CN114584188A - Anti-eavesdropping communication method based on multi-station cooperation - Google Patents

Anti-eavesdropping communication method based on multi-station cooperation Download PDF

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CN114584188A
CN114584188A CN202210035446.2A CN202210035446A CN114584188A CN 114584188 A CN114584188 A CN 114584188A CN 202210035446 A CN202210035446 A CN 202210035446A CN 114584188 A CN114584188 A CN 114584188A
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base station
user
rate
reachable
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CN114584188B (en
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丁国如
李岩
王海超
徐以涛
谷江春
李京华
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Army Engineering University of PLA
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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
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • 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
    • H04B7/0617—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 for beam forming
    • 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
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/60—Context-dependent security
    • H04W12/63—Location-dependent; Proximity-dependent
    • 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

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Abstract

An anti-eavesdrop communication method based on multi-station cooperation comprises a description module, an establishment module and an optimization module; the description module is used for describing the relation between the distribution of the neutralization capacity and the main beam direction in the multi-station cooperation-based anti-eavesdropping system; the establishing module is used for establishing a mathematical model based on the distribution of the user position and the capacity and the main beam direction; the optimization module is used for optimizing the mathematical model; the combination with other structures or methods effectively avoids the defects that the heuristic algorithm has certain blindness and is not optimal in the anti-eavesdropping angle.

Description

Anti-eavesdropping communication method based on multi-station cooperation
Technical Field
The invention relates to the technical field of anti-eavesdropping communication, in particular to an anti-eavesdropping communication method based on multi-station cooperation.
Background
The openness of the wireless channel makes it possible for the content of the communication to be eavesdropped by an eavesdropper, which may pose a risk to the security of the communication. With the rapid development of the wireless communication field, users have made higher demands on the security of communication services. Therefore, physical layer security techniques for achieving secure transmission of information have been widely studied.
Most existing work is based on passive and active eavesdropping schemes. Most of the passive eavesdropping schemes utilize artificial noise, so that a legal user can identify and filter the noise, and an eavesdropper cannot identify the noise, and the signal-to-interference-and-noise ratio of the eavesdropper user is greatly reduced. In an active eavesdropping scene, an eavesdropper can aim a wave beam at the eavesdropper instead of a legal user by sending the same pilot frequency as the legal user to a base station in a mode of sending the pilot frequency to the base station, so that the eavesdropper can obtain good signal receiving quality. Meanwhile, technologies such as multi-point cooperative communication (CoMP) and Multiple Input Multiple Output (MIMO) are adopted to provide secure transmission for the communication system. The multi-point cooperation is applied to the fields of heterogeneous network safety coverage, unmanned aerial vehicle safety communication, multi-beam satellite communication and the like.
The above work does not consider that the cooperative property of simultaneous multipoint cooperative communication and the sparsity of the channel in the angle domain in the MIMO technology are often separately performed, which indicates that there is another aspect of improving the security of the communication system.
Disclosure of Invention
In order to solve the above problems, the present invention proposes to effectively utilize the advantages of MIMO and CoMP to solve the anti-eavesdropping problem, and proposes a cooperative beam forming method in the angular domain, which can further utilize the spatial distribution characteristics of capacity in the MIMO system to improve the security. The method comprises the following specific steps:
an anti-eavesdropping communication method based on multi-station cooperation comprises the following steps:
step 1: describing the relation between the distribution of the reachable rate and the direction of the main beam in the anti-eavesdropping system based on the multi-station cooperation;
step 2: establishing a mathematical model of distribution of the reachable rate and the main beam direction based on the user position;
and step 3: establishing an optimization problem according to a mathematical model;
and 4, step 4: base station and beam angle selection algorithms based on Nelder-Mead were designed.
Preferably, in step 1, the description of the relationship between the distribution of the reachable rate and the main beam direction in the anti-eavesdropping system based on multi-station cooperation is performed, where the description includes:
the method comprises the steps that an information source sends an original message to a core network, the core network divides the original message into M sub-messages bit by bit and sends the M sub-messages to corresponding base stations through wired channels; m base stations send the sub-messages to users equipped with single antennas through a line-of-sight MIMO channel; the user recovers the original message by combining the sub-messages;
and the users positioned in the beam overlapping area can receive M sub-messages and recover the original message at the same time, and the users positioned outside the beam overlapping area can only receive partial sub-messages or no sub-messages.
Preferably, the mathematical model for establishing the distribution of the achievable rates and the main beam azimuth based on the user position in step 2 of the present invention includes the following contents:
base station i is equipped with NiThe antenna array elements uniformly cover the arrival angle interval of [0, pi ]) according to a uniform linear array with half-wavelength intervals of the antennas; the transmission signal of the base station i antenna array is represented as
Figure BDA0003468180440000031
Wherein P isiDenotes the transmission power, fiIs a precoding vector and fi1, s denotes a transmission symbol and 1;
when the distance between the user and the base station is far larger than the distance between the adjacent antenna units, the directions from the antenna units to the user are the same; let xiAnd yiFor the abscissa and ordinate of base station i, e2×1Is the user's location, then angle of arrivalIs shown as
Figure BDA0003468180440000032
Wherein: l represents the position of the user, x (l) and y (l) represent the abscissa and ordinate of l, respectively, and the abscissa and ordinate of base station i are xiAnd yiThe array direction of base station i is gammai(shown in FIG. 2), let distance d be between base station i and useri，
Figure BDA0003468180440000033
For large-scale fading, λ, of the radiation direction characteristic of the antenna elementiFor the carrier wavelength of the base station i,
Figure BDA0003468180440000034
is that the variance is sigma2The signal received by the base station i from the user is
Figure BDA0003468180440000035
Wherein
Figure BDA0003468180440000036
Is white Gaussian noise, v (θ)i) For base station i with respect to the angle of departure thetaiIs defined as an array response vector of
Figure BDA0003468180440000037
The signal-to-noise ratio of the signal received by the base station is
Figure BDA0003468180440000038
To be maximally positioned in the direction
Figure BDA0003468180440000039
Gamma of receiveriUsing conjugate beam forming, the precoding vector is set to
Figure BDA0003468180440000041
Substituting (6) into (5) to obtain the current base station i opposite direction
Figure BDA0003468180440000042
In the direction theta in beam formingiIs expressed as the signal-to-noise ratio of the user
Figure BDA0003468180440000043
As the number of antennas approaches infinity, the array response vectors for different angles become asymptotically orthogonal, i.e., orthogonal
Figure BDA0003468180440000044
The original signal is divided into M sub-signals, which propagate through M channels, respectively; let BiIs the bandwidth at which the BSi signals, the rate of BSi to a user located at l
Figure BDA0003468180440000045
Can be expressed as
Figure BDA0003468180440000046
Wherein
Figure BDA0003468180440000047
Is the base station i main beam angle.
Definition vector s ∈ {0,1}M×1Indicating which base stations are selected, the ith element of s is 1 indicating that the ith base station is selected, and 0 indicating that the ith base station is not selected; defining achievable rates as error-free transmission of information in a systemIs expressed as
Figure BDA0003468180440000048
Formula (10) describes the relationship between the reachable rate and the user position, formula (8) describes the sparsity of the angle domain, and the reachable rates of different positions also show similar characteristics; particularly, when the number of antennas provided in the base station is large, the area covered by the main beam of all the selected base stations is defined as an effective receiving area, and when the number of antennas approaches infinity, the effective receiving area converges to one point.
Preferentially, the establishing of the optimization problem according to the mathematical model in the step 3 of the invention specifically comprises the following steps:
find out
Figure BDA0003468180440000051
To maximize the reachable rate R (l) of the user, i.e. the position of the user should be the point with the maximum sum capacity, and the target is expressed by mathematics
Figure BDA0003468180440000052
Where is the set of real numbers and ξ is any receiver position. C1 indicates that the user's location is covered by all selected base stations; c2 indicates that at least k base stations are selected; c3 is the guarantee of a safe rate.
Preferably, the base station and beam angle selection algorithm based on Nelder-Mead in step 4 of the invention specifically comprises:
to more effectively handle the problem P1, a scheme s and a beam angle under a given scheme are selected for the base station
Figure BDA0003468180440000053
Optimizing; specifically, a two-layer structure is adopted, the beam angle is optimized on the lower layer, and the base station selects the upper layer; the following layer is used for searching
Figure BDA0003468180440000054
And the corresponding user reachable rate under the given s condition, the upper layer optimizes s through the result returned by the lower layer;
step 4-1: optimizing the beam angle: adjustment of
Figure BDA0003468180440000055
To minimize the distance between the user location and the maximum reachable rate point until convergence to 0; the beam angle selection problem only considers communication via the main beam,
Figure BDA0003468180440000056
is expressed as
Figure BDA0003468180440000057
So that the previous constraint is absorbed by the target, adjusting the beam angle under the constraint of C1 until the maximum reachable rate point moves to the user position;
for P2, an algorithm is proposed to obtain
Figure BDA0003468180440000058
The self-adaptive Nelder-Mead algorithm is adopted, and the complexity of the scenes of k base stations is O (klogk);
solving for
Figure BDA0003468180440000061
Setting a user position l as an initial point, setting the reachable rate as an objective function, and substituting the reachable rate into an adaptive Nelder-Mead algorithm to obtain a coordinate xi of a maximum reachable rate point and the reachable rate thereof;
the Nelder-Mead algorithm can only solve the unconstrained problem, therefore, P2 needs to be converted to
P2.1:
Figure BDA0003468180440000062
Wherein
Figure BDA0003468180440000063
For absorbing the constraint of P2, denoted as
Figure BDA0003468180440000064
Setting up
Figure BDA0003468180440000065
As an initial point, P2.1 is targeted to the objective function, then
Figure BDA0003468180440000066
(13) Final value and error of
Figure BDA0003468180440000067
Obtaining the result by an algorithm;
if the resulting δ converges to 0, i.e., C3 is satisfied, the resulting
Figure BDA0003468180440000068
Is a valid solution; otherwise, it shows that there is a point with higher reachable rate than the user, and the currently given base station selection scheme is not suitable for the current user position;
step 4-2: optimizing base station selection: based on the beam angle design proposed in step 4-1, the problem P1 is rewritten as
Figure BDA0003468180440000069
R (l, s) represents the achievable rate of the user located at l under the condition that the base station selects the scheme s and the corresponding beam angle obtained in step 4-1, and if the scheme u is not suitable for the current user location, R (l, u) is defined to be 0,
if P3.1 is searched for a poor way, the total number of the search results is determined in accordance with the constraint of (15)
Figure BDA0003468180440000071
For the scenario of M base stations, the complexity of the poor search is O (2)MMlogM)；
First selects the instituteIf some base stations are not suitable for the position of the current user, closing the base station closest to the user, and repeating the steps until a suitable scheme appears or the minimum base station selection number is reached; step 4-2, circulating for M-k +1 times, wherein the time complexity of the algorithm is O (M)2logM)。
By adopting the technical scheme, compared with the prior art, the invention has the following advantages:
1. the invention introduces an optimization algorithm based on Nelder-mead to realize the maximization of users and capacity under the safety limit of a physical layer;
2. the invention can solve the problem of eavesdropping prevention in a cooperative communication scene from an angle domain;
3. the low-complexity base station selection algorithm can solve the problem of high complexity of the poor search method.
Drawings
Fig. 1 is a flowchart of a planning method of an anti-eavesdropping system based on multi-station cooperation according to the present invention.
Fig. 2 is a system scenario diagram in an embodiment of the invention.
FIG. 3 is a graph of angular relationships in an embodiment of the present invention.
FIG. 4 is a graph of a location profile of normalized achievable rates near a user.
Fig. 5 is a schematic diagram of parameter settings for evaluating the proposed beam azimuth optimization algorithm.
Fig. 6 shows a distribution of the distance between the effective user s and the maximum capacity point s and the total capacity difference between the effective user s and the maximum sum capacity.
Fig. 7 is a diagram of simulation results for 8, 16, 32, 64, and 128 antenna scenarios.
Fig. 8 shows a schematic diagram of the position distribution of the optimized achievable rate in the 8-antenna scenario.
Fig. 9 shows a schematic diagram of the position distribution of achievable rates in a 32-antenna scenario.
Detailed Description
For a given user position, after the core network calculates the main beam azimuth angle of the corresponding base station, the base station makes the beam cross in a small area containing the user, and only the terminals in the area can receive multiple paths of information at the same time and synthesize and recover the original information. The users outside the area lack at least one path of information and cannot complete the combination, so that the original information cannot be known.
The invention will be further described with reference to the following figures and examples.
An anti-eavesdropping communication method based on multi-station cooperation comprises the following steps:
step 1: describing the relation between the distribution of the reachable rate and the direction of the main beam in the anti-eavesdropping system based on the multi-station cooperation;
the content of the description comprises:
the source sends the original message to the core network. Then, the core network divides the original message into M sub-messages bit by bit, and sends the M sub-messages to corresponding base stations through wired channels. The M base stations send sub-packets to the users equipped with single antennas via line-of-sight MIMO channels (only line-of-sight paths are considered). Finally, the user restores the original message by combining the sub-messages. Therefore, users in the beam overlapping region can receive M sub-messages and recover the original message at the same time, while users not in the region can receive only partial sub-messages or no sub-messages, which is not enough to recover the original message.
Step 2: establishing a mathematical model of distribution of the reachable rate and the main beam direction based on the user position; the method comprises the following steps:
base station i is equipped with NiA uniform linear array of half-wavelength spaced antennas, each antenna element uniformly covering an angle of arrival interval of [0, π). The transmission signal of the base station i antenna array can be expressed as
Figure BDA0003468180440000081
Wherein P isiRepresenting the transmission power, fiIs a precoding vector and fi1, s denotes a transmission symbol and | s | ═ 1.
When the distance between the user and the base station is far larger than the distance between the adjacent antenna units, the direction from each antenna unit to the user isThe same; let xiAnd yiFor the abscissa and ordinate of base station i, e2×1Is the user's location, then the angle of arrival is expressed as
Figure BDA0003468180440000091
Wherein: l represents the position of the user, x (l) and y (l) represent the abscissa and ordinate of l, respectively, and the abscissa and ordinate of base station i are xiAnd yiThe array direction of base station i is gammai(shown in FIG. 2), let distance d be between base station i and useri，
Figure BDA0003468180440000092
For large-scale fading, λ, of the radiation direction characteristic of the antenna elementiFor the carrier wavelength of the base station i,
Figure BDA0003468180440000093
is that the variance is sigma2The signal received by the base station i from the user is
Figure BDA0003468180440000094
Wherein
Figure BDA0003468180440000095
Is gaussian white noise. v (theta)i) For base station i with respect to the angle of departure thetaiIs defined as an array response vector of
Figure BDA0003468180440000096
The signal-to-noise ratio of the signal received by the base station is
Figure BDA0003468180440000097
To maximize the bitIn the direction of
Figure BDA0003468180440000098
Gamma of receiveriUsing conjugate beam forming, the precoding vector is set to
Figure BDA0003468180440000099
Substituting (6) into (5) to obtain the current base station i opposite direction
Figure BDA00034681804400000910
In the direction theta during beam formingiCan be expressed as
Figure BDA0003468180440000101
As the number of antennas approaches infinity, the array response vectors for different angles become asymptotically orthogonal, i.e., orthogonal
Figure BDA0003468180440000102
In fig. 2, the original signal is divided into M sub-signals, which propagate through M channels, respectively; let BiIs the bandwidth at which the BSi signals, the rate of BSi to a user located at l
Figure BDA0003468180440000103
Can be expressed as
Figure BDA0003468180440000104
Wherein
Figure BDA0003468180440000105
Is the base station i main beam angle.
Definition vector s ∈ {0,1}M×1Indicating which base stationsIs selected. Specifically, an ith element of s is 1, which indicates that the ith base station is selected, and 0 indicates that the ith base station is not selected. Defining the achievable rate as the maximum rate at which information can be transmitted without errors in the system can be expressed as
Figure BDA0003468180440000106
Equation (10) describes the relationship between the achievable rate and the user location. (8) The sparsity of an angle domain is described, and the reachable rates of different positions also show similar characteristics, especially when the number of antennas equipped on a base station is large. And defining the place covered by the main beam of all the selected base stations as an effective receiving area. As the number of antennas approaches infinity, the effective receive area converges to a point. Thus, we can achieve anti-eavesdropping communication by handing over the beams of the base station to the location of the user.
It is considered that each eavesdropper is equipped with an antenna that can receive the sub-messages like a user, which means that the location distribution of the rate reachable by the eavesdropper is the same as the location distribution of the rate reachable by the user. From the discussion above, the safe rate is a function of position, expressed as [ R (l) -R (ξ)e)]+. To meet the requirements of secure communication, it should be ensured that R (l) -R (ξ)e) Everywhere is non-negative. In other words, the rate of reach of an eavesdropper is always lower than that of the user.
And step 3: establishing an optimization problem according to a mathematical model; the method specifically comprises the following steps:
find out
Figure BDA0003468180440000111
To maximize the reachable rate R (l) of the user, i.e. the position of the user should be the point with the maximum sum capacity, and the target is expressed by mathematics
Figure BDA0003468180440000112
Where is the set of real numbers and ξ is any receiver position. C1 indicates that the user's location is covered by all selected base stations; c2 indicates that at least k base stations are selected; c3 is the guarantee of a safe rate.
The constraint of equation (11) is important. Without this constraint, the highest achievable rate for the user is obtained, but it does not guarantee the data rate required for physical layer security. However, constraints keep the sum of eavesdroppers lower than the user at all times, i.e. obtained
Figure BDA0003468180440000113
The physical layer security can be guaranteed.
Significant power gain can be provided for main beam centerline users. An intuitive approach is to direct the two main beams directly towards the user, i.e.
Figure BDA0003468180440000114
This scheme is easy to calculate. The location distribution of reachable capacity is shown in fig. 4, where the location of the user is not the maximum reachable rate point.
Fig. 4 is a distribution of locations near a user normalized achievable rate. It can be seen that the maximum achievable rate point is not where the user is located as the intersection of the main beam centerlines. This is an inverse intuitive phenomenon.
As can be seen from equation (10), the achievable rate is a function of distance and relative azimuth. By increasing the feed rate
Figure BDA0003468180440000115
The determined angular gain or reduction being dnThe determined path loss can realize the maximization of the reachable rate. In fig. 4, the relative azimuth of the intersection is
Figure BDA0003468180440000116
Indicating the maximum angular gain, but is further from the base station than the optimum point, which results in a larger path loss that varies faster than the angular gain near the user.
And 4, step 4: designing a base station and a beam angle selection algorithm based on Nelder-Mead; the method specifically comprises the following steps:
the self-adaptive Nelder-Mead algorithm isThe algorithm for solving the local minimum of the multivariate function has the advantages that the function is not needed to be derived and can be converged to the local minimum quickly. For an N-ary function (where the function argument is represented by an N-dimensional vector), the algorithm requires providing an initial point x in the function argument space0From this point, the algorithm looks for a local minimum. The algorithm can be applied to non-linear programming without the need for the first derivative of the objective function.
To more efficiently handle the problem P1, an algorithm is proposed to select a scheme s and a beam angle under a given scheme for the base station
Figure BDA0003468180440000121
And (6) optimizing. Specifically, the proposed algorithm uses a two-layer structure, the beam angle is optimized in the lower layer, and the base station selects the upper layer. That is, the following layer is used for seeking
Figure BDA0003468180440000122
And the user reachable rate under the corresponding given s condition, the upper layer optimizes s through the results returned by the lower layer.
Step 4-1: the beam angle is optimized. Inspired by the phenomenon of countering intuition, consider the adjustment
Figure BDA0003468180440000123
To minimize the distance between the user location and the maximum reachable rate point until convergence to 0. The beam angle selection problem only considers communication via the main beam.
Figure BDA0003468180440000124
Can be expressed as
Figure BDA0003468180440000125
P2 is easier to implement than P1 because it allows previous constraints to be absorbed by the target. The beam angle may be adjusted under the constraints of C1 until the maximum reachable rate point moves to the user position.
Processing P2, an algorithm is proposed to obtain
Figure BDA0003468180440000126
The process adopts an adaptive Nelder-Mead algorithm, and the complexity of the k base station scenes is O (klogk).
Solving for
Figure BDA0003468180440000127
And setting the user position l as an initial point, and setting the reachable rate as an objective function. And substituting the coordinate xi of the maximum reachable rate point and the reachable rate of the maximum reachable rate point into an adaptive Nelder-Mead algorithm.
The Nelder-Mead algorithm can only solve the unconstrained problem, therefore, P2 needs to be converted to
P2.1:
Figure BDA0003468180440000131
Wherein
Figure BDA0003468180440000132
To absorb the constraint of P2, which can be expressed as
Figure BDA0003468180440000133
P2.1 can be solved directly by the adaptive Nelder-Mead algorithm. Setting up
Figure BDA0003468180440000134
As an initial point, P2.1 is targeted to the objective function, then
Figure BDA0003468180440000135
(13) Final value and error of
Figure BDA0003468180440000136
Can be derived by an algorithm.
If the resulting δ converges to 0, i.e., C3 is satisfied, the resulting
Figure BDA0003468180440000137
Is a valid solution. Otherwise, it indicates that there is a point with a higher reachable rate than the user, and the currently given base station selection scheme is not suitable for the current user location.
Step 4-2: and optimizing base station selection. Based on the beam angle design proposed in step 4-1, the problem P1 can be rewritten as
Figure BDA0003468180440000138
R (l, s) represents the achievable rate of the user at l under the conditions of the base station selection scheme s and the corresponding beam angle obtained in step 4-1. If scheme u does not fit in the current user location, R (l, u) ═ 0 is defined.
If P3.1 is searched for a poor way, the total number of the search results is determined in accordance with the constraint of (15)
Figure BDA0003468180440000139
And (4) seed preparation. For the scenario of M base stations, the complexity of the poor search is O (2)MMlogM). Therefore, it is necessary to develop a low complexity algorithm.
An algorithm is presented that utilizes heuristic methods and base station selection advantages. Specifically, all base stations are selected first as in the heuristic approach. If the selection is not suitable for the position of the current user, the base station closest to the user is closed, because the invalid solution is easy to occur when the base station is covered by the main beam of other base stations, which is often the case when the base station is close to the user. The above steps are repeated until a suitable scheme occurs or the minimum number of base station selections is reached.
For the worst case, step 4-2 cycles M-k +1 times. The temporal complexity of the proposed algorithm is therefore O (M)2logM), much less time-complex than the poor search.
The description module is used for describing the anti-eavesdropping system based on multi-station cooperation;
the establishing module is used for establishing a mathematical model of the main beam direction based on the user position;
the optimization module is used for proposing an optimization problem according to the mathematical model;
the Nelder-Mead algorithm module is used for introducing a Nelder-Mead algorithm;
the algorithm module is used for calculating a base station selection scheme and a base station beam angle.
In one embodiment of the present invention, the Python language is used for system simulation. The following examples examine the effectiveness of the unmanned aerial vehicle data distribution optimization method under the energy constraint designed by the invention.
In this embodiment, the proposed beam azimuth optimization algorithm is evaluated. Parameter settings as shown in fig. 5, 100 different user positions are randomly generated in the region { (x, y) | -300< x <300 and-300 < y <300 }. Setting the minimum number of selected base stations to 2
Fig. 6 shows a distribution of the distance between the effective user s and the capacity maximum point s and the total capacity difference between the effective user s and the maximum and capacity, and it can be seen that the distance and the difference value decrease as the number of antennas increases. A point not located in (0,0) indicates that there is a point higher than the user capacity. But no point is located in (0, 0). The results show that the counter-intuitive phenomenon that the user is not the point of maximum capacity, which is contrary to C3, is common among users in different locations. Furthermore, in the distribution corresponding to the proposed scheme, all points in fig. 6 converge to (0,0) after optimization.
Fig. 7 is a simulation result for 8, 16, 32, 64 and 128 antenna scenarios. As can be seen from fig. 7, the total capacity of the users increases with the number of antennas, and the average achievable rate of the users in the proposed algorithm approaches the average achievable rate obtained by the poor search method. The algorithm can greatly reduce the complexity and has little influence on the performance.
Fig. 8 shows the position distribution of the optimized achievable rates in the 8-antenna scenario, and it can be seen that the achievable rates of all the points are smaller than the achievable rate of the user's position. In fig. 4, an inverse visual phenomenon is discovered and optimized according to its simulation configuration parameters. It can be seen that this phenomenon has been eliminated in figure 8.
Fig. 9 shows the position distribution of achievable rates in a 32-antenna scenario, and it can be seen that only a small fraction of the area has good reception performance, indicating the effectiveness of the proposed algorithm.
The present invention has been described in an illustrative manner by the embodiments, and it should be understood by those skilled in the art that the present disclosure is not limited to the embodiments described above, but is capable of various changes, modifications and substitutions without departing from the scope of the present invention.

Claims (5)

1. An anti-eavesdropping communication method based on multi-station cooperation is characterized by comprising the following steps:
step 1: describing the relation between the distribution of the reachable rate and the direction of the main beam in the anti-eavesdropping system based on the multi-station cooperation;
step 2: establishing a mathematical model of distribution of the reachable rate and the main beam direction based on the user position;
and 3, step 3: establishing an optimization problem according to a mathematical model;
and 4, step 4: base station and beam angle selection algorithms based on Nelder-Mead were designed.
2. The method for preventing eavesdropping according to claim 1, wherein the description of the relationship between the distribution of the reachable rates in the system for preventing eavesdropping based on multi-station cooperation and the main beam direction in the step 1 comprises:
the method comprises the steps that an information source sends an original message to a core network, the core network divides the original message into M sub-messages bit by bit and sends the M sub-messages to corresponding base stations through wired channels; m base stations send the sub-messages to users equipped with single antennas through a line-of-sight MIMO channel; the user recovers the original message by combining the sub-messages;
and the users positioned in the beam overlapping area can receive M sub-messages and recover the original message at the same time, and the users positioned outside the beam overlapping area can only receive partial sub-messages or no sub-messages.
3. The method for preventing eavesdropping according to claim 2, wherein the step 2 of establishing a mathematical model of the distribution of the achievable rates and the main beam azimuth based on the user location comprises the following steps:
base station i is equipped with NiThe antenna array elements uniformly cover the arrival angle interval of [0, pi ]) according to a uniform linear array with half-wavelength intervals of the antennas; the transmission signal of the base station i antenna array is represented as
Figure FDA0003468180430000011
Wherein P isiRepresenting the transmission power, fiIs a precoding vector and | fi1, s denotes a transmission symbol and 1;
when the distance between the user and the base station is far larger than the distance between the adjacent antenna units, the directions from the antenna units to the user are the same; let xiAnd yiFor the abscissa and ordinate of base station i, e2×1Is the user's location, then the angle of arrival is expressed as
Figure FDA0003468180430000021
Wherein: l represents the position of the user, x (l) and y (l) represent the abscissa and ordinate of l, respectively, and the abscissa and ordinate of base station i are xiAnd yiThe array direction of base station i is gammaiLet distance d be from base station i to useri，
Figure FDA0003468180430000022
Large scale fading, lambda, of the radiation direction characteristic of the antenna elementiIs the carrier wavelength of the base station i,
Figure FDA0003468180430000023
is that the variance is sigma2The signal received by the base station i from the user is
Figure FDA0003468180430000024
Wherein
Figure FDA0003468180430000025
Is white Gaussian noise, v (θ)i) For base station i with respect to the angle of departure thetaiIs defined as an array response vector of
Figure FDA0003468180430000026
The signal-to-noise ratio of the signal received by the base station is
Figure FDA0003468180430000027
To be maximally positioned in the direction
Figure FDA0003468180430000028
Gamma of receiveriUsing conjugate beam forming, the precoding vector is set to
Figure FDA0003468180430000029
Substituting (6) into (5) to obtain the current base station i opposite direction
Figure FDA00034681804300000210
In the direction theta during beam formingiIs expressed as
Figure FDA0003468180430000031
As the number of antennas approaches infinity, the array response vectors for different angles become asymptotically orthogonal, i.e., orthogonal
Figure FDA0003468180430000032
The original signal is divided into M sub-signals, which propagate through M channels, respectively; let BiIs the bandwidth at which the BSi signals, the rate of BSi to a user located at l
Figure FDA0003468180430000033
Can be expressed as
Figure FDA0003468180430000034
Wherein
Figure FDA0003468180430000035
Is the base station i main beam angle.
Definition vector s ∈ {0,1}M×1Indicating which base stations are selected, the ith element of s is 1 indicating that the ith base station is selected, and 0 indicating that the ith base station is not selected; the achievable rate is defined as the maximum rate of error-free transmission of information in the system, expressed as
Figure FDA0003468180430000036
Formula (10) describes the relationship between the reachable rate and the user position, formula (8) describes the sparsity of the angle domain, and the reachable rates of different positions also show similar characteristics; particularly, when the number of antennas provided in the base station is large, the area covered by the main beam of all the selected base stations is defined as an effective receiving area, and when the number of antennas approaches infinity, the effective receiving area converges to one point.
4. The method for preventing eavesdropping according to claim 3, wherein the step 3 of establishing an optimization problem according to a mathematical model specifically comprises:
find out
Figure FDA0003468180430000037
To maximize the achievable rate R (l) of the user, i.e. the position of the user should be the point of maximum sum capacity, the target is expressed mathematically as
Figure FDA0003468180430000041
Where is the set of real numbers and ξ is any receiver position. C1 indicates that the user's location is covered by all selected base stations; c2 indicates that at least k base stations are selected; c3 is the guarantee of a safe rate.
5. The multi-station cooperation-based anti-eavesdropping communication method according to claim 4, wherein the designing of the Nelder-Mead-based base station and the beam angle selection algorithm in the step 4 specifically comprises:
to more effectively handle the problem P1, a scheme s and a beam angle under a given scheme are selected for the base station
Figure FDA0003468180430000042
Optimizing; specifically, a two-layer structure is adopted, the beam angle is optimized on the lower layer, and the base station selects the upper layer; the following layer is used for searching
Figure FDA0003468180430000043
And the corresponding user reachable rate under the given s condition, the upper layer optimizes s through the result returned by the lower layer;
step 4-1: optimizing the beam angle: adjustment of
Figure FDA0003468180430000044
To minimize the distance between the user location and the maximum reachable rate point until convergence to 0; the beam angle selection problem is only considered through the main beam passThe information is sent to the server via the internet,
Figure FDA0003468180430000045
is expressed as
Figure FDA0003468180430000046
So that the previous constraint is absorbed by the target, adjusting the beam angle under the constraint of C1 until the maximum reachable rate point moves to the user position;
for P2, an algorithm is proposed to obtain
Figure FDA0003468180430000047
An adaptive Nelder-Mead algorithm is adopted, and the complexity of a scene with k base stations is O (k log k);
solving for
Figure FDA0003468180430000051
Setting a user position l as an initial point, setting the reachable rate as an objective function, and substituting the reachable rate into an adaptive Nelder-Mead algorithm to obtain a coordinate xi of a maximum reachable rate point and the reachable rate thereof;
the Nelder-Mead algorithm can only solve the unconstrained problem, therefore, P2 needs to be converted to
Figure FDA0003468180430000052
Wherein
Figure FDA0003468180430000053
For absorbing the constraint of P2, denoted as
Figure FDA0003468180430000054
Setting up
Figure FDA0003468180430000055
As an initial point, P2.1 is the objective function, then
Figure FDA0003468180430000056
(13) Final value and error of
Figure FDA0003468180430000057
Obtaining an algorithm;
if the resulting δ converges to 0, i.e., C3 is satisfied, the resulting
Figure FDA0003468180430000058
Is a valid solution; otherwise, it shows that there is a point with higher reachable rate than the user, and the current given base station selection scheme is not suitable for the current user position;
step 4-2: optimizing base station selection: based on the beam angle design proposed in step 4-1, the problem P1 is rewritten as
Figure FDA0003468180430000059
R (l, s) represents the achievable rate of the user located at l under the condition that the base station selects the scheme s and the corresponding beam angle obtained in step 4-1, and if the scheme u is not suitable for the current user location, R (l, u) is defined to be 0,
if P3.1 is searched for a poor way, the total number of the search results is determined in accordance with the constraint of (15)
Figure FDA0003468180430000061
For the scenario of M base stations, the complexity of the poor search is O (2)MM log M)；
Firstly, selecting all base stations, if the selection is not suitable for the position of the current user, closing the base station closest to the user, and repeating the steps until a suitable scheme appears or the minimum base station selection number is reached; step 4-2, circulating for M-k +1 times, wherein the time complexity of the algorithm is O (M)2log M)。
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