CN106131823B - Relay transmission method based on safety of physical layer in eavesdropping user random distribution scene - Google Patents

Abstract

The invention discloses the relay transmission methods based on safety of physical layer in a kind of eavesdropping user random distribution scene, it include: 1) to be obtained under the scene of eavesdropping user random distribution based on random geometry theory, after independent eavesdropping coding twice, the security interrupt probability of double bounce relay transmission；2) under conditions of source node and limited relay node total transmission power, the optimization problem for maximizing safe transmission rate is constructed；3) it by the solution to constructed optimization problem, obtains that the maximized relay transmission method of safe transmission rate can be made, this method includes power distribution and code book rated design two parts.The present invention has comprehensively considered the reliability and safety of communication, the maximization to safe transmission rate is realized while meeting security interrupt probability constraints in the case where requiring no knowledge about eavesdropping user specific location.

Description

Relay transmission method based on physical layer security in the random distribution scenario of eavesdropping users

technical field

The invention belongs to the technical field of wireless communication, and in particular relates to a relay transmission method based on physical layer security in a scenario where eavesdropping users are randomly distributed.

Background technique

Due to the broadcast characteristics of wireless channels, the private information transmitted between nodes is easily eavesdropped by some illegal nodes (eavesdropping users), which poses a threat to the safe transmission of information. Traditional high-level encryption technology ensures information security based on the assumption that eavesdropping users have limited computing power. However, with the development of high-speed and efficient computing technologies such as quantum computing, the computing power of eavesdropping users will tend to be infinite, and high-level encryption technology will no longer be able to guarantee the absolute security of information. Correspondingly, the physical layer security technology does not rely on the restriction on the computing power of eavesdropping users, and can provide absolute security in the sense of information theory.

However, in many studies on physical layer security, it is assumed that the channel state of the eavesdropping user is known. In fact, this assumption is difficult to realize in reality, because the eavesdropping user usually keeps silent and does not send any signal, even the location distribution of the eavesdropping user is difficult to obtain. Therefore, how to design a transmission strategy to ensure secure communication without knowing the location distribution and channel state of eavesdropping users is a work of great research significance.

Contents of the invention

In view of the above defects or deficiencies, the purpose of the present invention is to provide a relay transmission method based on physical layer security in a random distribution scenario of non-eavesdropping users, which can maximize the secure transmission rate.

For achieving above object, technical method of the present invention is:

A method for relay transmission based on physical layer security in an eavesdropping user random distribution scenario, comprising the following steps:

1) Based on stochastic geometry theory, calculate the security outage probability after two-hop relay transmission under the condition that the eavesdropping users are randomly distributed and the eavesdropping users are not colluding, and construct the maximum security transmission rate under the constraint of the security outage probability Optimize model P1;

2) Transform the optimized model P1 into an equivalent simplified model P2;

3) Solve the model P2 to obtain the optimal transmission method, including power allocation and codebook rate selection. said

Step 1) is specifically:

a. Both the source node and the destination node are equipped with a single antenna, the relay is equipped with N _R antennas, and each eavesdropping user is equipped with N _E antennas. Use E _j to represent the j-th eavesdropping user, and use Φ _E,1 to indicate that at the first hop (Transmission from source node S to relay R) During the transmission process, the set of eavesdropping users distributed on the entire two-dimensional plane is used to calculate the channel capacity C _M,1 of the legal link at the first hop and the eavesdropping link Channel capacity C _E,1 , the calculation formulas are:

Among them, ρ ₁ represents the transmit signal-to-noise ratio of the first-hop transmitting node (source node S), ||h _SR || ² represents the small-scale fading gain of the legitimate link between source node S and relay R, and d _SR represents the distance between the source node S and the relay R, represents the small-scale fading gain of the eavesdropping link between the source node S and the eavesdropping user _Ej , Represents the distance between the source node S and the eavesdropping user E _j , α is the path loss factor;

b. Use E _j to represent the jth eavesdropping user, and use Φ _E,2 to represent the set of eavesdropping users distributed on the entire two-dimensional plane during the transmission process of the second hop (transmission from relay R to destination node D) , calculate the channel capacity C _{M,2 of} the legitimate link and the channel capacity CE,2 of the eavesdropping link at the second hop, and the calculation formulas are:

Among them, ρ ₂ represents the transmit signal-to-noise ratio of the second-hop transmitting node (relay R), ||h _RD || ² represents the small-scale fading gain of the legitimate link between relay R and destination node D, and d _RD represents The distance between relay R and destination node D, represents the small-scale fading gain of the eavesdropping link between relay R and eavesdropping user _Ej , Represents the distance between relay R and eavesdropping user E _j ;

c. For a given private information encoding rate R _S , use P _sec,1 to represent the security interruption probability of the first hop transmission, and the specific calculation formula is:

Among them, γ(N _E ,c _j ) is an incomplete gamma function;

d. For a given private information coding rate R _S that needs to be achieved, use P _sec,2 to represent the security interruption probability of the second hop transmission, and the specific calculation formula is:

e. Combining formula (5) and formula (6) to obtain the safety interruption probability after two-hop relay transmission, its specific expression is as follows:

in, Substitute for variables.

Described step 2) specifically is:

a. Define the safe transmission rate T _s , whose expression is:

Among them, R _s is the private information encoding rate of the codebook used in each hop (the R _s of the two hops are the same);

b. Use R _t,i to represent the codeword transmission rate of the codebook used in the i-th hop, then construct the optimization model P1 for maximizing the safe transmission rate as shown below:

Wherein, the expression of the safe outage probability P _out has been given in the formula (7), and ε is the threshold value of the pre-set tolerable safe outage probability.

The step 3) is specifically:

a. Since the safe transmission rate can only be maximized when the transmission power is completely used up, the last inequality constraint on the total power in model P1 can be ρ ₁ + ρ ₂ ≤ ρ ₀ , ρ ₁ ≥ 0, ρ ₂ ≥ 0 When the total conversion power ρ ₀ is used up, the constraint on the power allocation factor η is 0≤η≤1. Under this power allocation factor, there are ρ ₁ =ηρ ₀ and ρ ₂ =(1-η)ρ ₀ , and the model The simplified optimization model P2 corresponding to P1 is:

Among them, the formula The expression is:

b. Solve the model P2 to obtain the optimal transmission method under the given legal link channel state h=(||h _SR || ² ,||h _RD || ² ) as follows:

1) If the channel state of the legal link does not fall in the set of transmission conditions, then Then no transmission is performed, and the expression of the launch condition set H is as follows:

2) If the channel state of the legal link falls in the set of transmission conditions, i.e. h∈H, then transmit, the optimal power allocation factor η ^* (h) and the maximum private information encoding rate are the roots of the following system of binary equations:

The maximum safe transmission rate for:

At the same time, the optimal codeword transmission rate of the codebook used by the i-th hop (i=1,2) They are:

Compared with prior art, the beneficial effects of the present invention are:

The invention discloses a relay transmission method based on physical layer security in the random distribution scene of eavesdropping users. The proposed optimal transmission method can maximize the security transmission rate under the condition of satisfying the security interruption probability constraint and the total transmission power constraint ; The proposed method does not depend on eavesdropping on the user's location and channel state information, and is easier to implement in practical systems; Simulation experiments show that our proposed method (optimal solution/optimal power allocation) can maximize the safe transmission rate , and can be approximated by a simpler suboptimal method—SNR equalized power allocation—at high SNR.

Description of drawings

Fig. 1 is a system model diagram of the present invention;

Fig. 2 is the emulation verification to safe interruption probability expression (11) in the present invention;

Fig. 3 is under different path loss factors in the present invention, the change curve of safe transmission rate with power allocation factor;

Fig. 4 is under different eavesdropping user distribution densities in the present invention, the change curve of secure transmission rate with power allocation factor;

Fig. 5 is the change curve of the safe transmission rate with the power allocation factor under different total transmission signal-to-noise ratios in the present invention;

Fig. 6 shows the security throughput achieved by adopting the optimal transmission method under different configurations of the number of antennas in the present invention;

Fig. 7 shows the security throughput achieved by using different transmission methods in the present invention.

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings.

The present invention investigates a relay transmission system with randomly distributed eavesdropping users, as shown in FIG. 1 . The source node S wants to transmit the private information to the destination node D. Due to the lack of direct transmission link, the relay R is selected to forward the private information. Both the source node and the destination node are equipped with a single antenna, and the relay node is equipped with _NR antennas. Therefore, the complete transmission process includes two hops (two stages), the first hop is from the source node S to the relay R, and the second hop is from the relay R to the destination node D. There are randomly distributed eavesdropping users in the network, and each eavesdropping user is equipped with N _E antennas. Assume that the location distribution of eavesdropping users in these two hops is independent of each other, and they all obey a uniform Poisson point process (PPP distribution) with a density of _λE .

In order to prevent eavesdropping users from using maximum ratio combining to improve the ability to decode information, we adopt the RF relay forwarding strategy, so that only need to ensure the safe transmission of each hop, the final information is safe.

For the above system model, the main steps of the present invention include:

1) Based on stochastic geometry theory, calculate the security outage probability after two-hop relay transmission under the condition that the eavesdropping users are randomly distributed and the eavesdropping users are not colluding, and construct the maximum security transmission rate under the constraint of the security outage probability Optimize model P1;

2) Transform the optimized model P1 into an equivalent simplified model P2;

3) Solve the model P2 to obtain the optimal transmission method, including power allocation and codebook rate selection. said

Step 1) is specifically:

a. Use E _j to represent the jth eavesdropping user, and use Φ _E,1 to represent the eavesdropping users distributed on the entire two-dimensional plane during the transmission process of the first hop (transmission from the source node S to the relay R). Set, calculate the channel capacity C _M,1 of the legal link and the channel capacity C _E,1 of the eavesdropping link at the first hop, and the calculation formulas are:

Among them, ρ ₁ represents the transmit signal-to-noise ratio of the first-hop transmitting node (source node S), ||h _SR || ² represents the small-scale fading gain of the legitimate link between source node S and relay R, and d _SR represents the distance between the source node S and the relay R, represents the small-scale fading gain of the eavesdropping link between the source node S and the eavesdropping user _Ej , Represents the distance between the source node S and the eavesdropping user E _j , α is the path loss factor;

b. Use E _j to represent the jth eavesdropping user, and use Φ _E,2 to represent the set of eavesdropping users distributed on the entire two-dimensional plane during the transmission process of the second hop (transmission from relay R to destination node D) , calculate the channel capacity C _{M,2 of} the legitimate link and the channel capacity CE,2 of the eavesdropping link at the second hop, and the calculation formulas are:

Among them, ρ ₂ represents the transmit signal-to-noise ratio of the second-hop transmitting node (relay R), ||h _RD || ² represents the small-scale fading gain of the legitimate link between relay R and destination node D, and d _RD represents The distance between relay R and destination node D, represents the small-scale fading gain of the eavesdropping link between relay R and eavesdropping user _Ej , Represents the distance between relay R and eavesdropping user E _j ;

c. For a given private information encoding rate R _S , use P _sec,1 to represent the security interruption probability of the first hop transmission, and the specific calculation formula is:

Among them, γ(N _E ,c _j ) is an incomplete gamma function;

d. For a given private information coding rate R _S that needs to be achieved, use P _sec,2 to represent the security interruption probability of the second hop transmission, and the specific calculation formula is:

e, combine formula (5) and formula (6) to obtain the safety interruption probability after two-hop relay transmission, and its concrete expression is as follows:

in, Substitute for variables.

Described step 2) specifically is:

a. Define the safe transmission rate T _s , whose expression is:

Among them, R _s is the private information encoding rate of the codebook used in each hop (the R _s of the two hops are the same);

b. Use R _t,i to represent the codeword transmission rate of the codebook used in the i-th hop, then construct the optimization model P1 for maximizing the safe transmission rate as shown below:

Wherein, the expression of the safe outage probability P _out has been given in the formula (7), and ε is the threshold value of the pre-set tolerable safe outage probability.

The step 3) is specifically:

a. Since the safe transmission rate can only be maximized when the transmission power is completely used up, the last inequality constraint on the total power in model P1 can be ρ ₁ + ρ ₂ ≤ ρ ₀ , ρ ₁ ≥ 0, ρ ₂ ≥ 0 When the total conversion power ρ ₀ is used up, the constraint on the power allocation factor η is 0≤η≤1. Under this power allocation factor, there are ρ ₁ =ηρ ₀ and ρ ₂ =(1-η)ρ ₀ , and the model The simplified optimization model P2 corresponding to P1 is:

Among them, the formula The expression is:

b. Solve the model P2 to obtain the optimal transmission method under the given legal link channel state h=(||h _SR || ² ,||h _RD || ² ) as follows:

1) If the channel state of the legal link does not fall in the set of transmission conditions, then Then no transmission is performed, and the expression of the launch condition set H is as follows:

2) If the channel state of the legal link falls in the set of transmission conditions, i.e. h∈H, then transmit, the optimal power allocation factor η ^* (h) and the maximum private information encoding rate are the roots of the following system of binary equations:

The maximum safe transmission rate for:

At the same time, the optimal codeword transmission rate of the codebook used by the i-th hop (i=1,2) They are:

FIG. 2 is a simulation verification of the safety outage probability expression (11) in the present invention. We use Monte Carlo simulation to verify expression (11). The simulation scene is a circular area with a radius of 2000m centered on the source node S. The power allocation factor is preset as η=0.5, the path loss factor is α=3, the total transmission signal-to-noise ratio is ρ ₀ =30dB, and the eavesdropping user density is λ _E =10 ^-3 per square meter. Looking at this figure, it can be found that the derived safety outage probability (11) is in good agreement with the Monte Carlo simulation results.

Fig. 3 is a curve of safe transmission rate changing with power allocation factor under different path loss factors in the present invention. The asterisk is the optimal solution (η ^* (h), T _s ^* (h)) that can be achieved by using the optimal transmission method proposed by the present invention. Observing this figure, it can be found that the method proposed in the present invention can maximize the safe transmission rate, and as the path loss factor increases, the maximum transmission rate decreases.

Fig. 4 is a curve of safe transmission rate changing with power allocation factor under different eavesdropping user distribution densities in the present invention. The asterisks are the optimal solutions that can be achieved by adopting the optimal transmission method proposed by the present invention. Observing this figure, it can be found that the method proposed in the present invention can maximize the secure transmission rate, and as the density of eavesdropping users increases, the maximum transmission rate decreases.

FIG. 5 shows the security throughput achieved by adopting the optimal transmission method under different antenna number configurations in the present invention. The asterisks are the optimal solutions that can be achieved by adopting the optimal transmission method proposed by the present invention. Observing this figure, it can be found that the method proposed in the present invention can maximize the safe transmission rate, and as the total transmission signal-to-noise ratio increases, the maximum transmission rate increases and tends to a constant value.

FIG. 6 shows the security throughput achieved by adopting the optimal transmission method under different configurations of the number of antennas in the present invention. Observing this figure, it can be found that when N _R > _NE , the security rate is large, and when N _R < _NE , the security rate is extremely low. In the case of _{NR =} NE, as the number of antennas increases, the safe transmission rate increases and tends to a constant value.

Fig. 7 shows the security throughput achieved by using different transmission methods in the present invention. Equal power distribution is η ^eql = 0.5, SNR balanced power distribution is Observing this figure, it can be found that the method proposed by the present invention (optimal power allocation) is superior to the other two comparative methods. Moreover, under the condition of high SNR, the method proposed by the present invention can be approximated by SNR equalized power allocation.

Claims (3)

1. The relay transmission method based on physical layer security in the randomly distributed scene of eavesdropping users is characterized in that, comprising the following steps: 1) Based on stochastic geometry theory, calculate the security outage probability after two-hop relay transmission under the condition that the eavesdropping users are randomly distributed and the eavesdropping users are not colluding, and construct the maximum security transmission rate under the constraint of the security outage probability Optimize model P1; 2) Transform the optimized model P1 into an equivalent simplified model P2; The specific method is as follows: a. Define the safe transmission rate T _s , whose expression is: Among them, R _s is the private information encoding rate of the codebook used in each hop, and the R _s of the two hops are the same; b. Use R _t,i to represent the codeword transmission rate of the codebook used in the i-th hop, then construct the optimization model P1 for maximizing the safe transmission rate as shown below: Among them, the expression of the safety outage probability P _out has been given in the formula (7), and ε is the threshold value of the safety outage probability that can be tolerated in advance; 3) Solve the model P2 to obtain the optimal transmission method, including power allocation and codebook rate selection. 2. the relay transmission method based on physical layer security in the eavesdropping user random distribution scene according to claim 1, is characterized in that, the specific method of described step 1) is as follows: a. Both the source node and the destination node are equipped with a single antenna, the relay is equipped with N _R antennas, and each eavesdropping user is equipped with N _E antennas. Use E _j to represent the j-th eavesdropping user, and use Φ _E,1 to indicate that at the first hop That is, during the transmission process from the source node S to the relay R, a set of eavesdropping users distributed on the entire two-dimensional plane is formed, and the channel capacity C _M,1 of the legal link at the first hop and the channel capacity of the eavesdropping link are calculated Capacity C _E,1 , the calculation formulas are: Among them, ρ ₁ represents the transmit signal-to-noise ratio of the first-hop transmitting node, that is, the source node S, ||h _SR || ² represents the small-scale fading gain of the legal link between the source node S and the relay R, and d _SR represents the source the distance between node S and relay R, represents the small-scale fading gain of the eavesdropping link between the source node S and the eavesdropping user _Ej , Represents the distance between the source node S and the eavesdropping user E _j , α is the path loss factor; b. Use E _j to represent the jth eavesdropping user, and use Φ _E,2 to represent the set of eavesdropping users distributed on the entire two-dimensional plane during the second hop, during transmission from relay R to destination node D, Calculate the channel capacity C _M,2 of the legal link and the channel capacity C _E,2 of the eavesdropping link at the second hop, and the calculation formulas are: Among them, ρ ₂ represents the transmitting signal-to-noise ratio of the second-hop transmitting node, that is, the relay R, ||h _RD || ² represents the small-scale fading gain of the legal link between the relay R and the destination node D, and d _RD represents the medium Following the distance between R and destination node D, represents the small-scale fading gain of the eavesdropping link between relay R and eavesdropping user _Ej , Represents the distance between relay R and eavesdropping user E _j ; C. For a given private information encoding rate R _S , use P _sec,1 to represent the security interruption probability of the first hop transmission, and the specific calculation formula is: Among them, γ(N _E ,c _j ) is an incomplete gamma function; d. For a given private information coding rate R _S that needs to be achieved, use P _sec,2 to represent the security interruption probability of the second hop transmission, and the specific calculation formula is: e, combine formula (5) and formula (6) to obtain the safety interruption probability after two-hop relay transmission, and its concrete expression is as follows: in, Substitute for variables. 3. the relay transmission method based on physical layer security in the randomly distributed scene of eavesdropping users according to claim 1, is characterized in that, the concrete method of described step 3) is as follows: a. Since the safe transmission rate can only be maximized when the transmission power is completely used up, the last inequality constraint on the total power in model P1 is transformed into ρ ₁ +ρ ₂ ≤ρ ₀ ,ρ ₁ ≥0,ρ ₂ ≥0 When the total power ρ ₀ is all used up, the constraint on the power allocation factor η is 0≤η≤1. Under this power allocation factor, there are ρ ₁ =ηρ ₀ and ρ ₂ =(1-η)ρ ₀ , and the model P1 The corresponding simplified optimization model P2 is: Among them, the formula The expression is: b. Solve the model P2 to obtain the optimal transmission method under the given legal link channel state h=(||h _SR || ² ,||h _RD || ² ) as follows: 1) If the channel state of the legal link does not fall in the set of transmission conditions, then Then no transmission is performed, and the emission condition set The expression of is as follows: 2) If the channel state of the legal link falls in the set of transmission conditions, then Then transmit, the optimal power allocation factor η ^* (h) and the maximum private information encoding rate are the roots of the following system of binary equations: The maximum safe transmission rate for: At the same time, the optimal codeword transmission rate of the codebook used by the i-th hop (i=1,2) They are: