanism 303 is used for decomposing singular values of the beam forming precoding matrix in the cell, namely the square matrix model, converting the square matrix result into a singular matrix form, converting the cell communication signals into an expression mode of singular values and eigenvalues, and transmitting the matrix signals to the singular value decomposition mechanism 304.
The singular value decomposition mechanism 304 is configured to convert matrices with different dimensions, extract values on diagonal lines of the singular value matrix to some extent, convert a spatial mapping result of the matrix, and transmit a signal to the singular value representation arrangement mechanism 305.
The singular value representation and arrangement mechanism 305 is used for performing singular value representation on a vector matrix of input signals in the wireless communication system, performing arrangement distribution processing on important useful signal data of a target user, simultaneously discarding useless part of interference data information, and sending the data to the singular value matrix representation mechanism 306.
And a singular value matrix representation mechanism 306, configured to complement the matrix data information after singular value evolution processing to the eigenvectors after dimensionality reduction of the precoding matrix is left, and represent the left and right singular value matrices and the mapped eigenvectors as the precoding matrix.
In one implementation, the number of iterations of the singular value matrix calculation may be 4, the channel length may be 64, and the pilot interval may be 6.
Referring to fig. 4, a schematic flow chart illustrating a lagrangian dual mechanism provided by the embodiment of the present invention is processed, where the system includes an original problem optimization mechanism 401, a strong dual mechanism 402, a weak dual mechanism 403, and a KKT constraint mechanism 404, where:
an original problem optimization mechanism 401, configured to process a singular value decomposition result, apply an optimization mode in a machine learning algorithm, add a certain constraint value to the singular value decomposition result, apply a constraint condition to a cost function to process a transmit power limit of a base station side transmitting end, a total number of users that can intervene in a cell, and a range that can be radiated by a cell base station, maximize a generalized lagrangian parameter according to the above actual scene constraint condition, optimize an input signal matrix of a large scale size according to shannon limit precoding in a communication system, apply a dual function to decompose a lagrangian problem, convert a maximum optimization problem and a minimum exchange position into a maximum value solving problem and a minimum value solving problem, convert the maximization processing into a maximum infinite problem, define an optimal value of an original problem, apply an infinite parameter to process a bias derivative, and decomposing the generalized Lagrange function, and sending an optimization result under the constraint condition to the strong dual mechanism module 402 and the weak dual mechanism module 403.
And the strong dual mechanism module 402 is used for solving the initial signal matrix of large size, setting a lower bound on the constraint condition by using a Lagrangian dual function, representing the maximum and minimum problem of the generalized Lagrangian function as a constraint optimization problem, and fusing the constraint conditions together to obtain an unconstrained optimization target. And strictly constraining under the strong dual condition to meet the convex optimization corresponding condition, and strictly filling the zero-value points existing in the convex optimization corresponding condition to the constraint condition under the actual multi-user cell scene. The dual problem is not equal to the optimal solution of the original function, but meets certain condition keys, when the constraint condition tends to be strong dual, the constraint condition needs to be strictly considered, the dual function is set to be equivalent to the target user number limitation problem and the base station transmitting end power problem, and the generated signal matrix is sent to the KKT constraint condition mechanism 404.
And the weak dual mechanism module 403 is used for the large-scale initial signal matrix after the optimization processing of the original problem, representing the maximum and minimum problem of the generalized Lagrangian function as a constrained optimization problem, and fusing constraint conditions together to obtain an unconstrained optimization target. And setting a lower bound on the constraint condition by using a Lagrange dual function. The lower bound function is established under weak dual property and is not bound by constraint conditions under actual multi-user cell scene. The dual problem is not equal to the optimal solution of the original function, the dual function is set to be equivalent to the target user number limitation problem and the base station transmitting end power problem, and the precoding matrix generated by the weak dual mechanism is sent to the KKT constraint mechanism 404.
In another embodiment of the present invention, a machine learning cascade optimization model is provided, which, when running in a pre-coding module, implements the beamforming vectors provided by the embodiments of the present invention.
Specifically, the machine learning cascade optimization model includes:
acquiring an input signal of a transmitting end of a wireless communication system;
determining to implement a dimension reduction space mapping mechanism according to the size of the obtained input signal;
generating a precoding matrix under a regularized interference zero forcing mechanism;
performing singular value decomposition processing according to the pre-coding matrix after interference suppression to generate a beam matrix represented by characteristic values and left and right singular matrixes;
and (4) performing original problem optimization, strong and weak dual mechanism and KKT constraint processing on the precoding matrix after singular value processing in a Lagrangian dual module to generate a precoded beam matrix.
In each scheme provided by the embodiment of the invention, the generated dimension-reduced mapping space can be adjusted according to the size of the input data signal matrix in the wireless communication system, and the precoding matrix represented by the eigenvalue and the left and right singular matrixes is realized through a singular value decomposition mechanism, so that the utilization rate of network resources and the precoding calculation efficiency can be improved.
In summary, the present invention provides a method for beamforming precoding system, which aims at the problems of increased interference, long transmission distance, weakened gain effect and poor precoding performance in a wireless communication system. At a transmitting end of a base station side, precoding interference regularization zero setting is realized, and in a beam precoding module, transformation of a precoding matrix under a constraint condition is realized by using cost function optimization. Meanwhile, the transmission of high-quality beam vector signals in a channel is ensured, and meanwhile, network blockage is reduced and large-size calculation complexity is avoided. Processing the beam matrix array direction weight of a transmitting end under the condition of ensuring the accuracy of a pre-coded beam vector; when the size of the input precoding matrix is too large or the information content is too large, the cascade module selects a beam vector reservation which is useful for a target user according to conditions such as the transmission distance of a cell base station, the emissivity of the cell base station, the number of subcarriers and the like. The transmitting signal can be well transmitted in the channel with interference, the utilization rate of network resources can be effectively improved, and the calculation complexity is reduced.
The beamforming pre-coding algorithm based on RZF-singular value-Lagrange is characterized in that regularization pre-coding and dimension reduction mapping technology are utilized, high-quality beam vector signals are transmitted in a channel, meanwhile, the utilization rate of network resources is improved, and the beam vectors are aligned to target user signals. When the size of the signal matrix is overlarge, the weighting processing of the beam vector further ensures the problems of optimization and constraint conditions, and effectively improves the precoding efficiency.
The method has the main innovation points that when the interference problem is generated in signal transmission, the phase delay and the weight are combined in a regularized pre-coding mode, the vector dimension of a wave beam is reduced, the signal amplitude and the position of two receiving and transmitting ends controlled by an antenna array source are improved, and the space-time interference of other data is inhibited; when the size of the non-uniform matrix of the beam direction of the wireless network system is too large, the modules in the forms of beam weight processing, dimensionality reduction space mapping of singular value decomposition and dual cascade are utilized to carry out importance sequential arrangement distribution on the representation of the vector singular value, and the pre-coding matrix is converted into an expression mode of characteristic values and left and right singular values, so that the problem of high calculation complexity is solved; meanwhile, the original problem and the selection of strong and weak duality are utilized to carry out feasible processing on the lower bound function and the complementary problem under strict duality definition, the constraint condition is subjected to processing in a feasible domain, and the transmission of high-quality beam vector signals in a channel is ensured. The method effectively solves the problem of redundant data information at a user terminal caused by the interference of channels in a wireless communication system, poor precoding capacity and high calculation complexity, and avoids the direction problem of the beam vector main lobe and side lobe in a multi-user cell system. The network time delay is reduced, the calculation complexity and the channel interference condition are reduced, and the resource utilization rate and the precoding efficiency of the satellite wireless communication network are improved.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" is intended to exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
All the embodiments in the present specification are described in a related manner, and the same and similar parts among the embodiments may be referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, as for the method, electronic device, computer-readable storage medium, and computer program product embodiments, the description is relatively simple as it is substantially similar to the system embodiments, and reference may be made to some descriptions of the method embodiments for relevant points.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (4)
1. A beamforming precoding system method, the algorithm comprising: a regularization zero forcing module, a singular value decomposition module, and a lagrange dual module, wherein,
1) the regularization zero forcing module is used for carrying out precoding processing on signal data of a receiving end in a wireless communication system, designing a beam vector of a signal of a transmitting end by using an orthogonal matrix antenna array, eliminating interference among users generated in a downlink, and sending the pre-coding matrix subjected to regularization zero forcing processing to the singular value decomposition module;
2) the singular value decomposition module is used for screening out redundant signals contained in the interference information, mapping the pre-coding matrix to a low-dimensional matrix space coordinate system, converting the input signals into a singular value decomposition form, enabling the output matrix to be represented by a characteristic value and a singular matrix of a singular value matrix, and sending the matrix subjected to singular value decomposition processing to the Lagrangian dual module;
3) the Lagrangian dual module is used for physical condition constraint generated in actual communication system transmission, in order to avoid inversion of a large-size precoding matrix of a beam forming matrix in an actual constraint scene, optimization mode processing is carried out on a cost function, the matrix obtained by the singular value decomposition module is used for strengthening dual and KKT conditions, and an obtained Lagrangian dual optimization result is used as a precoding result matrix.
2. The method according to claim 1, wherein the regularized zero-forcing module of step 1) comprises an interference zero-forcing mechanism of a precoding matrix, a beam vector orthogonalization mechanism, wherein:
1) the interference zero forcing mechanism is used for a high-complexity signal input matrix related to the multi-antenna technology, when the regular zero forcing step in a pre-coding module is reached, the input signal matrix with a larger size is transmitted to RZF for interference zero forcing processing, a main lobe of a beam vector is aligned to a target user signal to be transmitted, a zero value and a side lobe are aligned to an interference signal part, a certain weight value is respectively given to the main lobe and the side lobe, weighting selection processing is carried out, and the part of signals are transmitted to the beam vector orthogonalization mechanism module;
2) the beam vector orthogonalization mechanism is used for a group of combinations formed by phase delay or time delay and fixed weight, orthogonalizes the position beam of a sensor and the signal beam of a target user, optimizes the transmitted signal of precoding, and orthogonally selects the weighted signal to obtain a precoding matrix processed by a regularized zero forcing module:
W=HH(HHH+αI)-1。
3. the method of claim 1, wherein the generating singular value decomposition module of step 2) comprises: a real symmetric matrix, a non-real symmetric matrix in an actual scene, wherein,
1) the real symmetric matrix mechanism is used for mapping the pre-coded signals to a low-dimensional space after the input end signals are subjected to interference zero forcing processing, and decomposing the pre-coded matrix into an orthogonal matrix and an expression mode of a characteristic value under a common real symmetric matrix scene;
2) the non-real symmetric matrix under the actual scene is used for performing singular value decomposition on the beam forming matrix in the communication system under the condition that the precoding signal is the non-real symmetric matrix under the actual scene, performing characteristic value decomposition on the singular value matrix, and converting the singular value matrix into a dimensionality reduction signal matrix for screening out redundancy:
W=λ1u1v1 T+λ2u2v2 T+...+λNuNvN T。
4. the method according to claim 1, wherein the lagrangian dual module of step 3) comprises an original problem mechanism, a strong and weak dual mechanism, a KKT condition mechanism, wherein:
1) the original problem mechanism is used for processing the decomposition result of a singular value, performing constraint conditions on a cost function to process the transmission power limit of a base station side transmitting end, the total number of users capable of being intervened in a cell and the radiation range of the cell base station, performing generalized Lagrangian parameter maximization according to the actual scene constraint conditions, performing decomposition processing on the Lagrangian problem by using a dual function, and sending the optimization result under the constraint conditions to a strong and weak dual mechanism module;
2) the strong and weak dual mechanism module is used for solving an initial signal matrix with a large size, setting a lower bound on a constraint condition by using a Lagrangian dual function, strictly considering the constraint condition when the constraint condition tends to be strong dual, and setting the dual function as the equivalence of the target user number limitation problem and the base station transmitting end power problem;
3) the KKT condition mechanism is used for meeting the optimization problem of the Lagrangian function under the strict dual premise, bringing the beam constraint problem in the original input pre-coding signal and the zero point in the Lagrangian dual function into the KKT condition, simplifying the constraint condition to obtain a feasible domain, limiting the constraint condition limiting feasible solution of the situation-based discussion processing, and obtaining the pre-coding result under the actual scene.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115225130A (en) * | 2022-07-29 | 2022-10-21 | 国网四川省电力公司乐山供电公司 | Communication method, device and medium based on 5G beam forming technology |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102932806A (en) * | 2012-10-29 | 2013-02-13 | 电子科技大学 | Coordinated zero forcing beamforming method |
| US20170235316A1 (en) * | 2015-07-27 | 2017-08-17 | Genghiscomm Holdings, LLC | Airborne Relays in Cooperative-MIMO Systems |
| US20190089427A1 (en) * | 2015-06-17 | 2019-03-21 | Intel Corporation | Method for determining a precoding matrix and precoding module |
| CN110149127A (en) * | 2019-06-19 | 2019-08-20 | 南京邮电大学 | A kind of D2D communication system precoding vector optimization method based on NOMA technology |
-
2020
- 2020-06-02 CN CN202010491373.9A patent/CN113162664A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102932806A (en) * | 2012-10-29 | 2013-02-13 | 电子科技大学 | Coordinated zero forcing beamforming method |
| US20190089427A1 (en) * | 2015-06-17 | 2019-03-21 | Intel Corporation | Method for determining a precoding matrix and precoding module |
| US20170235316A1 (en) * | 2015-07-27 | 2017-08-17 | Genghiscomm Holdings, LLC | Airborne Relays in Cooperative-MIMO Systems |
| CN110149127A (en) * | 2019-06-19 | 2019-08-20 | 南京邮电大学 | A kind of D2D communication system precoding vector optimization method based on NOMA technology |
Non-Patent Citations (2)
| Title |
|---|
| LI JIALING 等: "Deep Learning-Based Massive MIMO CSI Feedback", 《IEEE》 * |
| 徐悦: "Massive MIMO系统中预编码技术的研究", 《硕士学位论文》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115225130A (en) * | 2022-07-29 | 2022-10-21 | 国网四川省电力公司乐山供电公司 | Communication method, device and medium based on 5G beam forming technology |
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