CN109150257B - Large-scale MIMO beam domain secure multicast wireless transmission method - Google Patents

Large-scale MIMO beam domain secure multicast wireless transmission method Download PDF

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CN109150257B
CN109150257B CN201810889397.2A CN201810889397A CN109150257B CN 109150257 B CN109150257 B CN 109150257B CN 201810889397 A CN201810889397 A CN 201810889397A CN 109150257 B CN109150257 B CN 109150257B
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multicast
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rate
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CN109150257A (en
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尤力
陈旭
王闻今
孙晨
卢安安
高西奇
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Southeast University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H04B7/043—Power distribution using best eigenmode, e.g. beam forming or beam steering
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0626—Channel coefficients, e.g. channel state information [CSI]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/0848—Joint weighting
    • H04B7/0854—Joint weighting using error minimizing algorithms, e.g. minimum mean squared error [MMSE], "cross-correlation" or matrix inversion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/06—Selective distribution of broadcast services, e.g. multimedia broadcast multicast service [MBMS]; Services to user groups; One-way selective calling services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/046—Wireless resource allocation based on the type of the allocated resource the resource being in the space domain, e.g. beams
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W72/00—Local resource management
    • H04W72/04—Wireless resource allocation
    • H04W72/044—Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention provides a large-scale MIMO beam domain secure multicast wireless transmission method, wherein a large-scale antenna array is configured at a base station side of wireless communication, and a large-scale beam set covering the whole cell is generated at the base station side by a method of simulating multi-beam forming or digital multi-beam forming or simulating and digital mixed beam forming. And the base station counts the channel state information according to the beam domains of the legal user and the eavesdropping user and performs power distribution on the transmission signals of the beam domains. The beam domain power allocation algorithm comprises an iterative algorithm based on deterministic equivalence and CCCP, and a beam domain power allocation matrix is obtained by solving a convex optimization problem through iteration. And the beam domain power distribution result is dynamically updated along with the change of the statistical channel state information in the multicast process. The method provided by the invention solves the problems of complexity and safety of multicast transmission of a large-scale MIMO wireless communication system.

Description

Large-scale MIMO beam domain secure multicast wireless transmission method
Technical Field
The invention belongs to the field of communication, and particularly relates to a beam domain safe wireless transmission method using a large-scale antenna array in a multicast communication scene.
Background
Under the condition of limited spectrum resources, the spectrum efficiency and the power efficiency of a wireless communication system can be greatly improved by adopting a large-scale Multiple-input Multiple-Output (MIMO) technology, so that the method adapts to the continuously increasing wireless service requirements. And under the multicast communication scene, the base station simultaneously transmits the same information to the target user group. Meanwhile, due to the openness of wireless networks, the phenomenon that an illegal user eavesdrops on information becomes more and more serious. How to ensure the security of information transmission becomes one of the problems that the wireless communication system needs to solve. With the improvement of the computing capability and the computing speed of the computer, the traditional network layer encryption method is no longer reliable. In addition to or instead of the encryption method, the physical layer security method is intended to improve the security of the wireless communication system from the viewpoint of information theory.
In a large-scale MIMO secure communication process in a multicast scenario, in order to obtain a higher secure multicast rate, a base station side needs to design a transmission signal of a multicast user. Most of the traditional methods utilize instant channel information to implement multicast transmission, and the instant channel information is difficult to obtain in an actual system. In addition, the secure multicast rate in secure multicast transmission is a non-convex function, and a global optimal solution is usually difficult to obtain by multicast precoding design. And when the number of base station side antennas is large, the realization complexity of solving by using the traditional interior point method is high. Therefore, the invention provides a large-scale MIMO beam domain secure multicast wireless transmission method which has lower complexity and utilizes statistical channel information.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a method for carrying out safe multicast wireless transmission by utilizing statistical channel information and a large-scale antenna array under the condition that a base station side carries out multicast on a legal user group and an illegal wiretapping user exists.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a large-scale MIMO beam domain secure multicast wireless transmission method comprises the following steps:
(1) under the scene that a base station carries out multicast communication with a user group, the base station configured with a large-scale antenna array generates a beam set capable of covering the whole cell by a method of simulating multi-beam forming or digital multi-beam forming or simulating and digital mixed beam forming;
(2) the base station utilizes the beam domain statistical channel state information of legal users and illegal eavesdropping users in the multicast user group to construct and solve the beam domain multicast power distribution optimization problem to carry out power distribution on the transmitted signals; the optimization target of the beam domain multicast power allocation optimization problem is a lower bound value of a maximized safe multicast rate, and the optimization variable is a covariance matrix of signals sent by a base station; the constraint condition is that the covariance matrix of the signals sent by the base station meets the power constraint; the lower bound value of the secure multicast rate is the difference value between the minimum multicast user rate and the upper bound of the eavesdropping user rate;
(3) in the dynamic moving process of each user, along with the change of the beam domain statistical channel state information between the base station and the users in the multicast user group, the base station side dynamically implements beam domain power distribution and the multicast process is dynamically updated.
In the step (1), the base station generates a large-scale wave beam set capable of covering the whole cell to realize the wave beam domain division of the space resources, the base station performs the safe multicast communication with the users in the multicast user group on the same time-frequency resource, and the process of the safe multicast communication is implemented on the wave beam domain.
And (3) the base station in the step (2) performs power distribution on the transmitted signals by using the beam field statistical channel state information of the legal user and the illegal eavesdropping user in the multicast user group. Since the illegal eavesdropping user masquerades as a legal user in the multicast user group, the legal user and the illegal eavesdropping user in the multicast user group send uplink detection signals in an uplink channel detection stage, and the base station estimates beam domain statistical channel state information required for implementing user beam domain power distribution or beam selection according to the received detection signals. The specific power allocation algorithm is an iterative algorithm based on a deterministic equivalence and Concave-convex process (CCCP).
The CCCP-based power allocation method includes:
(a) and performing first-order Taylor expansion approximation on the upper bound of the rate of the eavesdropping user in the lower bound expression of the safe multicast rate, and converting the non-convex problem into a convex optimization problem about beam domain power distribution. The Taylor expansion process needs to calculate the derivative of the upper bound of the rate of the intercepted user in the lower bound expression of the safe multicast rate with respect to the power distribution matrix of the beam domain.
(b) And obtaining a solution of the problem by using an interior point method or other optimization methods, calculating a secure multicast rate according to the obtained solution, updating a derivative of an upper bound of the eavesdropping user rate in the secure multicast rate on a beam domain power distribution matrix according to the solution, generating a new optimization problem, and solving the new optimization problem. The process of solving the convex optimization problem, updating the derivative value, substituting the derivative value into the optimization target to generate a new convex optimization problem, solving the convex optimization problem is repeated until the safe multicast rate converges.
The deterministic equivalence method comprises the following steps:
(a) and according to the large-dimensional random matrix theory, iterative calculation of the deterministic equivalent auxiliary variable is carried out by utilizing the beam domain statistical channel state information until convergence.
(b) And calculating the deterministic equivalent expression of the multicast rate in the lower bound of the safe multicast rate by using the deterministic equivalent auxiliary variable obtained by iteration.
(c) And the deterministic equivalent expression of the multicast rate is brought into the optimization problem of the multicast power distribution in the beam domain, so that the expected operation with high complexity is avoided.
In the step 3), as each user moves dynamically, the beam domain statistical channel state information between the base station and each user changes, and the base station re-implements the beam domain power allocation according to the changed statistical channel state information, thereby implementing dynamic update of the multicast process. The change of the beam domain statistical channel state information is related to a specific application scenario, a typical statistical time window is several times or tens of times of a short-time transmission time window, and the acquisition of the related statistical channel state information is also performed over a larger time width.
Has the advantages that: compared with the prior art, the invention has the following advantages:
1. the base station and each user in the multicast user group implement the safe multicast communication on the wave beam domain, and can be matched with the space characteristic of a wireless channel, thereby obtaining the improvement of power efficiency and spectral efficiency brought by using a large-scale antenna array, and simultaneously ensuring the safety of the multicast wireless communication.
2. The method designs the sending signal by utilizing the beam domain statistical channel state information of the illegal eavesdropping user and the legal user in the multicast user group, the required beam domain statistical channel state information of each user can be obtained by sparse detection signals, and the multicast transmission method is simultaneously suitable for time division duplex and frequency division duplex systems.
3. By using an iterative algorithm based on deterministic equivalence and CCCP, the implementation complexity of the secure multicast communication is remarkably reduced, and the method can obtain approximately optimal performance.
Drawings
Fig. 1 is a flowchart of a beam-space massive MIMO secure multicast wireless transmission method using statistical channel state information.
Fig. 2 is a schematic diagram of a massive MIMO multicast system with eavesdropping users.
Fig. 3 is a flow chart of an iterative algorithm based on deterministic equivalence and CCCP.
Detailed Description
In order to make the technical field of the invention better understand, the following description is combined with the accompanying drawings in the embodiment of the invention.
As shown in fig. 1, a large-scale MIMO beam-space secure multicast wireless transmission method using statistical channel state information disclosed in the embodiments of the present invention mainly includes the following steps:
1) the base station configures a large-scale antenna array, and generates a large-scale beam set capable of covering the whole cell by a beam forming method. In this step, the base station generates a large-scale beam set capable of covering the whole cell by using an analog multi-beam forming method or a digital multi-beam forming method, thereby realizing beam domain division of space resources. The base station carries out safe multicast communication with legal users on the same time-frequency resource, and the process of the safe multicast communication is implemented on a wave beam domain.
2) The base station utilizes the beam domain statistical channel state information of legal users and illegal eavesdropping users in the multicast user group to carry out power distribution on the sending signals by constructing and solving the beam domain multicast power distribution optimization problem, or to distribute beams or beam subsets for the legal user group users to carry out safe multicast communication.
3) In the dynamic moving process of each user, along with the change of the beam domain statistical channel state information between the base station and the users in the multicast user group, the base station side dynamically implements beam domain power distribution and the multicast process is dynamically updated.
The method according to the embodiment of the present invention is described in detail below with reference to fig. 2, which illustrates a large-scale MIMO multicast system scenario in which an unauthorized eavesdropping user exists. Considering a single-cell scenario, the base station configures M (M is 10)2Or 103Order of magnitude) transmit antennas spaced one-half wavelength apart. There are K multicast target users in the cell, each user configures NrThe root receives the antenna. In addition, there is one configuration N in a celleAn illegal eavesdropping of the root receiving antenna. The base station can transform the transmitted space domain signals to the beam domain by adopting an analog multi-beam forming method or a digital multi-beam forming method or an analog and digital mixed beam forming method. Then, the base station transmits the downlink multicast signal in the beam domain.
Considering that the eavesdropping user pretends to be idle user in the cell, in the channel detection stage, both legal user and illegal eavesdropping user in the multicast user group send uplink detection signal, the base station estimates the wave beam domain statistical channel state information of the legal user and the eavesdropping user according to the received detection signal, namely
Figure GDA0002443513730000041
And
Figure GDA0002443513730000042
wherein HkAnd HeveThe beam domain channel matrices for the kth legitimate user and the illegitimate eavesdropping user, respectively, operator ⊙ is the Hadamard product of the matrices, the conjugate of the matrices,
Figure GDA0002443513730000043
representing the desired operation.
Suppose the beam-domain multicast signal transmitted by the base station is x, and the covariance matrix of the transmitted signal is
Figure GDA0002443513730000044
The multicast user rate may be expressed as:
Figure GDA0002443513730000051
wherein min represents the minimum operation, log represents the logarithm operation, det represents the determinant of the matrix, and H is the conjugate transpose of the matrix.
The upper bound on the eavesdropping user rate can be expressed as:
Figure GDA0002443513730000052
thus a lower bound for the safe multicast rate is obtained:
Rsec,lb(Λ)＝[Rmc(Λ)-Reve,ub(Λ)]+(3)
wherein [ x ]]+The larger of 0 and x is represented to ensure that the secure multicast rate is not negative. In consideration of the low correlation on the base station side of the beam domain channel, the base station transmits mutually independent data streams on each beam, i.e. the matrix Λ is a diagonal matrix. Note that in beam-domain secure communication, in order to obtain higher secure multicast and rate, the covariance matrix Λ of the transmitted signal needs to be optimized, that is, the transmit beam is power-allocated on the base station side, that is, the following optimization problem is solved:
Figure GDA0002443513730000053
the objective function of the problem is non-convex, the global optimal solution is difficult to obtain, and the realization complexity is high. Therefore, the embodiment of the invention adopts an iterative algorithm based on deterministic equivalence and CCCP to solve the beam domain multicast power distribution optimization problem.
The CCCP-based power distribution method comprises the following steps:
a. and performing first-order Taylor expansion approximation on the upper bound of the rate of the intercepted user in the lower bound expression of the secure multicast rate to convert the non-convex problem into a convex optimization problem about beam domain power distribution. This process requires calculating the derivative of the upper bound of the eavesdropping user rate in the lower bound expression of the secure multicast rate with respect to the beam domain power allocation matrix.
b. And obtaining a solution of the problem by using an interior point method or other optimization methods, calculating the secure multicast rate according to the obtained solution of the optimization problem, updating a derivative of an upper bound of the eavesdropping user rate in the secure multicast rate with respect to the power distribution matrix according to the obtained solution, substituting the derivative value into an optimization target to generate a new optimization problem, and solving again. And repeating the processes of solving the convex optimization problem, updating the derivative value, substituting the derivative value into the optimization target to generate a new convex optimization problem and solving the convex optimization problem until the safe multicast rate is converged, namely the difference of the safe multicast rates of the adjacent two iteration results is less than a given threshold value.
Since the channels need to be traversed using Monte-Carlo emulation when the reachable traversal of the computing system is lower bound for secure multicast rates. In order to reduce the computational complexity, the present embodiment calculates the certainty equivalence of the lower bound of the reachable traversal secure multicast rate by using the large-dimension random matrix theory on the basis of the CCCP iterative algorithm. The method can obtain the approaching result of the lower bound of the safe multicast rate only by counting the channel state information in the beam domain.
The deterministic equivalence method comprises the following steps:
a. and according to the large-dimensional random matrix theory, iterative calculation of the deterministic equivalent auxiliary variable is carried out by utilizing the beam domain statistical channel state information until convergence.
b. And calculating the deterministic equivalent expression of the multicast rate in the lower bound of the safe multicast rate by using the deterministic equivalent auxiliary variable obtained by iteration.
c. And the deterministic equivalent expression of the multicast rate is brought into the optimization problem of the multicast power distribution in the beam domain, so that the expected operation with high complexity is avoided.
Fig. 3 shows the implementation process of the iterative algorithm based on deterministic equivalence and CCCP, and the detailed process of the algorithm is as follows:
step 1: initializing covariance matrix Λ of transmitted signals(0)The iteration number indication i is set to 0. Covariance matrix of initial transmission signalArray Λ(0)And then, distributing power P/N for the N wave beams with the strongest wave beam gain according to the wave beam domain statistical channel information, wherein P is the total power constraint of the base station. The value of N may be as follows: calculating the difference value of the beam domain channel correlation matrix of each user and the beam domain channel correlation matrix of the eavesdropping user,
Figure GDA0002443513730000061
Rdiff_kis an M x M diagonal matrix with diagonal elements of
Figure GDA0002443513730000062
The beam set with the energy coverage for this user up to 80% may be taken, and then the beam sets of all K multicast users are taken and collected to obtain the set y, N being the number of elements in the set y.
Step 2: using Λ(i)Iterative computation of deterministic equivalent auxiliary variable gamma used in ith iterationk、
Figure GDA0002443513730000063
And
Figure GDA0002443513730000064
Figure GDA0002443513730000065
Figure GDA0002443513730000066
Figure GDA0002443513730000067
until the auxiliary variable is converged, namely the change value of the auxiliary variable in the iterative process is less than a given threshold value. Wherein, Bk(X) and Ck(X) is a diagonal matrix whose diagonal elements can be calculated as
[Bk(X)]j,j＝tr{diag{[Ωk]:,j}X} (8)
Figure GDA0002443513730000071
Meanwhile, calculating the equivalence of the safety multicast and the rate lower bound certainty according to the obtained auxiliary variable
Figure GDA0002443513730000072
Is composed of
Figure GDA0002443513730000073
And step 3: and converting the optimization problem into the following lower convex optimization problem by using an upper bound item of the wiretapping user rate in the lower bound of the CCCP linearization multicast rate:
Figure GDA0002443513730000074
where tr (-) represents the operation of computing the traces of the matrix.
And 4, step 4: reve,ubThe gradient of (Λ) is a diagonal matrix, the diagonal elements in which can be accurately calculated using statistical channel state information:
Figure GDA0002443513730000075
r is to beeve,ubAnd (a) substituting the gradient calculation result into an optimization target, and solving the convex optimization problem in the step (11) by using an interior point method or other convex optimization methods.
And 5: calculating the boundary certainty equivalence under the new secure multicast rate according to the formula (10) according to the obtained solution
Figure GDA0002443513730000076
Step 6: comparing new secure multicast rates with bounded certainty identity
Figure GDA0002443513730000077
And the calculated knot of the last iterationFruit
Figure GDA0002443513730000078
If the difference between the two is less than or equal to the preset threshold value epsilon1The iteration ends and Λ at this point is the solution to the optimization problem. Otherwise, let i equal to i +1, go back to step 2.
In the moving process of each user, along with the change of the beam domain statistical channel state information between the base station and the user, the base station side repeats the steps according to the updated statistical channel state information to carry out beam domain multicast power distribution. Thereby realizing the dynamic update of the multicast transmission process. The change of the beam domain statistical channel state information is related to a specific application scenario, a typical statistical time window is several times or tens of times of a short-time transmission time window, and the acquisition of the related statistical channel state information is also performed on a larger time width.
It should be noted that the above mentioned embodiments are only specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes or substitutions within the technical scope of the present invention, and all such changes or substitutions should be covered by the scope of the present invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (4)

1. A large-scale MIMO beam domain secure multicast wireless transmission method is characterized in that: the method comprises the following steps:
(1) under the scene that a base station carries out multicast communication with a user group, the base station configured with a large-scale antenna array generates a beam set capable of covering the whole cell by a method of simulating multi-beam forming or digital multi-beam forming or simulating and digital mixed beam forming;
(2) the base station utilizes the beam domain statistical channel state information of legal users and illegal eavesdropping users in the multicast user group to construct and solve the beam domain multicast power distribution optimization problem to carry out power distribution on the transmitted signals; the beam domain multicast power allocation optimization problem is expressed as:
Figure FDA0002443513720000011
s.t.tr{Λ}≤P
Λ≥0
wherein the content of the first and second substances,
Figure FDA0002443513720000012
for the multicast rate of the base station,
Figure FDA0002443513720000013
for eavesdropping on the upper bound of the user rate, HkAnd HeveWave beam domain channel matrixes of a kth legal user and an illegal eavesdropping user respectively, Λ is a covariance matrix of a transmitted signal, I is a unit matrix, P is total power constraint of a base station,
Figure FDA0002443513720000014
representing the desired operation, det representing the determinant of the matrix, tr (-) representing the traces of the computation matrix;
solving the optimization problem of the multicast power distribution in the beam domain comprises optimizing an upper bound of the rate of the intercepted user based on a concave-convex process (CCCP) iterative algorithm and optimizing the rate of the multicast user based on a deterministic equivalence method; the method for optimizing the upper bound of the eavesdropping user rate based on the CCCP iterative algorithm specifically comprises the following steps:
(a) performing first-order Taylor series expansion approximation on an upper rate bound of an eavesdropping user in a lower bound expression of the secure multicast rate, converting a non-convex problem into a convex optimization problem about beam domain power distribution, and converting the optimization problem into a solution of the following problem:
Figure FDA0002443513720000015
s.t.tr{Λ}≤P
Λ≥0
in the Taylor series expansion process, the derivative of the upper bound of the rate of the intercepted user with respect to the beam domain power distribution matrix needs to be calculated
Figure FDA0002443513720000016
Figure FDA0002443513720000017
Is a diagonal matrix, diagonal elements
Figure FDA0002443513720000021
Wherein the superscript i is the number of iterations, M is the number of base station transmitting antennas, NeIn order to eavesdrop the number of receiving antennas of a user illegally,
Figure FDA0002443513720000022
(b) obtaining a solution of the problem by using a convex optimization method, updating a derivative of an upper bound of the eavesdropping user rate in the secure multicast rate on a beam domain power distribution matrix according to the obtained solution, substituting the derivative value into an optimization target to form a new convex optimization problem, and solving again; repeating the process of solving the convex optimization problem, updating the derivative value, bringing the derivative value into the optimization target to generate a new convex optimization problem and solving the convex optimization problem until the safe multicast rate is converged;
optimizing the multicast user rate based on a deterministic equivalence method, specifically comprising:
(a) according to the large-dimension random matrix theory, iterative computation of a deterministic equivalent auxiliary variable gamma is carried out by utilizing the beam domain statistical channel state informationk、
Figure FDA0002443513720000023
And
Figure FDA0002443513720000024
until convergence; wherein:
Figure FDA0002443513720000025
Figure FDA0002443513720000026
Bk(X) and Ck(X) is a diagonal matrix, [ B ]k(X)]j,j＝tr{diag{[Ωk]:,j}X}，
Figure FDA0002443513720000027
Figure FDA0002443513720000028
The superscript i denotes the number of iterations, the subscript j denotes the matrix element row and column number, ⊙ denotes the matrix Hadamard product;
(b) calculating the deterministic equivalent expression of the multicast user rate in the lower bound of the safe multicast rate by using the deterministic equivalent auxiliary variable obtained by iteration;
(c) the deterministic equivalent expression of the multicast user rate is brought into the optimization problem of the multicast power distribution in the beam domain, and the expected operation with high complexity is avoided;
(3) in the moving process of each user, along with the change of the statistical channel state information between the base station and each user, the base station side dynamically implements beam domain power allocation and the multicast process is dynamically updated.
2. The massive MIMO beam-space secure multicast wireless transmission method according to claim 1, wherein: in the step (1), the base station generates a large-scale wave beam set capable of covering the whole cell to realize the wave beam domain division of the space resources, the base station performs the safe multicast communication with the users in the multicast user group on the same time-frequency resource, and the process of the safe multicast communication is implemented on the wave beam domain.
3. The massive MIMO beam-space secure multicast wireless transmission method according to claim 1, wherein: and the beam domain statistical channel state information is estimated by the base station according to the received uplink detection signals sent by the legal user and the illegal eavesdropping user.
4. The massive MIMO beam-space secure multicast wireless transmission method according to claim 1, wherein: in the dynamic moving process of each user, along with the change of statistical channel state information between the base station and each user, the base station side dynamically implements beam domain power allocation and the multicast process is dynamically updated; the change of the beam domain statistical channel state information is related to a specific application scene, and the statistical time window is several times or ten times of the short-time transmission time window.
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