Communication optimization method and system for rate splitting dual-polarization laminated metasurface transceiver

Abstract

The invention relates to a communication optimization method and system for a rate splitting dual-polarization laminated metasurface transceiver, and a communication system based on a jammer, a transmitter based on a rate splitting dual-polarization laminated metasurface and a plurality of receivers based on the rate splitting dual-polarization laminated metasurface. A communication anti-interference system model for joint regulation and control of a signal space and a channel space is constructed, system transmission and rate maximization of a communication system are used as objective functions, and the communication anti-interference system model is constructed under the conditions of a non-ideal angle error of a wireless channel and an unknown cross polarization coefficient. An optimization problem model to be solved is constructed according to the total power threshold information of the transmitter and the user rate threshold information of the receiver by taking the information transmission rate requirement of the receiver, the maximum power constraint and the first dual-polarization metamaterial unit model as constraint conditions, and then the optimization problem model is solved respectively to realize communication optimization of the communication system.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a communication optimization method and system for a rate-splitting dual-polarization stacked metasurface transceiver. Background Art

[0002] The inherent openness of the wireless channel propagation environment makes wireless communications increasingly vulnerable to security impacts such as interference and information interception. Traditional anti-interference and anti-information interception security communication methods mainly include direct sequence spread spectrum, frequency hopping, adaptive power control, cooperative relay transmission, artificial noise and multi-antenna technology. The above-mentioned security communication methods are usually limited to the processing of the transceiver end. However, the fading of the wireless channel is uncontrollable and is also the fundamental path for interference injection and information interception. Therefore, it has become the main limiting factor for improving the security performance of wireless communication systems. Digital programmable intelligent metasurfaces enabled by information metamaterials use a large number of passive reflective elements integrated on the plane to intelligently configure the wireless propagation environment through software programming. It has great potential and application prospects in improving the ability of wireless communication security transmission. The communication anti-interference method based on the intelligent metasurface relay, transmitter and receiver has the potential to reconstruct the wireless channel, improve the channel diversity gain and increase the freedom of channel identification, respectively.

[0003] Channel space anti-interference technology can also provide degrees of freedom in the frequency domain, polarization domain, and power domain. Therefore, the anti-interference technology that combines signal space and channel space is expected to further increase the degrees of freedom of anti-interference space. How to use RIS (Reconfigurable Intelligence Surface) to dynamically and flexibly control the characteristics of electromagnetic waves, explore anti-interference technology for joint control of signal space and channel space, establish the intrinsic connection between signal space such as semantic space, polarization domain, and coding domain and channel space used for wireless channel control, meet the needs of wireless communication and anti-interference at the same time, break the traditional design thinking of stacking and combining anti-interference means, and design a communication anti-interference system covering signal waveform control, wireless channel reconstruction, high channel diversity gain, and high channel identification freedom is one of the key basic technical issues that need to be solved in this field. Summary of the invention

[0004] In view of the problems existing in the above-mentioned traditional technology, a communication optimization method of a rate-splitting dual-polarization stacked metasurface transceiver and a communication system are provided.

[0005] In order to achieve the above objectives, the embodiments of the present invention adopt the following technical solutions: On the one hand, a communication optimization method for a rate-splitting dual-polarization stacked metasurface transceiver is provided, which is applied to a communication system. The communication system includes a jammer, a transmitter based on the rate-splitting dual-polarization stacked metasurface, and multiple receivers based on the rate-splitting dual-polarization stacked metasurface. The jammer uses a dual-polarization omnidirectional antenna to transmit high-power suppression interference to interrupt the communication link between the transmitter and the receiver. The transmitter includes a transmitting dual-polarization RS processing module, a transmitting dual-polarization active antenna, and a transmitting stacked metasurface that are cascaded in sequence. The receiver includes a receiving stacked metasurface, a receiving dual-polarization active antenna, and a receiving dual-polarization RS processing module that are cascaded in sequence. The transmitting stacked metasurface wirelessly communicates with the receiving stacked metasurface through a dual-polarization channel. The transmitting dual-polarization active antenna and the receiving dual-polarization active antenna are both composed of a horizontally polarized element and a vertically polarized element arranged in sequence to form a uniform planar array. The communication optimization method comprises the steps of: Setting the total power threshold information of the transmitter and the user rate threshold information of the receiver; Taking the system transmission and rate maximization of the communication system as the objective function, the optimization problem model to be solved is constructed according to the total power threshold information of the transmitter and the user rate threshold information of the receiver; under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit module are used as the constraints of the optimization problem model; The non-ideal angle error parameters of the wireless channel are discretized and the unknown cross-polarization coefficients are processed. Then, the heuristic beam optimization algorithm is used to solve the optimization problem model to obtain the optimal receiving digital beamforming vector under different polarization directions. The optimization problem model is solved by using the dimension reduction dominated minimization algorithm to obtain the optimal transmit digital beamforming vector and the optimal broadcast rate coefficient vector under different polarization directions; Utilize based K The cyclic coordinate descent algorithm of the dimensional bisection method solves the optimization problem model and obtains the optimal transmit dual-polarization smart metasurface coefficient matrix and the optimal receive dual-polarization smart metasurface coefficient matrix; K is the number of receivers; The communication system after communication optimization is obtained by debugging the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization intelligent metasurface coefficient matrix and the optimal receiving dual-polarization intelligent metasurface coefficient matrix under different polarization directions.

[0006] On the other hand, a communication system is also provided, including a transmitter based on a rate-splitting dual-polarization stacked metasurface and a plurality of receivers based on the rate-splitting dual-polarization stacked metasurfaces, wherein a jammer uses a dual-polarization omnidirectional antenna to transmit high-power suppression interference to interrupt the communication link between the transmitter and the receiver, the transmitter includes a transmitting dual-polarization RS processing module, a transmitting dual-polarization active antenna, and a transmitting stacked metasurface that are cascaded in sequence, the receiver includes a receiving stacked metasurface, a receiving dual-polarization active antenna, and a receiving dual-polarization RS processing module that are cascaded in sequence, the transmitting stacked metasurface wirelessly communicates with the receiving stacked metasurface through a dual-polarization channel, and the transmitting dual-polarization active antenna and the receiving dual-polarization active antenna are both composed of a horizontally polarized element and a vertically polarized element arranged in sequence to form a uniform planar array; The communication system realizes communication optimization according to the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization smart metasurface coefficient matrix and the optimal receiving dual-polarization smart metasurface coefficient matrix under different polarization directions; wherein the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization smart metasurface coefficient matrix and the optimal receiving dual-polarization smart metasurface coefficient matrix under different polarization directions are obtained through the following steps: Setting the total power threshold information of the transmitter and the user rate threshold information of the receiver; Taking the system transmission and rate maximization of the communication system as the objective function, the optimization problem model to be solved is constructed according to the total power threshold information of the transmitter and the user rate threshold information of the receiver; under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit module are used as the constraints of the optimization problem model; The non-ideal angle error parameters of the wireless channel are discretized and the unknown cross-polarization coefficients are processed. Then, the heuristic beam optimization algorithm is used to solve the optimization problem model to obtain the optimal receiving digital beamforming vector under different polarization directions. The optimization problem model is solved by using the dimension reduction dominated minimization algorithm to obtain the optimal transmit digital beamforming vector and the optimal broadcast rate coefficient vector under different polarization directions; Utilize based K The cyclic coordinate descent algorithm of the dimensional bisection method solves the optimization problem model and obtains the optimal transmit dual-polarization smart metasurface coefficient matrix and the optimal receive dual-polarization smart metasurface coefficient matrix; K is the number of receivers.

[0007] One of the above technical solutions has the following advantages and beneficial effects: The communication optimization method and system of the rate-splitting dual-polarization stacked metasurface transceiver mentioned above, based on a communication system of a jammer, a transmitter based on a rate-splitting dual-polarization stacked metasurface, and multiple receivers based on a rate-splitting dual-polarization stacked metasurface, constructs a communication anti-interference system model with joint regulation of signal space and channel space, takes system transmission and rate maximization of the communication system as the objective function, and takes the information transmission rate requirements, maximum power constraints and dual-polarization metamaterial unit module 1 of the receiver as constraints under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient. According to the total power threshold information of the transmitter and the user rate threshold information of the receiver, an optimization problem model to be solved is constructed, and then the optimization problem model is solved respectively to obtain the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization intelligent metasurface coefficient matrix and the optimal receiving dual-polarization intelligent metasurface coefficient matrix under different polarization directions, so as to realize communication optimization of the communication system.

[0008] Compared with traditional technologies, the above scheme includes system model design and robust optimization algorithm, combines signal space and channel space degrees of freedom, designs a communication anti-interference transceiver architecture with signal waveform control capability, high channel diversity gain and high channel identification freedom, and proposes a dimensionality reduction-dominated minimization and K The cyclic coordinate descent algorithm of the N+1-dimensional dichotomy method provides theoretical support for realizing the "N+1-dimensional" endogenous anti-interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the conventional technology, the drawings required for use in the embodiments or the conventional technology descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0010] Figure 1 A schematic flow chart of a communication optimization method for a rate-splitting dual-polarization stacked metasurface transceiver in one embodiment; Figure 2 A communication anti-interference system model based on RS-DPSM combination in one embodiment; Figure 3 A schematic diagram of the RS-DPSM transceiver architecture in one embodiment; Figure 41 is a part of the normalized beam pattern in an embodiment, (a) is the broadcast beam of the RS-DPSM transmitter on v, (b) is the unicast beam of the RS-DPSM transmitter on h, (c) is the broadcast beam of the RS-DPRIS transmitter on v, and (d) is the unicast beam of the RS-DPRIS transmitter on h; Figure 5 1 is another part of the normalized beam pattern in an embodiment, (e) is the broadcast beam of the RS-DPMIMO transmitter on v, (f) is the unicast beam of the RS-DPMIMO transmitter on h, (g) is the receiving beam of the RS-DPSM transmitter on v, and (h) is the receiving beam of the RS-DPRIS transmitter on v; Figure 6 The relationship between the transmission rate and the number of each metasurface unit in one embodiment; Figure 7 is a relationship between the transmission sum rate and the XPD coefficient of the communication channel in one embodiment; Figure 8 is a relationship between the transmission sum rate and the interference channel angle uncertainty in one embodiment; Fig. 9 is a relationship between a transmission sum rate and a signal to interference noise ratio in one embodiment; Fig.10 FIG. 1 is a schematic diagram of the architecture of a communication system in an embodiment. DETAILED DESCRIPTION

[0011] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the accompanying drawings and Examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art of the present invention. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0012] It should be noted that the reference to "embodiment" in this article means that the specific features, structures or characteristics described in conjunction with the embodiment may be included in at least one embodiment of the present invention. The presentation of this phrase at various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It will be appreciated by those skilled in the art that the embodiments described herein may be combined with other embodiments. The term "and / or" used in the specification of the present invention and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0013] The following will describe the implementation of the present invention in detail with reference to the accompanying drawings in the embodiment diagram of the present invention.

[0014] In one embodiment, a communication optimization method for a rate-splitting dual-polarization stacked metasurface transceiver is provided, which is applied to a communication system. The communication system includes a jammer, a transmitter based on the rate-splitting dual-polarization stacked metasurface, and a plurality of receivers based on the rate-splitting dual-polarization stacked metasurface. The jammer uses a dual-polarization omnidirectional antenna to transmit high-power suppression interference to interrupt the communication link between the transmitter and the receiver. The transmitter includes a transmitting dual-polarization RS processing module, a transmitting dual-polarization active antenna, and a transmitting stacked metasurface that are cascaded in sequence. The receiver includes a receiving stacked metasurface, a receiving dual-polarization active antenna, and a receiving dual-polarization RS processing module that are cascaded in sequence. The transmitting stacked metasurface wirelessly communicates with the receiving stacked metasurface through a dual-polarization channel. The transmitting dual-polarization active antenna and the receiving dual-polarization active antenna are both composed of a horizontally polarized element and a vertically polarized element arranged in sequence to form a uniform planar array. like Figure 1 As shown, the above communication optimization method may include the following processing steps S10 to S20: S10, setting the total power threshold information of the transmitter and the user rate threshold information of the receiver; S12, taking the system transmission and rate maximization of the communication system as the objective function, constructing the optimization problem model to be solved according to the total power threshold information of the transmitter and the user rate threshold information of the receiver; under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, taking the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit module as the constraint conditions of the optimization problem model; S14, discretizing the non-ideal angle error parameters of the wireless channel and processing the unknown cross-polarization coefficients, and then using the heuristic beam optimization algorithm to solve the optimization problem model to obtain the optimal receiving digital beamforming vectors under different polarization directions; S16, solving the optimization problem model using a dimensionality reduction dominated minimization algorithm to obtain the optimal transmit digital beamforming vector and the optimal broadcast rate coefficient vector under different polarization directions; S18, using K The cyclic coordinate descent algorithm of the dimensional bisection method solves the optimization problem model and obtains the optimal transmit dual-polarization smart metasurface coefficient matrix and the optimal receive dual-polarization smart metasurface coefficient matrix; K is the number of receivers; S20, debugging the communication system after communication optimization according to the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization intelligent supersurface coefficient matrix and the optimal receiving dual-polarization intelligent supersurface coefficient matrix under different polarization directions.

[0015] The communication optimization method of the rate-splitting dual-polarization stacked metasurface transceiver mentioned above is based on a communication system of a jammer, a transmitter based on a rate-splitting dual-polarization stacked metasurface, and multiple receivers based on a rate-splitting dual-polarization stacked metasurface. A communication anti-interference system model with joint control of signal space and channel space is constructed. The objective function is to maximize the system transmission and rate of the communication system. Under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit module are used as constraints. According to the total power threshold information of the transmitter and the user rate threshold information of the receiver, an optimization problem model to be solved is constructed. Then, the optimization problem model is solved respectively to obtain the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization intelligent metasurface coefficient matrix and the optimal receiving dual-polarization intelligent metasurface coefficient matrix under different polarization directions, so as to realize the communication optimization of the communication system.

[0016] Compared with traditional technologies, the above scheme includes system model design and robust optimization algorithm, combines signal space and channel space degrees of freedom, designs a communication anti-interference transceiver architecture with signal waveform control capability, high channel diversity gain and high channel identification freedom, and proposes a dimensionality reduction-dominated minimization and K The cyclic coordinate descent algorithm of the N+1-dimensional dichotomy method provides theoretical support for realizing the "N+1-dimensional" endogenous anti-interference.

[0017] It can be understood that the communication optimization method of the rate splitting dual-polarization stacked metasurface transceiver provided can be applied to Figure 2 In the application environment shown in FIG. 1 , the proposed rate splitting dual-polarized stacked metasurface (RS-DPSM) transceiver is shown in FIG. Figure 3 As shown, its architecture includes a transmitting dual-polarization RS processing module, a transmitting dual-polarization active antenna, a transmitting stacked metasurface, a receiving stacked metasurface, a receiving dual-polarization active antenna and a receiving dual-polarization RS processing module.

[0018] In one embodiment, the transmitting dual-polarized RS processing module includes a cascaded information splitting unit, an information merging unit, an information encoding unit, and a dual-polarized digital beamforming unit, wherein the information splitting unit is used to split the uncoded transmission information sequence into transmission broadcast information and transmission unicast information, the information merging unit is used to merge all transmission broadcast information into a single super broadcast information, the information encoding unit is used to encode the super broadcast information and the transmission unicast information into transmission symbols respectively, and the dual-polarized digital beamforming unit is used to perform beamforming on the two transmission symbols in different polarization directions. The receiving dual-polarized RS processing module is used to implement the inverse process of the transmitting dual-polarized RS processing module.

[0019] Specifically, the transmitting dual-polarization RS processing module is mainly composed of module units such as an information splitting unit, an information merging unit, an information encoding unit, and a dual-polarization digital beamforming unit, wherein the information splitting unit is used to split the uncoded transmission information sequence into transmission broadcast information and transmission unicast information, the information merging unit is used to merge all transmission broadcast information into a single super broadcast information for decoding by all receivers, the information encoding unit is used to encode the super broadcast information and the transmission unicast information into transmission symbols, and the dual-polarization digital beamforming unit is mainly used to beamform the transmission symbols corresponding to the two types of information in different polarization directions, thereby avoiding crosstalk between the two transmission symbols. The receiving dual-polarization RS processing module is the inverse process of the transmitting dual-polarization RS processing module, and also mainly includes module units such as a dual-polarization digital beamforming unit, an information decoding unit, an information splitting unit, and an information merging unit.

[0020] Both the transmitting dual-polarization active antenna and the receiving dual-polarization active antenna are composed of a horizontally polarized element and a vertically polarized element arranged in sequence to form a uniform planar array, while both the transmitting stacked metasurface and the receiving stacked metasurface are composed of multiple layers of metasurfaces stacked between the transmitting dual-polarization active antenna and the receiving dual-polarization active antenna to form a cascade structure. Since each dual-polarization metamaterial unit in the transmitting stacked metasurface and the receiving stacked metasurface is controlled by two controllers, and each controller independently controls the electromagnetic wave characteristics in one polarization direction, a dual-polarization metamaterial unit can be regarded as a combination of two single-polarization metamaterial units, thereby improving the channel diversity gain and channel identification freedom without increasing the aperture size.

[0021] In one embodiment, multiple receivers zero-stuck interference and decode communication signals, achieving joint regulation of signal space and channel space, effectively suppressing mutual interference between nodes while improving anti-interference performance.

[0022] For the convenience of discussion, K Indicates the number of receivers. N L = N L1× N L2 Indicates the number of transmitting dual-polarization active antennas, N U,k = N U,k1 × N U,k2 Indicates k The number of dual-polarization active antennas for each receiver, N L1 It indicates the number of units placed along the horizontal direction of the transmitting dual-polarized antenna array. N L2 It indicates the number of units placed along the longitudinal direction of the transmitting dual-polarized antenna array. N U,k1 Indicates k The number of units placed horizontally on the dual-polarized antenna array of a receiver, N U,k2 Indicates k The number of units placed along the longitudinal direction of the dual-polarized antenna array of the receiver; the symbol v represents the vertical polarization direction and the symbol h represents the horizontal polarization direction. In addition, it is assumed that the transmitting stacked metasurface (which can be recorded as Tx-DPSM) and the k The receiving stacked metasurface (which can be recorded as Rx-DPSM) is composed of an A-layer dual-polarization metasurface and an R-layer dual-polarization metasurface, and the Tx-DPSM a Layer M L,a = M L,a1 × M L,a2 Dual-polarization metamaterial unit and Rx-DPSM r Layer M U,kr = M U,kr1 × M U,kr2 dual-polarization metamaterial unit, where M L,a1 Indicates Tx-DPSM a The number of units placed along the horizontal direction of the layer array surface, M L,a2 Indicates Tx-DPSM a The number of units placed along the longitudinal direction of the layer array surface, M U,kr1 Indicates k Rx-DPSM r The number of units placed along the horizontal direction of the layer array surface, M U,kr2 Indicates k Rx-DPSM r The number of units placed along the longitudinal direction of the layer array surface,k Not greater than K A positive integer, a is a positive integer not greater than A, r is a positive integer not greater than R.

[0023] In the RS-DPSM transmitter, the information sequence is first sent M k Split into broadcast information M C，k and unicast information M P，k Then, each broadcast information M C，1 ,…, M C，K Merge into a single super broadcast message M C , which is then encoded into the transmission symbol of the broadcast information S C At the same time, each unicast information M P，1 ,…, M P，K Transmission symbols encoded into unicast information S P，1 ,…, S P，K Next, the transmission symbol S C and S P，1 ,…, S P，K Digital beamforming is performed in different polarization directions, i.e. ,in and denote the transmit digital beamforming vectors in the v and h polarization directions, respectively.

[0024] The steps of the communication optimization method may be as follows: Step 1: Set the total power threshold information of the transmitter P max And user rate threshold information R k,min .

[0025] Step 2: Take the system transmission and rate maximization as the objective function, where k The information received by each RS-DPSM receiver includes broadcast information M C Unicast Information M P，k , the non-ideal angle error in the wireless channel Under the condition of unknown cross-polarization coefficient O, the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit mode 1 are taken as constraints, and the optimization problem is constructed with the goal of maximizing system transmission and rate. The receiving digital beamforming vectors under different polarization directions are designed by joint optimization. and , the broadcast rate coefficient vector and transmit digital beamforming vector and , and the transmit dual-polarization RIS coefficient matrix And receive dual polarization RIS coefficient matrix is the optimization variable. The optimization problem model to be solved is constructed as follows: ; in, Indicates k The transmission rate of the partial broadcast information corresponding to each RS-DPSM receiver is R P , k Indicates k The achievable transmission rate of unicast information for each RS-DPSM receiver is R C , k Indicates k The achievable transmission rate of the total broadcast information of each RS-DPSM receiver is n Indicates the unit number. C 1 to C 4 represent the constraints respectively.

[0026] Step 3: Convert the wireless channel non-ideal angle error The parameters are discretized and the unknown cross-polarization coefficient O is processed. Then, the heuristic beam optimization algorithm is used to solve the optimization problem and obtain the optimal receiving digital beamforming vector.

[0027] Specifically, the LMMSE (Linear Minimum Mean Square Error Estimation) criterion is used to optimize the receiving digital beamforming vector and ,have: ; Among them, the intermediate variables are as follows: ; ; ; ; ; ;

[0028] in, and represents the Rx-DPSM equivalent phase shift coefficient matrix, and represents the jammer power, and represents the shared channel coefficient in the interference channel, and represents the far-field channel in the transmission channel, and represents the Tx-DPSM equivalent phase shift coefficient matrix. However, due to and There is a non-ideal angle error in the wireless channel And the unknown cross-polarization coefficient O, so it cannot be directly solved by the above formula and , and represents the noise power in the two polarization directions, represents the identity matrix. By uniform discretization Continuous angles in and ,Right now: .

[0029] in, and Represents the azimuth angle and elevation The number of sampling points can be used to obtain the interference channel Worst case CSI (channel state information) ,have: ; in, for The corresponding discretization .

[0030] Then, the unknown cross-polarization coefficient O is processed using the quadratic function property, and the worst-case XPD (cross-polarization discrimination) coefficient is for: ; Based on this, Convert to , the worst-case receive digital beamforming vector can be obtained and Closed-form solution: ; Among them, the intermediate variables are as follows:

[0031] In one embodiment, step 4: using a dimensionality reduction dominated minimization algorithm to solve the optimization problem to obtain the optimal transmit digital beamforming vector and , and the broadcast rate coefficient vector That is, in the process of solving the optimization problem model using the dimensionality reduction dominated minimization algorithm, the high-dimensional optimization variables to be optimized are reduced in dimension using the low-dimensional subspace, and the objective function is approximated by the MM algorithm and converted into a convex quadratic constrained quadratic programming problem.

[0032] Specifically, in solving the receiving digital beamforming vectors in two polarization directions and Afterwards, the broadcast rate coefficient vector and transmit digital beamforming vector and For optimization, the corresponding optimization sub-problem can be mathematically expressed as:

[0033] However, the above optimization sub-problems also have , non-convex objective function, high-dimensional optimization variables and multiple constraints make it difficult to solve. Therefore, for the above problem, we first use the method in step 3 to remove the optimization subproblem Then, and The expression is converted into an equivalent form to facilitate the subsequent processing of its non-convexity, the dimension of the optimization variable, and multiple constraints, namely: ; ; Thus, the high-dimensional optimization variables can be and Reduce the dimension to a low-dimensional variable. Specifically, for and , which can be represented by their low-dimensional subspace and Linear representation, that is and ,in, and represents a unique solution. In addition, the low-dimensional subspace with full row rank and It can be further expressed as: ; in, .

[0034] Based on this, the optimization variables and Transformed into and Therefore, the optimization subproblem is equivalently converted to: ; in, Indicates that and Constraints C Although the dimension of the optimization variables has been significantly reduced, the optimization subproblem is still difficult to solve due to multiple constraints. To address this problem, the full power property is proposed to remove the maximum power constraint. .

[0035] Due to the constraints The equality condition is satisfied at the optimal solution, that is, the transmit beam power is equal to the maximum transmit power. Therefore, the optimization sub-problem can be transformed into: ; In the formula, Indicates that middle Replace with In addition, The expression is: ; in, , . Using the solution of the optimization subproblem and ,pass and Obtain the solution to the original optimization subproblem, where is the conversion factor.

[0036] However, the non-convex and The expression makes the optimization subproblem still unsolvable. Therefore, the MM (Majorization-Minimization) algorithm is used to approximate and ,have: ; ; in, ;

[0037] Then, we can let the two intermediate variables and , so that and It can be further simplified to and .also, and It can be further decomposed into: ; Among them, the intermediate variables can be as follows: ; ;

[0038] Therefore, we can get and middle and The equivalent form is as follows: ; Substituting these two formulas into the above optimization subproblem of this step and discarding the constant term, the optimization subproblem can be restated as: ; in, ,and: ; This low-complexity QCQP (Quadratic Constrained Quadratic Programming) problem can be solved using CVX (a commonly used Matlab convex optimization solver), and then used and Obtaining the optimal transmit digital beamforming vector and and the broadcast rate coefficient vector .

[0039] Step 5: Utilize K The optimal transmit dual-polarization RIS coefficient matrix is ​​obtained by using the cyclic coordinate descent algorithm of the dimensional bisection method. And receive dual polarization RIS coefficient matrix .

[0040] Specifically, first optimize the transmit dual-polarization RIS coefficient matrix .make and ,against The optimization sub-problem is:

[0041] Using matrix transformation, the The optimization subproblem can be equivalently converted to:

[0042] Next, using the Lagrange multiplier and The constraints and Introducing the above In the objective function of the optimization sub-problem, there are: ; in, .

[0043] Then use the CCD (conjugate gradient method) algorithm to solve the The optimization sub-problem of is as follows: First Divide optimization variable; in In the iteration process, first let The solution obtained in the previous iteration , and then update middle variables ; Finally, alternate optimization is performed until convergence to a stable solution. Specifically, First, it can be expanded to: ; in, From this we can get Optimization variables , and then updated by the following CCD algorithm: ; Among them, update middle variables The optimization subproblem can be expressed as: ; Obviously, according to the properties of conjugate function, we can get the update The closed-form solution of is: ; However, there is still a problem in this optimization subproblem: how to solve the optimal Lagrange multiplier and Here is the question. K Dimensional bisection to search for the optimal and , that is, use the bisection method to search for a Lagrange multiplier in turn, and finally alternately search to converge to the optimal solution. The optimization problem of the optimal Lagrange multiplier is ; in, and As shown in the optimal Lagrangian multiplier optimization subproblem above. Then, the optimal Lagrangian multiplier optimization problem is searched through the following steps to obtain and ,Right now: like , .like , .

[0044] like , .like , .

[0045] Otherwise, due to and About , A monotonically decreasing function can be searched using binary search and .

[0046] Through the above CCD algorithm and K Dimensional bisection alternating optimization and , , we can get the optimal transmit dual-polarization RIS coefficient matrix .

[0047] In some embodiments, Figure 4 and Figure 5As shown in the figure, the normalized beam patterns of different transceiver architectures in the vertical and horizontal polarization directions are given, (a) is the broadcast beam of the RS-DPSM transmitter on v, (b) is the unicast beam of the RS-DPSM transmitter on h, (c) is the broadcast beam of the RS-DPRIS transmitter on v, (d) is the unicast beam of the RS-DPRIS transmitter on h, (e) is the broadcast beam of the RS-DPMIMO transmitter on v, (f) is the unicast beam of the RS-DPMIMO transmitter on h, (g) is the receiving beam of the RS-DPSM transmitter on v, and (h) is the receiving beam of the RS-DPRIS transmitter on v. The following conclusions can be drawn: First, all unicast beams can aim the maximum beam direction at the target receiver (i.e., receiver Rx1), but due to the strong correlation between the receiver channels, the unicast beam can only produce a null in the area where the receiver Rx3 is located, causing serious mutual interference to the receiver Rx2. Secondly, thanks to the application of the dual-polarization RS module, the transmitter generates a broadcast beam aimed at all receivers, which greatly suppresses the mutual interference between nodes. In addition, the receiver can aim the receiving beam at the transmitter Tx area, and at the same time produce a null of at least -50dB in the jammer area, which verifies the effectiveness of the interference null of the architecture proposed in this specification. Finally, the beam amplitude and null depth generated by the RS-DPSM transceiver are about 10dB larger than those of other comparative architectures, indicating that its transmitter channel diversity gain and receiver channel identification freedom are further improved.

[0048] like Figure 6 As shown, the transmission rate and the number of metamaterial units in each layer are given. M The relationship between RS-SPSM and RS-DPRIS is a rate-splitting single-polarization stacked metasurface, RS-DPRIS is a rate-splitting single-polarization single-layer metasurface, NoRS-DPSM is a rate-splitting dual-polarization stacked metasurface, and RS-DPMIMO is a rate-splitting dual-polarization stacked multiple-input multiple-output system. The following conclusions can be drawn: First, the transmission and rate are proportional to M This is because the increase M It will improve the channel diversity gain and channel identification freedom; secondly, the communication anti-interference performance based on RS-DPSM combination is significantly better than other comparison schemes, which shows that the method proposed in this specification significantly improves the signal space and channel space freedom, and achieves better communication anti-interference performance; finally, with M As the number of variables increases, the performance gap between the method proposed in this specification and the SCA (Continuous Convex Approximation)-CCP algorithm becomes larger and larger. This is because the SCA-CCP algorithm will fall into a suboptimal solution when there are multiple high-dimensional variables and constraints. This further verifies the effectiveness of the method proposed in this specification.

[0049] like Figure 7As shown, the transmission rate and communication channel XPD coefficient are given It can be found that due to the crosstalk caused by cross polarization, all dual-polarization anti-interference systems decreases with the increase of However, thanks to the adjustment capability of RS in the power domain, this specification can select a better polarization channel based on RS-DPSM joint communication anti-interference to avoid the performance loss caused by the XPD effect, and at the same time, combined with its higher channel diversity gain and channel identification freedom, it can achieve higher transmission and rate.

[0050] like Figure 8 As shown in the figure, the relationship between the transmission sum rate and the interference channel angle uncertainty is given. It can be seen that the transmission sum rate increases with the non-ideal angle error of the wireless channel. The increase of the communication interference reduction is reduced, and the communication interference prevention based on RS-DPSM combined in this specification can achieve a higher transmission rate than other schemes. In addition, the communication interference prevention based on RS-SPSM combined is affected by The influence of communication interference is great, and the communication anti-interference given in this manual almost maintains The above results show that the communication anti-interference based on RS-DPSM can utilize the signal-channel spatial freedom to suppress mutual interference while resisting interference attacks, so it has strong robustness. In addition, it can be seen that the performance gap between SCA-CCP and the method proposed in this specification increases with This is because the SCA-CCP algorithm introduces multiple auxiliary variables and obtains a suboptimal solution of the DPSM beamforming matrix vector through CVX, making it difficult to It has strong robustness when it increases, and the method proposed in this specification directly obtains the optimal closed-form solution of the optimization variable, which has strong robustness.

[0051] like Fig. 9 As shown in the figure, the relationship between the transmission sum rate and the signal to interference noise ratio (SJNR) is given. The following conclusions can be drawn: First, the transmission sum rate of all schemes decreases as the signal to interference noise ratio decreases; second, the anti-interference performance of the communication based on RS-DPSM joint is more robust at low signal to interference noise ratio, because DPSM brings higher channel diversity gain and channel identification freedom; finally, as the signal to interference noise ratio decreases, the performance gap between the method proposed in this specification and the SCA-CCP algorithm becomes larger and larger, because the SCA-CCP algorithm directly optimizes the entire P, while the RMM-CCD proposed in this specification obtains the optimal closed-form solution for each optimization variable in P.

[0052] It should be understood that although Figure 2 and Figure 3The steps in the method are shown in sequence as indicated by the arrows, but the steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of the steps, and the steps can be executed in other orders. Figure 2 and Figure 3 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequentially, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0053] In one embodiment, Fig.10 As shown, a communication system 100 is provided, which may include a transmitter based on a rate-splitting dual-polarization stacked metasurface and multiple receivers based on a rate-splitting dual-polarization stacked metasurface, wherein a jammer uses a dual-polarization omnidirectional antenna to transmit high-power suppression interference to interrupt the communication link between the transmitter and the receiver, the transmitter includes a transmitting dual-polarization RS processing module, a transmitting dual-polarization active antenna, and a transmitting stacked metasurface that are cascaded in sequence, the receiver includes a receiving stacked metasurface, a receiving dual-polarization active antenna, and a receiving dual-polarization RS processing module that are cascaded in sequence, the transmitting stacked metasurface communicates wirelessly with the receiving stacked metasurface through a dual-polarization channel, and the transmitting dual-polarization active antenna and the receiving dual-polarization active antenna are both composed of a horizontal polarization element and a vertical polarization element arranged in sequence to form a uniform planar array. The communication system realizes communication optimization according to the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization intelligent metasurface coefficient matrix, and the optimal receiving dual-polarization intelligent metasurface coefficient matrix under different polarization directions. Among them, the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization smart metasurface coefficient matrix and the optimal receiving dual-polarization smart metasurface coefficient matrix under different polarization directions are obtained through the following steps: Setting the total power threshold information of the transmitter and the user rate threshold information of the receiver; Taking the system transmission and rate maximization of the communication system as the objective function, the optimization problem model to be solved is constructed according to the total power threshold information of the transmitter and the user rate threshold information of the receiver; under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit module are used as the constraints of the optimization problem model; The non-ideal angle error parameters of the wireless channel are discretized and the unknown cross-polarization coefficients are processed. Then, the heuristic beam optimization algorithm is used to solve the optimization problem model to obtain the optimal receiving digital beamforming vector under different polarization directions. The optimization problem model is solved by using the dimension reduction dominated minimization algorithm to obtain the optimal transmit digital beamforming vector and the optimal broadcast rate coefficient vector under different polarization directions; Utilize based K The cyclic coordinate descent algorithm of the dimensional bisection method solves the optimization problem model and obtains the optimal transmit dual-polarization smart metasurface coefficient matrix and the optimal receive dual-polarization smart metasurface coefficient matrix; K is the number of receivers.

[0054] The above-mentioned communication system 100, based on a jammer, a transmitter based on a rate-splitting dual-polarization stacked metasurface, and a communication system of multiple receivers based on a rate-splitting dual-polarization stacked metasurface, constructs a communication anti-interference system model with joint control of signal space and channel space, takes the system transmission and rate maximization of the communication system as the objective function, and under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, takes the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit module as constraints, and constructs an optimization problem model to be solved according to the total power threshold information of the transmitter and the user rate threshold information of the receiver, and then solves the optimization problem model respectively to obtain the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization intelligent metasurface coefficient matrix and the optimal receiving dual-polarization intelligent metasurface coefficient matrix under different polarization directions, so as to realize communication optimization of the communication system.

[0055] Compared with traditional technologies, the above scheme includes system model design and robust optimization algorithm, combines signal space and channel space degrees of freedom, designs a communication anti-interference transceiver architecture with signal waveform control capability, high channel diversity gain and high channel identification freedom, and proposes a dimensionality reduction-dominated minimization and K The cyclic coordinate descent algorithm of the N+1-dimensional dichotomy method provides theoretical support for realizing the "N+1-dimensional" endogenous anti-interference.

[0056] In one embodiment, the transmit dual-polarized RS processing module includes a cascaded information splitting unit, an information merging unit, an information encoding unit, and a dual-polarized digital beamforming unit, wherein the information splitting unit is used to split an uncoded transmission information sequence into transmission broadcast information and transmission unicast information, the information merging unit is used to merge all transmission broadcast information into a single super broadcast information, the information encoding unit is used to encode the super broadcast information and the transmission unicast information into transmission symbols, respectively, and the dual-polarized digital beamforming unit is used to perform beamforming on the two transmission symbols in different polarization directions; The receiving dual-polarization RS processing module is used to implement the inverse process of the transmitting dual-polarization RS processing module.

[0057] In one embodiment, a plurality of receivers null out interference and decode the communication signal.

[0058] In one embodiment, in the process of solving the optimization problem model using the dimensionality reduction dominated minimization algorithm, the high-dimensional optimization variables to be optimized are reduced in dimension using a low-dimensional subspace, and the objective function is approximated by the MM algorithm and then converted into a convex quadratic constrained quadratic programming problem.

[0059] It can be understood that for the specific limitations of the communication system 100, reference can be made to the corresponding limitations of the communication optimization method of the rate-splitting dual-polarization stacked metasurface transceiver mentioned above, which will not be repeated here.

[0060] A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus dynamic random access memory (RambusDRAM, referred to as RDRAM) and interface dynamic random access memory (DRDRAM).

[0061] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0062] The above embodiments only express several implementation methods of the present invention, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of protection of the invention. It should be pointed out that, for those of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the attached claims.

Claims

1. A communication optimization method for a rate-splitting dual-polarization stacked metasurface transceiver, characterized in that: Applied to a communication system, the communication system includes a jammer, a transmitter based on a rate-splitting dual-polarization stacked metasurface, and a plurality of receivers based on the rate-splitting dual-polarization stacked metasurfaces, the jammer uses a dual-polarization omnidirectional antenna to transmit high-power suppression interference to interrupt the communication link between the transmitter and the receiver, the transmitter includes a transmitting dual-polarization RS processing module, a transmitting dual-polarization active antenna, and a transmitting stacked metasurface that are cascaded in sequence, the receiver includes a receiving stacked metasurface, a receiving dual-polarization active antenna, and a receiving dual-polarization RS processing module that are cascaded in sequence, the transmitting stacked metasurface wirelessly communicates with the receiving stacked metasurface through a dual-polarization channel, and the transmitting dual-polarization active antenna and the receiving dual-polarization active antenna are both composed of a horizontally polarized element and a vertically polarized element arranged in sequence to form a uniform planar array; The communication optimization method comprises the steps of: Setting the total power threshold information of the transmitter and the user rate threshold information of the receiver; Taking the system transmission and rate maximization of the communication system as the objective function, constructing an optimization problem model to be solved according to the total power threshold information of the transmitter and the user rate threshold information of the receiver; Under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit module are used as the constraints of the optimization problem model; Discretizing the non-ideal angle error parameters of the wireless channel and processing the unknown cross-polarization coefficients, and then using a heuristic beam optimization algorithm to solve the optimization problem model to obtain optimal receiving digital beamforming vectors under different polarization directions; The optimization problem model is solved by using a dimensionality reduction dominated minimization algorithm to obtain an optimal transmit digital beamforming vector and an optimal broadcast rate coefficient vector under different polarization directions; Utilize based K The optimization problem model is solved by a cyclic coordinate descent algorithm of a dimensional bisection method to obtain an optimal transmit dual-polarization smart metasurface coefficient matrix and an optimal receive dual-polarization smart metasurface coefficient matrix; K is the number of receivers; The communication system after communication optimization is obtained by debugging the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization intelligent supersurface coefficient matrix and the optimal receiving dual-polarization intelligent supersurface coefficient matrix under different polarization directions.

2. The communication optimization method of the rate splitting dual-polarization stacked metasurface transceiver according to claim 1 is characterized in that: The transmit dual-polarized RS processing module includes a cascaded information splitting unit, an information merging unit, an information encoding unit and a dual-polarized digital beamforming unit, wherein the information splitting unit is used to split an uncoded transmission information sequence into transmission broadcast information and transmission unicast information, the information merging unit is used to merge all transmission broadcast information into a single super broadcast information, the information encoding unit is used to encode the super broadcast information and the transmission unicast information into transmission symbols respectively, and the dual-polarized digital beamforming unit is used to perform beamforming on the two transmission symbols in different polarization directions; The receiving dual-polarization RS processing module is used to implement the inverse process of the transmitting dual-polarization RS processing module.

3. The communication optimization method of the rate splitting dual-polarization stacked metasurface transceiver according to claim 1 or 2, characterized in that: A plurality of said receivers null out interference and decode the communication signal.

4. The communication optimization method of the rate splitting dual-polarization stacked metasurface transceiver according to claim 1 is characterized in that: In the process of solving the optimization problem model using the dimensionality reduction dominated minimization algorithm, the high-dimensional optimization variables to be optimized are reduced in dimension using the low-dimensional subspace, and the objective function is approximated by the MM algorithm and then converted into a convex quadratic constrained quadratic programming problem.

5. A communication system, characterized in that: The communication system includes a transmitter based on a rate-splitting dual-polarization stacked metasurface and a plurality of receivers based on a rate-splitting dual-polarization stacked metasurface, wherein a jammer uses a dual-polarization omnidirectional antenna to transmit high-power suppression interference to interrupt the communication link between the transmitter and the receiver, the transmitter includes a transmitting dual-polarization RS processing module, a transmitting dual-polarization active antenna, and a transmitting stacked metasurface that are cascaded in sequence, the receiver includes a receiving stacked metasurface, a receiving dual-polarization active antenna, and a receiving dual-polarization RS processing module that are cascaded in sequence, the transmitting stacked metasurface wirelessly communicates with the receiving stacked metasurface through a dual-polarization channel, and the transmitting dual-polarization active antenna and the receiving dual-polarization active antenna are both composed of a horizontally polarized element and a vertically polarized element arranged in sequence to form a uniform planar array; The communication system realizes communication optimization according to the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization smart metasurface coefficient matrix and the optimal receiving dual-polarization smart metasurface coefficient matrix under different polarization directions; wherein the optimal receiving digital beamforming vector, the optimal transmitting digital beamforming vector, the optimal broadcast rate coefficient vector, the optimal transmitting dual-polarization smart metasurface coefficient matrix and the optimal receiving dual-polarization smart metasurface coefficient matrix under different polarization directions are obtained by the following steps: Setting the total power threshold information of the transmitter and the user rate threshold information of the receiver; Taking the system transmission and rate maximization of the communication system as the objective function, constructing an optimization problem model to be solved according to the total power threshold information of the transmitter and the user rate threshold information of the receiver; under the conditions of non-ideal angle error of the wireless channel and unknown cross-polarization coefficient, taking the information transmission rate requirement of the receiver, the maximum power constraint and the dual-polarization metamaterial unit model as the constraint conditions of the optimization problem model; Discretizing the non-ideal angle error parameters of the wireless channel and processing the unknown cross-polarization coefficients, and then using a heuristic beam optimization algorithm to solve the optimization problem model to obtain optimal receiving digital beamforming vectors under different polarization directions; The optimization problem model is solved by using a dimensionality reduction dominated minimization algorithm to obtain an optimal transmit digital beamforming vector and an optimal broadcast rate coefficient vector under different polarization directions; Utilize based K The optimization problem model is solved by a cyclic coordinate descent algorithm of a dimensional bisection method to obtain an optimal transmit dual-polarization smart metasurface coefficient matrix and an optimal receive dual-polarization smart metasurface coefficient matrix; K is the number of the receivers.

6. The communication system according to claim 5, characterized in that: The transmit dual-polarized RS processing module includes a cascaded information splitting unit, an information merging unit, an information encoding unit and a dual-polarized digital beamforming unit, wherein the information splitting unit is used to split an uncoded transmission information sequence into transmission broadcast information and transmission unicast information, the information merging unit is used to merge all transmission broadcast information into a single super broadcast information, the information encoding unit is used to encode the super broadcast information and the transmission unicast information into transmission symbols respectively, and the dual-polarized digital beamforming unit is used to perform beamforming on the two transmission symbols in different polarization directions; The receiving dual-polarization RS processing module is used to implement the inverse process of the transmitting dual-polarization RS processing module.

7. The communication system according to claim 5 or 6, characterized in that: A plurality of said receivers null out interference and decode the communication signal.

8. The communication system according to claim 5, characterized in that: In the process of solving the optimization problem model using the dimensionality reduction dominated minimization algorithm, the high-dimensional optimization variables to be optimized are reduced in dimension using the low-dimensional subspace, and the objective function is approximated by the MM algorithm and then converted into a convex quadratic constrained quadratic programming problem.

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