CN106131823B - Relay transmission method based on safety of physical layer in eavesdropping user random distribution scene - Google Patents
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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
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a relay transmission method based on physical layer security in a randomly distributed scene of an eavesdropping user.
Background
Due to the broadcasting characteristic of the wireless channel, private information transmitted between nodes is easily intercepted by some illegal nodes (eavesdropping users), thereby threatening the safe transmission of the information. The traditional high-level encryption technology is based on the assumption that the calculation capacity of an eavesdropping user is limited to ensure the information security. However, with the development of high-speed and high-efficiency computing technologies such as quantum computing, the computing power of eavesdropping users tends to be infinite, and high-level encryption technologies can no longer guarantee absolute security of information. Accordingly, the physical layer security technique does not rely on the limitation of the calculation capability of the eavesdropping user, and can provide absolute security in the information theory sense.
However, in many studies on physical layer security, it is assumed that the channel state of an eavesdropping user is known. In practice, this assumption is difficult to realize in reality, since the eavesdropping user usually remains silent, does not transmit any signal, and even the location distribution of the eavesdropping user is difficult to obtain. Therefore, it is a significant research work to design a transmission strategy to ensure secure communication without knowing the location distribution and channel state of the eavesdropping user.
Disclosure of Invention
In view of the above drawbacks or deficiencies, an object of the present invention is to provide a relay transmission method based on physical layer security in a randomly distributed scenario without eavesdropping, which can maximize a secure transmission rate.
In order to achieve the above purpose, the technical method of the invention is as follows:
a relay transmission method based on physical layer security in a randomly distributed scene of an eavesdropping user comprises the following steps:
1) based on a random geometric theory, calculating the safe interruption probability after two-hop relay transmission under the conditions that the positions of eavesdropping users are randomly distributed and the eavesdropping users are not colluded, and constructing an optimization model P1 for maximizing the safe transmission rate under the constraint of the safe interruption probability;
2) converting the optimization model P1 into an equivalent simplified model P2;
3) and solving the model P2 to obtain an optimal transmission method, including power distribution and codebook rate selection. The above-mentioned
The step 1) is specifically as follows:
a. the source node and the destination node are both provided with a single antenna, and the relay is provided with NRRoot antenna, each eavesdropping user being provided with NERoot antenna, using EjUsing phi on behalf of the jth eavesdropping userE,1Representing a set of eavesdropping users distributed on the whole two-dimensional plane in the first-hop (from the source node S to the relay R) transmission process, and calculating the channel capacity C of a legal link at the first hopM,1And eavesdropping the channel capacity C of the linkE,1The calculation formulas are respectively as follows:
where ρ is1Represents the transmission signal-to-noise ratio of the first hop transmitting node (source node S) | | hSR||2Small scale fading gain, d, representing the legal link between source node S and relay RSRRepresenting the distance between the source node S and the relay R,representing source node S and eavesdroppingUser EjEavesdropping on the small-scale fading gain of the link,representing source node S and eavesdropping user Ejα is the path loss factor;
b. using EjUsing phi on behalf of the jth eavesdropping userE,2Representing the set of eavesdropping users distributed over the whole two-dimensional plane during the transmission of the second hop (from the relay R to the destination node D), calculating the channel capacity C of the legal link at the second hopM,2And eavesdropping the channel capacity C of the linkE,2The calculation formulas are respectively as follows:
where ρ is2Represents the transmission signal-to-noise ratio, | h, of the second hop transmitting node (relay R)RD||2Small scale fading gain, D, representing a legitimate link between the relay R and the destination node DRDRepresenting the distance between the relay R and the destination node D,representing relays R and eavesdropping users EjEavesdropping on the small-scale fading gain of the link,representing relays R and eavesdropping users EjThe distance between them;
c. coding rate R for given required private informationSBy Psec,1The probability of the safe interruption of the first hop transmission is represented by a specific calculation formula:
wherein, gamma (N)E,cj) Is an incomplete gamma function;
d. coding rate R for given required private informationSBy Psec,2The probability of the safe interruption of the second hop transmission is represented by the specific calculation formula:
e. and (3) combining the formula (5) and the formula (6) to obtain the safety interruption probability after two-hop relay transmission, wherein the specific expression is as follows:
wherein,is a variable substitution.
The step 2) is specifically as follows:
a. defining a secure transmission rate TsThe expression is as follows:
wherein R issPrivate information coding rate of codebook used for each hop (two-hop R)sThe same);
b. with Rt,iThe code word transmission rate of the codebook used by the ith hop is represented, and then the code word transmission rate is constructedThe secure transfer rate maximization optimization model P1 is shown below:
wherein the probability of safe interruption PoutThe expression of (c) is given in equation (7), and epsilon is a threshold value of the tolerable safe interruption probability which is set in advance.
The step 3) is specifically as follows:
a. since the safe transmission rate cannot be maximized until the transmission power is completely exhausted, the last inequality constraint ρ about the total power in the model P1 can be set1+ρ2≤ρ0,ρ1≥0,ρ2Total power rho converted to not less than 00The constraint of the power distribution factor η, i.e. 0 & lt, η & lt, 1 when all are used up, and the power distribution factor has rho1=ηρ0And ρ2=(1-η)ρ0Then the simplified optimization model P2 corresponding to model P1 is:
wherein, the formulaThe expression of (a) is:
b. solving the model P2 to obtain the channel state h (| | h) at a given legal linkSR||2,||hRD||2) The following optimal transmission method is as follows:
1) if the legal link channel state does not fall in the transmissionIn a set of conditionsThen no transmission is made and the expression of the set of transmission conditions H is as follows:
2) if the legal link channel state falls in the emission condition set, namely H belongs to H, the transmission is carried out, and the optimal power distribution factor η*(h) And maximum private information encoding rateIs the root of the following system of equations:
the maximum safe transmission rateComprises the following steps:
meanwhile, the optimal codeword transmission rate of the codebook used in the ith hop (i ═ 1,2)Respectively as follows:
compared with the prior art, the invention has the beneficial effects that:
the invention discloses a relay transmission method based on physical layer security in a random distribution scene of eavesdropping users, and the proposed optimal transmission method can maximize the safe transmission rate under the condition of meeting the safety interruption probability constraint and the total transmission power constraint; the proposed method does not rely on eavesdropping of the user's location and channel state information, and is easier to implement in a practical system; simulation experiments show that the proposed method (optimal solution/optimal power allocation) can maximize the safe transmission rate and can be approximated by a simpler suboptimal method, namely signal-to-noise ratio equalization power allocation, under high signal-to-noise ratio.
Drawings
FIG. 1 is a diagram of a system model of the present invention;
FIG. 2 is a simulation verification of the safe outage probability expression (11) in the present invention;
FIG. 3 is a graph of safe transmission rate versus power allocation factor for different path loss factors in accordance with the present invention;
FIG. 4 is a graph of the change of the safe transmission rate with the power allocation factor under different eavesdropping user distribution densities in the present invention;
FIG. 5 is a graph of safe transmission rate versus power allocation factor for different total SNR for transmissions in accordance with the present invention;
FIG. 6 is a graph illustrating the safety throughput achieved by the optimal transmission method under different antenna number configurations in the present invention;
fig. 7 is a graph of the secure throughput achieved with different transmission methods in the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
The present invention investigates a relay transmission system in which eavesdropping users are randomly distributed in positions, as shown in fig. 1. The source node S is to transmit the private information to the destination node D, and due to the absence of the direct transmission link, the relay R is selected to forward the private information. The source node and the destination node are both provided with a single antenna, and the relay node is provided with NRA root antenna. Thus, the complete transmission process involves two hops (two phases), the first hop from the source node S to the relay R and the second hop from the relay R to the destination node D. There are wiretapping users with randomly distributed positions in the network, and each wiretapping user is equipped with NEA root antenna. It is assumed that the position distribution of the eavesdropping users in the two hops is independent of each other and is subject to the density of lambdaEUniform poisson point process (PPP distribution).
In order to avoid eavesdropping on the capability of improving decoding information by adopting maximum ratio combination, an RF relay forwarding strategy is adopted, so that the final information is safe only by ensuring the safe transmission of each hop.
Aiming at the system model, the main steps of the invention comprise:
1) based on a random geometric theory, calculating the safe interruption probability after two-hop relay transmission under the conditions that the positions of eavesdropping users are randomly distributed and the eavesdropping users are not colluded, and constructing an optimization model P1 for maximizing the safe transmission rate under the constraint of the safe interruption probability;
2) converting the optimization model P1 into an equivalent simplified model P2;
3) and solving the model P2 to obtain an optimal transmission method, including power distribution and codebook rate selection. The above-mentioned
The step 1) is specifically as follows:
a. using EjFor representing j-th eavesdroppingAt home using phiE,1Representing a set of eavesdropping users distributed on the whole two-dimensional plane in the first-hop (from the source node S to the relay R) transmission process, and calculating the channel capacity C of a legal link at the first hopM,1And eavesdropping the channel capacity C of the linkE,1The calculation formulas are respectively as follows:
where ρ is1Represents the transmission signal-to-noise ratio of the first hop transmitting node (source node S) | | hSR||2Small scale fading gain, d, representing the legal link between source node S and relay RSRRepresenting the distance between the source node S and the relay R,representing source node S and eavesdropping user EjEavesdropping on the small-scale fading gain of the link,representing source node S and eavesdropping user Ejα is the path loss factor;
b. using EjUsing phi on behalf of the jth eavesdropping userE,2Representing the set of eavesdropping users distributed over the whole two-dimensional plane during the transmission of the second hop (from the relay R to the destination node D), calculating the channel capacity C of the legal link at the second hopM,2And eavesdropping the channel capacity C of the linkE,2The calculation formulas are respectively as follows:
where ρ is2Represents the transmission signal-to-noise ratio, | h, of the second hop transmitting node (relay R)RD||2Small scale fading gain, D, representing a legitimate link between the relay R and the destination node DRDRepresenting the distance between the relay R and the destination node D,representing relays R and eavesdropping users EjEavesdropping on the small-scale fading gain of the link,representing relays R and eavesdropping users EjThe distance between them;
c. coding rate R for given required private informationSBy Psec,1The probability of the safe interruption of the first hop transmission is represented by a specific calculation formula:
wherein, gamma (N)E,cj) Is an incomplete gamma function;
d. coding rate R for given required private informationSBy Psec,2The probability of the safe interruption of the second hop transmission is represented by the specific calculation formula:
e. and (3) combining the formula (5) and the formula (6) to obtain the safety interruption probability after two-hop relay transmission, wherein the specific expression is as follows:
wherein,is a variable substitution.
The step 2) is specifically as follows:
a. defining a secure transmission rate TsThe expression is as follows:
wherein R issPrivate information coding rate of codebook used for each hop (two-hop R)sThe same);
b. with Rt,iRepresenting the codeword transmission rate of the codebook used for the ith hop, a secure transmission rate maximization optimization model P1 is constructed as follows:
wherein the probability of safe interruption PoutThe expression of (c) is given in equation (7), and epsilon is a threshold value of the tolerable safe interruption probability which is set in advance.
The step 3) is specifically as follows:
a. since the safe transmission rate cannot be maximized until the transmission power is completely exhausted, the last inequality constraint ρ about the total power in the model P1 can be set1+ρ2≤ρ0,ρ1≥0,ρ2Total power rho converted to not less than 00All usingThe constraint of the power distribution factor η at the end, namely 0 is more than or equal to η is more than or equal to 1, and rho is under the power distribution factor1=ηρ0And ρ2=(1-η)ρ0Then the simplified optimization model P2 corresponding to model P1 is:
wherein, the formulaThe expression of (a) is:
b. solving the model P2 to obtain the channel state h (| | h) at a given legal linkSR||2,||hRD||2) The following optimal transmission method is as follows:
1) if the legal link channel state does not fall within the set of transmission conditionsThen no transmission is made and the expression of the set of transmission conditions H is as follows:
2) if the legal link channel state falls in the emission condition set, namely H belongs to H, the transmission is carried out, and the optimal power distribution factor η*(h) And maximum private information encoding rateIs the root of the following system of equations:
the maximum safe transmission rateComprises the following steps:
meanwhile, the optimal codeword transmission rate of the codebook used in the ith hop (i ═ 1,2)Respectively as follows:
fig. 2 is a simulation verification of the safety interruption probability expression (11) in the present invention, a monte carlo simulation is adopted to verify the expression (11), a simulation scene is a circular region with a radius of 2000m and a source node S as a center, a power distribution factor is preset to η ═ 0.5, a path loss factor is preset to α ═ 3, and a total transmission signal-to-noise ratio is ρ030dB, the eavesdropping user density is lambdaE=10-3Per square meter. Observing this graph, it can be seen that the derived safing outage probability (11) matches the monte carlo simulation results.
FIG. 3 is a graph of the change of the safe transmission rate with the power allocation factor under different path loss factors in the present invention, and the asterisk is the optimal solution (η) that can be achieved by the optimal transmission method proposed by the present invention*(h),Ts *(h) ). Observing the graph, the method provided by the invention can maximize the safe transmission rate, and the maximum transmission rate is reduced along with the increase of the path loss factor.
Fig. 4 is a graph showing the variation of the security transmission rate with the power allocation factor under different distribution densities of eavesdropping users in the present invention. The asterisks are the optimal solutions that can be achieved by adopting the optimal transmission method provided by the invention. Observing the graph, the method provided by the invention can maximize the safe transmission rate, and the maximum transmission rate is reduced along with the increase of the eavesdropping user density.
Fig. 5 shows the safety throughput achieved by 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 provided by the invention. Observing the graph, the method provided by the invention can maximize the safe transmission rate, and the maximum transmission rate is increased and tends to be constant as the signal-to-noise ratio of the total transmission is increased.
Fig. 6 shows the safety throughput achieved by the optimal transmission method under different antenna number configurations in the present invention. Observing the graph, it can be found that when N isR>NEWhen the safe rate is large, when NR<NEThe safe rate is extremely low. In NR=NEIn this case, as the number of antennas increases, the safe transmission rate increases and tends to be constant.
FIG. 7 illustrates the safety throughput achieved by the present invention using different transmission methods, equal power allocation ηeqlSignal-to-noise ratio equalising power allocation, i.e. 0.5From this figure it can be seen that the proposed method of the present invention (optimal power allocation) is superior to the two remaining comparative methods. And, under the condition of high signal-to-noise ratio, the method provided by the invention can be approximated by signal-to-noise ratio equalization power allocation.
Claims (3)
1. The relay transmission method based on physical layer security in the randomly distributed scene of the eavesdropping user is characterized by comprising the following steps:
1) based on a random geometric theory, calculating the safe interruption probability after two-hop relay transmission under the conditions that the positions of eavesdropping users are randomly distributed and the eavesdropping users are not colluded, and constructing an optimization model P1 for maximizing the safe transmission rate under the constraint of the safe interruption probability;
2) converting the optimization model P1 into an equivalent simplified model P2;
the specific method comprises the following steps:
a. defining a secure transmission rate TsThe expression is as follows:
wherein R issFor private information coding rate of the codebook used per hop, R of two hopssThe same is true;
b. with Rt,iRepresenting the codeword transmission rate of the codebook used for the ith hop, a secure transmission rate maximization optimization model P1 is constructed as follows:
wherein the probability of safe interruption PoutThe expression of (c) is given in formula (7), and epsilon is a preset threshold value of tolerable safety interruption probability;
3) and solving the model P2 to obtain an optimal transmission method, including power distribution and codebook rate selection.
2. The relay transmission method based on physical layer security in a randomly distributed scenario of eavesdropping users according to claim 1, wherein the specific method of step 1) is as follows:
a. the source node and the destination node are both provided with a single antenna, and the relay is provided with NRRoot antenna, each eavesdropping user being provided with NERoot antenna, using EjUsing phi on behalf of the jth eavesdropping userE,1Representing a set formed by eavesdropping users distributed on the whole two-dimensional plane in the process of first hop, namely transmission from a source node S to a relay R, and calculating the channel capacity C of a legal link at the time of the first hopM,1And eavesdropping the channel capacity C of the linkE,1The calculation formulas are respectively as follows:
where ρ is1Represents the transmission signal-to-noise ratio, | h, of the first hop transmitting node, i.e., the source node SSR||2Small scale fading gain, d, representing the legal link between source node S and relay RSRRepresenting the distance between the source node S and the relay R,representing source node S and eavesdropping user EjEavesdropping on the small-scale fading gain of the link,representing source node S and eavesdropping user Ejα is the path loss factor;
b. using EjUsing phi on behalf of the jth eavesdropping userE,2Representing the set formed by eavesdropping users distributed on the whole two-dimensional plane in the process of transmitting from the relay R to the destination node D at the second hop, and calculating the channel capacity C of the legal link at the second hopM,2And eavesdropping the channel capacity C of the linkE,2The calculation formulas are respectively as follows:
where ρ is2Represents the transmission signal-to-noise ratio, | h, of the second hop transmission node, i.e., the relay RRD||2Small scale fading gain, D, representing a legitimate link between the relay R and the destination node DRDRepresenting the distance between the relay R and the destination node D,representing relays R and eavesdropping users EjEavesdropping on the small-scale fading gain of the link,representing relays R and eavesdropping users EjThe distance between them;
C. coding rate R for given required private informationSBy Psec,1The probability of the safe interruption of the first hop transmission is represented by a specific calculation formula:
wherein, gamma (N)E,cj) Is an incomplete gamma function;
d. coding rate R for given required private informationSBy Psec,2The probability of the safe interruption of the second hop transmission is represented by the specific calculation formula:
e. and (3) combining the formula (5) and the formula (6) to obtain the safety interruption probability after two-hop relay transmission, wherein the specific expression is as follows:
wherein,is a variable substitution.
3. The relay transmission method based on physical layer security in a randomly distributed scenario of eavesdropping users according to claim 1, wherein the specific method of step 3) is as follows:
a. since the safe transmission rate cannot be maximized until the transmission power is completely exhausted, the last inequality constraint ρ about the total power in the model P1 is set1+ρ2≤ρ0,ρ1≥0,ρ2Total power rho converted to not less than 00The constraint of the power distribution factor η, i.e. 0 & lt, η & lt, 1 when all are used up, and the power distribution factor has rho1=ηρ0And ρ2=(1-η)ρ0Then the simplified optimization model P2 corresponding to model P1 is:
wherein, the formulaThe expression of (a) is:
b. solving the model P2 to obtain the channel state h (| | h) at a given legal linkSR||2,||hRD||2) The following optimal transmission method is as follows:
1) if the legal link channel state does not fall within the set of transmission conditionsThen no transmission is made, the conditions are setThe expression of (a) is as follows:
2) if the legal link channel state falls within the set of transmission conditionsThen transmission is made with the optimum power allocation factor η*(h) And maximum private information encoding rateIs the root of the following system of equations:
the maximum safe transmission rateComprises the following steps:
meanwhile, the optimal codeword transmission rate of the codebook used in the ith hop (i ═ 1,2)Respectively as follows:
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US9100405B2 (en) * | 2007-10-17 | 2015-08-04 | Dispersive Networks Inc. | Apparatus, systems and methods utilizing dispersive networking |
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CN103475441A (en) * | 2013-07-26 | 2013-12-25 | 北京邮电大学 | Cooperative interference transmission method based on clusters in wireless multi-hop network |
CN104301098A (en) * | 2014-09-01 | 2015-01-21 | 北京航空航天大学 | Opportunistic quantum network coding method |
CN105007578A (en) * | 2015-06-05 | 2015-10-28 | 西安交通大学 | Uplink secure transmission method based on downlink auxiliary feedback in 5G communication system |
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