CN114584188B - Anti-eavesdrop communication method based on multi-station cooperation - Google Patents

Abstract

A multi-station collaboration-based anti-eavesdrop communication method comprises a description module, an establishment module and an optimization module; the description module is used for describing the relationship between the distribution of the neutralization capacity and the main beam azimuth in the multi-station collaboration-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 azimuth; the optimization module is used for optimizing the data model; the method effectively avoids the defects that the heuristic algorithm has certain blindness and is not optimal at the anti-eavesdropping angle by combining with other structures or methods.

Description

An anti-eavesdropping communication method based on multi-station coordination

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 coordination.

Background technique

The openness of the wireless channel makes the communication content may be eavesdropped by eavesdroppers, which may pose a risk to communication security. With the rapid development of the wireless communication field, users put forward higher requirements on the security of communication services. Therefore, the physical layer security technology for the purpose of realizing information security transmission has been extensively studied.

Most existing works are based on passive wiretapping schemes and active wiretapping schemes. Most of the passive eavesdropping schemes use artificial noise, which enables legitimate users to identify and filter out noise while eavesdroppers cannot identify noise, which greatly reduces the signal-to-interference-noise ratio of eavesdroppers. In the active eavesdropping scenario, the eavesdropper sends the same pilot frequency as the legitimate user to the base station, so that the base station directs the beam to the eavesdropper instead of the legitimate user, so that the eavesdropper can obtain good signal reception quality. At the same time, technologies such as Coordinated Multipoint Communication (CoMP) and Multiple Input Multiple Output (MIMO) can provide secure transmission for the communication system. Multi-point coordination is applied in the fields of heterogeneous network security coverage, unmanned aerial vehicle security communication, multi-beam satellite communication, etc.

The above works did not take into account the further combination of the cooperative characteristics of multi-point cooperative communication and the sparse characteristics of the channel in the angle domain in MIMO technology, and are often carried out separately, which shows that there are other ways to improve the security of communication systems aspect.

Contents of the invention

In order to solve the above problems, the present invention proposes to effectively utilize the advantages of MIMO and CoMP to solve the problem of anti-eavesdropping, and proposes a method of cooperative beamforming in the angle domain, which can further utilize the spatial distribution characteristics of capacity in MIMO systems to Improve security. details as follows:

An anti-eavesdropping communication method based on multi-station coordination, comprising the steps of:

Step 1: Describe the relationship between the distribution of the attainable rate and the orientation of the main beam in the anti-eavesdropping system based on multi-station coordination;

Step 2: Establish a mathematical model of the distribution of the accessible rate based on the user position and the orientation of the main beam;

Step 3: Establish an optimization problem based on the mathematical model;

Step 4: Design the base station and beam angle selection algorithm based on Nelder-Mead.

Preferably, in the step 1 of the present invention, the distribution of the attainable rate in the anti-eavesdropping system based on multi-station coordination and the relationship between the main beam orientation are described, and the content of the description includes:

The source sends the original message to the core network, and the core network divides the original message into M sub-messages bit by bit, and sends them to the corresponding base stations through the wired channel; the M base stations send the sub-messages to the deployment unit The user of the antenna; the user restores the original message by combining sub-messages;

Users located in the beam overlapping area receive M sub-messages at the same time and restore the original message, and users located outside the beam-overlapping area can only receive part of the sub-messages or no sub-messages.

Preferably, the mathematical model of establishing the distribution of the accessible rate based on the user position and the main beam orientation in step 2 of the present invention includes the following content:

Base station i is equipped with a uniform linear array of N _i antennas at half-wavelength intervals, and each antenna element evenly covers the range of arrival angles of [0, π); the transmitted signal of base station i antenna array is expressed as

Where P _i represents the transmission power, f _i is the precoding vector and ||f _i ||=1, s represents the transmission symbol and |s|=1;

When the distance between the user and the base station is much greater than the distance between adjacent antenna units, the direction from each antenna unit to the user is the same; let x _i and y _i be the abscissa and ordinate of base station i, l∈ ^2×1 is the position of the user, then the angle of arrival is expressed as

为天线单元辐射方向特性的大尺度衰落，λ_i为基站i载波波长，

为方差为σ²的噪声，基站 i从用户处接收到的信号为Where: l represents the position of the user, x(l) and y(l) represent the abscissa and ordinate of l respectively, the abscissa and ordinate of base station i are x _i and y _i respectively, and the array direction of base station i is γ _i (shown in Figure 2), let the distance between base station i and user be d _i ,

is the large-scale fading of the radiation direction characteristic of the antenna unit, λ _i is the carrier wavelength of base station i,

is the noise with variance σ ² , the signal received by base station i from the user is

为高斯白噪声，v(θ_i)为基站i关于离开角θ_i的阵列响应矢量，定义为in

is Gaussian white noise, v(θ _i ) is the array response vector of base station i with respect to departure angle θ _i , defined as

The signal-to-noise ratio of the signal received by the base station is

的接收机的γ_i，采用共轭波束赋形，则预编码向量设定为In order to maximize the orientation

γ _i of the receiver, using conjugate beamforming, the precoding vector is set as

波束赋形时，在方向θ_i的用户的信噪比表示为Substitute (6) into (5) to get the direction of the base station i pair

When beamforming, the signal-to-noise ratio of the user in the direction θ _i is expressed as

When the number of antennas approaches infinity, the array response vectors for different angles are asymptotically orthogonal, that is,

可以表示为The original signal is divided into M sub-signals, which are transmitted through M channels respectively; if B _i is the bandwidth of the signal sent by BSi, then the rate from BSi to the user at l

It can be expressed as

为基站i主波束角度。in

is the main beam angle of base station i.

Define the vector s∈{0,1} ^M×1 to indicate which base stations are selected, the i-th element of s is 1, which means the i-th base station is selected, and 0 means it is not selected; define the reachable rate as the information in the system The maximum rate of error-free transmission, expressed as

Equation (10) describes the relationship between the reachable rate and the location of the user. Formula (8) describes the sparsity in the angle domain. The reachable rate at different locations also shows similar characteristics; especially the number of antennas equipped on the base station In many cases, the area covered by the main beams of all selected base stations is defined as the effective receiving area. When the number of antennas approaches infinity, the effective receiving area converges to a point.

Preferably, the establishment of an optimization problem based on a mathematical model in step 3 of the present invention specifically includes:

来最大化用户的可达速率R(l)，即用户的位置应为和容量最大点，目标用数学表述为turn up

To maximize the user's reachable rate R(l), that is, the user's position should be the point with the maximum capacity, and the goal is expressed mathematically as

where is the set of real numbers, and ξ is an arbitrary 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 safe speed.

Preferably, the design in step 4 of the present invention is based on the base station and beam angle selection algorithm of Nelder-Mead, specifically including:

进行优化；具体的，采用两层结构，波束角度优化在下面那层，基站选择在上面那层；下面那层用于寻找/>

和对应的给定s条件下的用户可达速率，上面那层通过下面那层返回的结果优化s；In order to deal with problem P1 more effectively, the base station selects the scheme s and the beam angle under the given scheme

To optimize; specifically, a two-layer structure is adopted, the beam angle is optimized on the lower layer, and the base station is selected on the upper layer; the lower layer is used to find />

And the corresponding user reachable rate under the given s condition, the upper layer optimizes s through the results returned by the lower layer;

来最小化用户位置和可达速率最大点之间的距离直至收敛到0；波束角度选择问题只考虑通过主波束通信，/>

的优化问题表示为Step 4-1: Optimizing Beam Angle: Adjust

To minimize the distance between the user position and the maximum reachable rate point until it converges to 0; the beam angle selection problem only considers the communication through the main beam, />

The optimization problem of is expressed as

Make the previous constraints absorbed by the target, and adjust the beam angle under the constraints of C1 until the maximum attainable rate moves to the user position;

采用了自适应Nelder-Mead算法，对于k个基站的场景，其复杂度为O(klogk)；For P2, an algorithm is proposed to obtain

The adaptive Nelder-Mead algorithm is adopted, and for the scenario of k base stations, the complexity is O(klogk);

设定用户位置l为初始点，可达速率为目标函数，代入自适应Nelder-Mead算法得到可达速率最大点的坐标ξ及其可达速率；solve

Set the user position l as the initial point, and the attainable rate as the objective function, and substitute the adaptive Nelder-Mead algorithm to obtain the coordinate ξ of the maximum attainable rate point and its attainable rate;

The Nelder-Mead algorithm can only solve unconstrained problems, therefore, P2 needs to be transformed into

其中/>

用来吸收P2的约束，表示为P2.1:

where />

The constraint used to absorb P2 is expressed as

为初始点，P2.1的目标为目标函数，则

(13)的最终值和误差/>

由算法得到；set up

is the initial point, and the objective of P2.1 is the objective function, then

The final value and error of (13) />

obtained by the algorithm;

就是有效解；否则，说明存在一个点拥有比用户更高的可达速率，当前给定的基站选择方案不适合当前用户位置；If the obtained δ converges to 0, that is, satisfies C3, the obtained

is an effective solution; otherwise, it means that there is a point with a higher reachable rate than the user, and the current given base station selection scheme is not suitable for the current user location;

Step 4-2: Optimize base station selection: Based on the beam angle design proposed in Step 4-1, problem P1 is rewritten as

R(l, s) represents the achievable rate of the user located at l under the conditions of the base station selection scheme s and the corresponding beam angle obtained in step 4-1. If the scheme u is not suitable for the current user location, define R(l, u)=0,

种，对于M个基站的场景，穷搜的复杂度为O(2^MMlogM)；If an exhaustive search is performed on P3.1, there are a total of

For the scenario of M base stations, the complexity of exhaustive search is O(2 ^M MlogM);

First select all base stations, if this selection is not suitable for the current user's location, close the base station closest to the user, repeat the above steps until a suitable solution appears or the minimum number of base station selections is reached; step 4-2 cycle M-k+1 times, the time complexity of the algorithm is O(M ² logM).

The present invention adopts above-mentioned technical scheme, has following advantages compared with prior art:

1. The present invention introduces an optimization algorithm based on Nelder-mead to maximize users and capacity under physical layer security restrictions;

2. The present invention can solve the problem of anti-eavesdropping in cooperative communication scenarios from the angle domain;

3. The proposed low-complexity base station selection algorithm can solve the problem of high complexity of the exhaustive search method.

Description of drawings

Fig. 1 is a flow chart of the planning method of the anti-eavesdropping system based on multi-station coordination in the present invention.

FIG. 2 is a schematic diagram of a system scenario in an embodiment of the present invention.

Fig. 3 is an angle relationship diagram in an embodiment of the present invention.

Fig. 4 Location distribution map of normalized reachable rate near users.

Fig. 5 is a schematic diagram of parameter settings for evaluating the proposed beam azimuth optimization algorithm.

Figure 6 shows the 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 capacity.

Fig. 7 is a schematic diagram of simulation results for scenarios with 8, 16, 32, 64 and 128 antennas.

Fig. 8 shows a schematic diagram of location distribution of optimized attainable rates in an 8-antenna scenario.

Figure 9 shows a schematic diagram of location distribution of attainable rates in a 32-antenna scenario.

Detailed ways

For a given user location, the core network calculates the main beam azimuth of the corresponding base station and asks the base station to cross the beam in a small area containing the user. Only the terminals in the area can receive multiple information at the same time and combine them for recovery. out the original information. Users outside the area lack information of at least one path and cannot complete the merger, and thus cannot obtain the original information.

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

An anti-eavesdropping communication method based on multi-station coordination, comprising the steps of:

Step 1: Describe the relationship between the distribution of the attainable rate and the orientation of the main beam in the anti-eavesdropping system based on multi-station coordination;

The content of this description includes:

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 them to corresponding base stations through wired channels. M base stations send sub-messages to users equipped with a single antenna through line-of-sight MIMO channels (only line-of-sight paths are considered). Finally, the user recovers the original message by combining sub-messages. Therefore, users located in the beam overlapping area can simultaneously receive M sub-messages and restore the original message, while users not located in this area can only receive some sub-messages or no sub-messages, which is not enough to restore the original message.

Step 2: Establish a mathematical model based on the distribution of the accessible rate based on the user's position and the orientation of the main beam; including the following:

Base station i is equipped with a uniform linear array of N _i antennas at half-wavelength intervals, and each antenna element evenly covers the angle of arrival interval of [0, π). The transmitted signal of base station i antenna array can be expressed as

Where P _i represents transmit power, f _i is a precoding vector and ||f _i ||=1, s represents a transmission symbol and |s|=1.

When the distance between the user and the base station is much greater than the distance between adjacent antenna units, the direction from each antenna unit to the user is the same; let x _i and y _i be the abscissa and ordinate of base station i, l∈ ^2×1 is the position of the user, then the angle of arrival is expressed as

为天线单元辐射方向特性的大尺度衰落，λ_i为基站i载波波长，

为方差为σ²的噪声，基站 i从用户处接收到的信号为Where: l represents the position of the user, x(l) and y(l) represent the abscissa and ordinate of l respectively, the abscissa and ordinate of base station i are x _i and y _i respectively, and the array direction of base station i is γ _i (shown in Figure 2), let the distance between base station i and user be d _i ,

is the large-scale fading of the radiation direction characteristic of the antenna unit, λ _i is the carrier wavelength of base station i,

is the noise with variance σ ² , the signal received by base station i from the user is

为高斯白噪声。v(θ_i)为基站i关于离开角θ_i的阵列响应矢量，定义为in

is Gaussian white noise. v(θ _i ) is the array response vector of base station i with respect to departure angle θ _i , defined as

The signal-to-noise ratio of the signal received by the base station is

的接收机的γ_i，采用共轭波束赋形，则预编码向量设定为In order to maximize the orientation

γ _i of the receiver, using conjugate beamforming, the precoding vector is set as

波束赋形时，在方向θ_i的用户的信噪比可表示为Substitute (6) into (5) to get the direction of the base station i pair

When beamforming, the signal-to-noise ratio of the user in the direction θ _i can be expressed as

When the number of antennas approaches infinity, the array response vectors for different angles are asymptotically orthogonal, that is,

可以表示为In Figure 2, the original signal is divided into M sub-signals, which are transmitted through M channels respectively; if B _i is the bandwidth of the signal sent by BSi, then the rate from BSi to the user at l

It can be expressed as

为基站i主波束角度。in

is the main beam angle of base station i.

Define a vector s ∈ {0,1} ^M×1 to denote which base stations are selected. Specifically, if the i-th element of s is 1, it means that the i-th base station is selected, and if it is 0, it means it is not selected. The achievable rate is defined as the maximum rate of error-free transmission of information in the system, which can be expressed as

Equation (10) describes the relationship between reachable rate and user location. The sparsity in the angle domain is described in (8), and the attainable rates at different locations also show similar characteristics, especially when the base station is equipped with a large number of antennas. The area covered by the main beam of all selected base stations is defined as the effective reception area. When the number of antennas approaches infinity, the effective receiving area converges to a point. Therefore, we can achieve anti-eavesdropping communication by placing the beam of the base station at the position of the user.

It is considered that each eavesdropper is equipped with an antenna and can receive sub-messages like a user, which means that the location distribution of the eavesdropper's reachable rate is the same as that of the above user's reachable rate. According to the above discussion, the security rate is a function of position, expressed as [R(l)-R(ξ _e )] ⁺ . In order to meet the requirements of secure communication, R(l)-R(ξ _e ) should be guaranteed to be non-negative everywhere. In other words, the achievable rate of the eavesdropper is always lower than that of the user.

Step 3: Establish an optimization problem based on the mathematical model; specifically include:

来最大化用户的可达速率R(l)，即用户的位置应为和容量最大点，目标用数学表述为turn up

To maximize the user's reachable rate R(l), that is, the user's position should be the point with the maximum capacity, and the goal is expressed mathematically as

where is the set of real numbers, and ξ is an arbitrary 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 safe speed.

可以保证物理层安全。The constraints of formula (11) are crucial. Without this constraint, the highest user achievable rate can be obtained, but it cannot guarantee the data rate required for physical layer security. However, the constraint keeps the sum capacity of the eavesdropper always lower than that of the user, i.e. the obtained

Physical layer security can be guaranteed.

这个方案很容易算出来。可达容量的位置分布如图4所示，其中用户的位置不是可达速率最大点。Can provide significant power gain for main beam centerline users. So an intuitive way is to point the two main beams directly at the user, i.e.

This scheme is easy to figure out. The location distribution of the reachable capacity is shown in Figure 4, where the user's location is not the point of maximum reachable rate.

Figure 4 shows the location distribution of the normalized achievable rate near the user. It can be seen that the attainable rate maximum point is not where the user is located as the intersection point of the centerlines of the main beams. This is counterintuitive.

决定的角增益或减少由d_n决定的路径损耗，可以实现可达速率的最大化。在图4中，交叉点的相对方位角为/>

表示最大的角增益，但它到基站的距离比最佳点远，这导致了比用户附近的角增益变化更快的更大的路径损耗。It can be seen from formula (10) that the attainable rate is a function of distance and relative azimuth. by increasing by

The maximum achievable rate can be achieved by reducing the angular gain determined by dn or by reducing the path loss determined by _dn . In Figure 4, the relative azimuth of the intersection point is />

represents the maximum angular gain, but it is farther from the base station than the optimum point, which results in a larger path loss that changes faster than the angular gain near the user.

Step 4: Design the base station and beam angle selection algorithm based on Nelder-Mead; specifically include:

The adaptive Nelder-Mead algorithm is an algorithm for finding the local minimum of a multivariate function. Its advantage is that it does not require function derivation and can quickly converge to the local minimum. For N-ary functions (here, the function arguments are represented by N-dimensional vectors), the algorithm needs to provide an initial point x ₀ in the function argument space, and the algorithm starts from this point to find the local minimum. The algorithm can be applied to nonlinear programming and does not require the first derivative of the objective function.

进行优化。具体的，提出的算法采用两层结构，波束角度优化在下面那层，基站选择在上面那层。也就是说，下面那层用于寻找/>

和对应的给定s条件下的用户可达速率，上面那层通过下面那层返回的结果优化s。In order to deal with problem P1 more efficiently, an algorithm is proposed to select the scheme s for the base station and the beam angle under the given scheme

optimize. Specifically, the proposed algorithm adopts a two-layer structure, the beam angle optimization is in the lower layer, and the base station selection is in the upper layer. That is, the lower layer is used to find />

And corresponding to the user reachable rate under the condition of given s, the upper layer optimizes s by the result returned by the lower layer.

来最小化用户位置和可达速率最大点之间的距离直至收敛到0。波束角度选择问题只考虑通过主波束通信。/>

的优化问题可以表示为Step 4-1: Optimizing the beam angle. Inspired by the counter-intuitive phenomenon, consider tweaking

to minimize the distance between the user position and the point of maximum attainable velocity until it converges to zero. The beam angle selection problem only considers communication through the main beam. />

The optimization problem of can be expressed as

Compared with P1, P2 is easier to implement because it makes the previous constraints absorbed by the target. The beam angle can be adjusted under the constraints of C1 until the maximum attainable rate moves to the user location.

这个过程采用了自适应Nelder-Mead算法，对于k个基站的场景，其复杂度为O(klogk)。Dealing with P2, an algorithm is proposed to obtain

This process adopts the adaptive Nelder-Mead algorithm, and for the scenario of k base stations, its complexity is O(klogk).

设定用户位置l为初始点，可达速率为目标函数。代入自适应Nelder-Mead算法可得到可达速率最大点的坐标ξ及其可达速率。solve

Set the user position l as the initial point, and the attainable rate as the objective function. By substituting the adaptive Nelder-Mead algorithm, the coordinate ξ of the point with the maximum reachable speed and its reachable speed can be obtained.

The Nelder-Mead algorithm can only solve unconstrained problems, therefore, P2 needs to be transformed into

其中/>

用来吸收P2的约束，它可以表示为P2.1:

where />

used to absorb the constraint of P2, it can be expressed as

为初始点，P2.1的目标为目标函数，则/>

(13)的最终值和误差

可以由算法得到。P2.1 can be solved directly with the adaptive Nelder-Mead algorithm. set up

is the initial point, and the objective of P2.1 is the objective function, then />

The final value and error of (13)

can be obtained by algorithm.

就是有效解。否则，说明存在一个点拥有比用户更高的可达速率，当前给定的基站选择方案不适合当前用户位置。If the obtained δ converges to 0, that is, satisfies C3, the obtained

is the effective solution. Otherwise, it means 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: Optimize base station selection. Based on the beam angle design proposed in step 4-1, problem P1 can be rewritten as

R(l, s) represents the achievable rate of the user at l obtained in step 4-1 under the conditions of the base station selection scheme s and the corresponding beam angle. If the scheme u is not suitable for the current user location, define R(l,u)=0.

种。对于M个基站的场景，穷搜的复杂度为O(2^MMlogM)。因此，需要开发出一种低复杂度的算法。If an exhaustive search is performed on P3.1, there are a total of

kind. For the scenario of M base stations, the complexity of exhaustive search is O(2 ^M MlogM). Therefore, a low-complexity algorithm needs to be developed.

An algorithm that takes advantage of heuristics and base station selection is proposed. Specifically, all base stations are first selected like a heuristic scheme. If this choice is not suitable for the current user's location, turn off the base station closest to the user, because invalid solutions are prone to occur when there are base stations covered by the main beam of other base stations, which often occurs when the base station is very close to the user. Repeat the above steps until a suitable solution appears or the minimum number of selected base stations is reached.

For the worst case, step 4-2 loops M-k+1 times. Therefore, the time complexity of the proposed algorithm is O(M ² logM), which is much lower than that of exhaustive search.

The description module is used to describe the anti-eavesdropping system based on multi-station coordination;

The establishment module is used to establish a mathematical model of the main beam orientation based on the user position;

The optimization module is used to propose an optimization problem according to a mathematical model;

The Nelder-Mead algorithm module is used to introduce the Nelder-Mead algorithm;

The algorithm module is used to calculate the base station selection scheme and the base station beam angle.

And a specific embodiment of the present invention is described as follows, and the system simulation adopts Python language. The following examples examine the effectiveness of the UAV data distribution optimization method designed in the present invention under energy constraints.

In this embodiment, the proposed algorithm for beam orientation optimization is evaluated. The parameter settings are shown in Figure 5, and 100 different user locations are randomly generated in the region {(x,y)|-300<x<300 and -300<y<300}. Set the minimum number of selected base stations to 2

Figure 6 shows the 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 capacity, it can be seen that as the number of antennas increases, the distance and the difference decrease . A point not in (0,0) indicates that there is a point with a higher than user capacity. But no point lies in (0,0). The results show that the counter-intuitive phenomenon that users are not at the point of maximum capacity and contrary to C3 is common among users in different locations. Moreover, in the distribution corresponding to the proposed scheme, all points in Fig. 6 converge to (0,0) after optimization.

Figure 7 shows the simulation results for 8, 16, 32, 64 and 128 antenna scenarios. It can be seen from Figure 7 that the total capacity of users increases as the number of antennas increases, and the average achievable rate of users in the proposed algorithm is close to the average achievable rate obtained by the exhaustive search method. It shows that the proposed algorithm can greatly reduce the complexity while having little impact on performance.

Figure 8 shows the location distribution of the optimized achievable rates in the 8-antenna scenario. It can be seen that the achievable rates of all points are lower than the achievable rates of the user's location. In Fig. 4, a counter-intuitive phenomenon was found and optimized according to its simulation configuration parameters. It can be seen that this phenomenon has been eliminated in Figure 8.

Figure 9 shows the location distribution of the attainable rate in the 32-antenna scenario. It can be seen that only a small part of the area has good reception performance, which shows the effectiveness of the proposed algorithm.

The present invention has been described above in the manner of illustrating the embodiments. It should be understood by those skilled in the art that the present disclosure is not limited to the embodiments described above, and various changes can be made without departing from the scope of the present invention. change and replace.

Claims (1)

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 velocity and the main beam azimuth in the multi-station collaboration-based anti-eavesdropping system;

the content of the description includes:

the information source sends the original message to the core network, the core network divides the original message into M sub-messages bit by bit, and sends the M sub-messages to the corresponding base station through the wired channel; m base stations send sub-messages to users equipped with single antennas through line-of-sight MIMO channels; the user recovers the original message by combining the sub-messages;

the users in the beam overlapping area receive M sub-messages and recover the original message at the same time, and the users outside the beam overlapping area can only receive partial sub-messages or no sub-messages;

step 2: establishing a mathematical model of the distribution of the achievable rates and the main beam azimuth based on the user position;

the method comprises the following steps:

base station i is equipped with N _i A uniform linear array of half wavelength intervals of the root antenna, each antenna array element uniformly covering the arrival angle interval of [0, pi); the transmitted signal of the base station i antenna array is represented as

Wherein P is _i Representing the transmit power, f _i Is a precoding vector and f _i ||=1, s represents a transmission symbol and |s|=1;

when the distance between the user and the base station is far greater than the distance between the adjacent antenna units, the directions from each antenna unit to the user are the same; let x be _i And y _i For the abscissa and ordinate of base station i,

for the user's location, the angle of arrival is expressed as

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 the base station i are x, respectively _i And y _i The array direction of the base station i is gamma _i Let the distance from base station i to user be d _i ，

Lambda, a large scale fading of the radiation direction characteristics of an antenna element _i For the base station i carrier wavelength,

for variance sigma ² Is the noise of the base station i received from the user as

Wherein the method comprises the steps of

Is Gaussian white noise, v (θ) _i ) For base station i about the departure angle θ _i Is defined as the array response vector of (a)

The signal to noise ratio of the signal received by the base station is

To maximize the orientation of

Gamma of the receiver of (2) _i With conjugate beam forming, the precoding vector is set to

Substituting (6) into (5) to obtain the direction of the base station i

In the beam forming, in the direction theta _i Is expressed as the signal to noise ratio of the user of (2)

When the number of antennas approaches infinity, the array response vectors for different angles are asymptotically orthogonal, i.e

The original signal is divided into M sub-signals, which propagate through M channels, respectively; let B _i Is the bandwidth of the BSi signaling, then the rate of BSi to the user at l

Can be expressed as

Wherein the method comprises the steps of

The angle of the main beam of the base station i;

definition vector s epsilon {0,1} ^M×1 An i-th element of s is 1, which indicates which base stations are selected, and a 0 indicates that the i-th base station is not selected; defining the achievable rate as the maximum rate of error-free transmission of information in the system, expressed as

The relation between the reachable velocity and the user position is described by a formula (10), the sparsity of the angle domain is described by a formula (8), and the reachable velocities of different positions also show similar characteristics; when the number of antennas equipped on the base station is large, defining the coverage area of the main beams of all the selected base stations as an effective receiving area, and when the number of antennas approaches infinity, converging the effective receiving area to a point;

step 3: establishing an optimization problem according to a mathematical model; the method specifically comprises the following steps:

find out

To maximize the user's achievable rate R (l), i.e. the user's location should be the sum capacity maximum, the goal is expressed mathematically as

Wherein the method comprises the steps of

Being a real set, ζ is any receiver position; c1 illustrates that the location of the user is covered by all selected base stations; c2 illustrates that at least k base stations are selected; c3 is a guarantee of safe rate;

step 4: designing a base station and a beam angle selection algorithm based on Nelder-Mead; the method specifically comprises the following steps:

to more effectively deal with the problem P1, a scheme s and beam angles under a given scheme are selected for the base station

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 lower layer is used to find +.>

And the corresponding user achievable rate given s, the upper layer returning better results through the lower layerTransforming s;

step 4-1: optimizing the beam angle: adjustment of

To minimize the distance between the user location and the maximum achievable rate point until convergence to 0; the beam angle selection problem only considers the communication via the main beam,/->

The optimization problem of (1) is expressed as

The previous constraint is absorbed by the target, and the beam angle is adjusted under the constraint of C1 until the maximum point of the achievable rate moves to the user position;

for P2, an algorithm is proposed to obtain

An adaptive Nelder-Mead algorithm is adopted, and for the scenes of k base stations, the complexity is O (klogk);

solving for

Setting a user position l as an initial point, taking the reachable rate as an objective function, and substituting the initial point into a self-adaptive Nelder-Mead algorithm to obtain a coordinate xi of the maximum reachable rate point and the reachable rate thereof;

the Nelder-Mead algorithm can only solve the unconstrained problem, and therefore, P2 needs to be converted into

Wherein the method comprises the steps of

Constraints for absorbing P2, expressed as

Setting up

For the initial point, the target of P2.1 is the target function

(13) Final value and error ∈>

Is obtained by an algorithm;

if the delta obtained converges to 0, i.e. C3 is satisfied, what is obtained

Is an effective solution; otherwise, it is indicated 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: optimizing base station selection: based on the beam angle design proposed in step 4-1, the problem P1 is rewritten as

Representing the achievable rate of the user at l under the conditions of base station selection scheme s and corresponding beam angle obtained in step 4-1, defining R (l, u) =0 if scheme u does not fit the current user position,

if P3.1 is searched in the poor, the compliance (15) constraint is satisfied in total

For the scene of M base stations, the complexity of the poor search is O (2 ^M MlogM)；

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 proper scheme appears or the minimum selection number of the base stations is reached; step 4-2 cycle M-k+1 times, the time complexity of the algorithm is O (M ² logM)。

Images