Covert communication method and system based on expired channel state information and relay selection

Abstract

The invention discloses a covert communication method based on expired channel state information and relay selection. The method comprises the following steps: constructing a transmission model of a covert communication system based on the expired channel state information; determining a selected relay node, a non-interruption condition of legal communication and a necessary condition for the relay node to send a hidden message; determining three detection error conditions that a communication interruption mechanism is determined and a detector judges whether the relay node sends a hidden message or not; determining detection error probabilities under three detection error conditions and an optimal detection threshold value enabling the total detection error probability to be minimum; and the average hidden transmission rate is determined on the premise that the hidden requirement is met. Based on non-ideal conditions of expired channel state information in actual communication, the invention provides an effective covert communication method for a covert communication system which is configured with greedy relays and based on relay selection, and can better meet the requirements of covert communication in actual application.

Description

Technical Field

[0001] The present invention belongs to the field of the integration of communication technology and emerging technologies, and relates to covert communication in wireless sensor networks. Specifically, it relates to a covert communication method and system based on expired channel state information and relay selection. Background Art

[0002] In the current rapid development of technology, the integration of communication technology and emerging technologies has brought significant improvements to various fields. For example, the intelligent fire warning system based on wireless sensor networks realizes fire protection intelligence and early warning timeliness, and can reduce fire losses; the power operation and maintenance management and control system based on drone visible light and thermal imaging technology can improve operation and maintenance efficiency and equipment detection accuracy, and ensure the stability of the power system. However, behind these applications, the issues of communication security and privacy are becoming increasingly prominent. The data interaction in fire warning and power operation and maintenance involves a large amount of sensitive information, such as building structures and personnel distributions in fire protection, and equipment parameters and power grid topologies in power equipment. Once maliciously stolen or tampered with, it will seriously threaten public safety.

[0003] In the field of wireless communication, due to the continuous movement of users, the dynamic changes in the surrounding environment, and the existence of various interference factors, the channel state shows a rapid and complex change trend. This inevitably leads to the situation that expired channel state information may be used in actual communication processes. In such a situation, the impact of expired channel state information on system performance must be fully considered. Summary of the Invention

[0004] Object of the Invention: To solve the problems of communication security and privacy in application scenarios such as wireless sensor networks and power operation and maintenance management and control networks, a covert communication method and system based on expired channel state information and relay selection are provided.

[0005] Technical Solution: To achieve the above object, the present invention provides a covert communication method based on expired channel state information and relay selection, including the following steps:

[0006] S1: Construct a transmission model of a covert communication system based on expired channel state information;

[0007] S2: Determine the selected relay nodes, the non-interruption condition of legitimate communication, and the necessary conditions for the relay nodes to send covert messages according to the transmission model;

[0008] S3: Determine the communication interruption mechanism and three detection error situations for the detector to judge whether the relay nodes send covert messages according to the non-interruption condition of legitimate communication and the necessary conditions for the relay nodes to send covert messages;

[0009] S4: Determine the detection error probabilities in three cases of detection errors, and the optimal detection threshold that minimizes the total detection error probability;

[0010] S5: Determine the average covert transmission rate on the premise of meeting the covert requirements.

[0011] Furthermore, the construction of the transmission model in step S1 specifically includes: Consider a multi-relay network containing a source S, a destination D, and N half-duplex decode-and-forward relays, denoted as R i , where i = 1, …, N, representing the index of each channel use; Each node is equipped with a single antenna. Given the deep fading situation, there is no direct link between S and D; In this system, S also acts as a listener to detect whether R i transmits its covert information to D; The channel coefficient of the link a → b (a, b ∈ {S, R i , D}) is represented by h ab , which is an independent zero-mean circularly symmetric complex Gaussian random variable with variance ; The estimated value of h ab is denoted as Due to the time-varying nature and delay of the channel, is an outdated version of h ab ; The communication is divided into two phases. In the first phase, S communicates with R i , and in the second phase, R i communicates with D. S detects whether there is covert communication between R i and D.

[0012] Furthermore, the determination of the selected relay nodes in step S2 includes:

[0013] Adopt partial relay selection to determine the selected relay R k ; In the relay selection phase, each relay starts a timer, which is an inverse function of . The relay whose timer expires first is the selected relay R k , and it notifies other nodes through a flag signal, expressed as:

[0014]

[0015] The estimated value of h ab is denoted as for communication transmission and detection; Due to the time-varying nature and delay of the channel, is an outdated version of h ab , and their relationship is expressed as:

[0016]

[0017] Among them, and is a circularly symmetric complex Gaussian random variable, and ρ ab is the correlation coefficient between h ab and ; according to Jakes' autocorrelation model, ρ ab = J 0 (2πf ab τ d ), where f ab is the maximum Doppler frequency of the link a→b, τ d is the delay, and J 0 (·) represents the zero-order Bessel function of the first kind.

[0018] Furthermore, the communication transmission in step S2 is divided into two stages:

[0019] In the first stage, S sends its message x SD to R k at a fixed rate r S . The received signal at R k is expressed as:

[0020]

[0021] where P S is the transmission power of S, x S (i) is the normalized signal transmitted by S, satisfying E{|x S (i)| 2} = 1, is the additive white Gaussian noise at R k .

[0022] In the second stage, when R k starts to transmit, the received signal at D is expressed as:

[0023]

[0024] where and P C are the transmission power of the legitimate message and the fixed transmission power of the covert message respectively. I = 0 means that R k does not transmit its covert message, and I = 1 means that R k transmits its covert message. x R (i) and x C (i) represent the signals of the legitimate message and the covert message respectively, satisfying E{|x R (i)| 2} = 1 and E{|x C (i)| 2} = 1, is the additive white Gaussian noise at D.

[0025] Furthermore, the non - interruption condition for legitimate communication and the necessary condition for the relay node to send a covert message in step S2 are specifically as follows:

[0026] Based on the expired channel state information, whether R k transmits depends on two necessary conditions: one is that R k can successfully decode x S ; the other is that D can also successfully decode, and the specific condition is expressed as:

[0027]

[0028] Among them, represents the received signal - to - noise ratio at R k ; represents the maximum received signal - to - noise ratio at D, represents the signal - to - noise ratio threshold, P M is the maximum transmit power of R k ; is the noise power at D;

[0029] Similarly, based on the actual channel state information, whether R k transmits depends on two necessary conditions: one is that R k can successfully decode x S ; the other is that D can also successfully decode, and the specific condition is expressed as:

[0030]

[0031] Among them, represents the received signal - to - noise ratio at R k ; γ D,I represents the received signal - to - noise ratio at D;

[0032] The signal - to - interference - plus - noise ratio for decoding x R is expressed as:

[0033]

[0034] To ensure that D can successfully decode the message, let It is obtained that:

[0035]

[0036] Considering the maximum power constraint at R k The necessary condition for R to perform covert transmission is expressed as: k

[0037] ​

[0038] After decoding x R subtract it from the signal received at D, so the signal-to-noise ratio for decoding x C is given by:

[0039]

[0040] Furthermore, in step S3, a communication interruption mechanism is determined. Once a communication interruption occurs, the detector determines that R k sends the covert information, and then three cases of detection errors are determined, specifically including:

[0041] Case 1: The actual communication is not interrupted and is further divided into three events, which are respectively represented as:

[0042]

[0043] Among them, represents the event that satisfies and R k does not send the covert message, represents the event that satisfies and R k sends the covert message;

[0044] Case 2: The actual communication between R k and D is interrupted and is further divided into two events, which are respectively represented as:

[0045]

[0046] Among them, represents the event that satisfies and R k does not send the covert message;

[0047] Case 3: The actual communication between S and R k is interrupted, that is,

[0048]

[0049] Among them, represents the event that R k does not send the message.

[0050] Furthermore, step S4 specifically includes:

[0051] First, when R k starts to transmit, S will detect whether R k transmits its covert information. The binary hypothesis of the received signal at S is expressed as:

[0052]

[0053] Among them, is the additive white Gaussian noise at S, H 1 and H 0 respectively represent the hypothesis that R k transmits a covert message with or without; the optimal detection scheme is the radiometer which is expressed as:

[0054]

[0055] Among them, τ is the decision threshold, D 1 and D 0 are binary decisions, corresponding to R k transmitting with or without a covert message respectively; due to channel reciprocity assuming the block length is infinite, n → ∞, T(n) is expressed as:

[0056]

[0057] In the high signal-to-noise ratio region, the expression of the conditional cumulative distribution function is:

[0058]

[0059] Among them, L is a constant,

[0060] the expression of the joint probability density function of the expired channel state information and the actual channel state information:

[0061]

[0062] Among them,

[0063] Case 1: Assume that when the necessary condition is satisfied, R k sends a covert message with probability φ. Given the decision threshold τ, the detection error probability of S is expressed as:

[0064]

[0065] Among them, Pr(H 1 ) = φ, Pr(H 0 ) = 1 - φ,

[0066]

[0067] j 1 = min(t 1 , t 3 ),j 2 = max(t1 ,t 3 ),

[0068] For a given τ, the detection error probability of S consists of two parts: the false alarm probability and the miss detection probability. Then, the false alarm probability conditioned on is expressed as:

[0069]

[0070] Similarly, the false alarm probability conditioned on is The miss detection probability conditioned on is expressed as:

[0071]

[0072] Substitute Equation (8) and Equation (9) into Equation (19) to determine the lower bound t 1 and the upper bound t 2 ; then, substitute Equation (20) into Equation (24) and Equation (25) respectively, and it can be calculated that and The probability expressions for each event in this case are as follows:

[0073]

[0074] Substitute Equation (21) and Equation (22) into Equation (26) and Equation (27) respectively, and it can be calculated that and

[0075] Case 2: The detection error probability of S is expressed as:

[0076]

[0077] where

[0078]

[0079] Then, the false alarm probability conditioned on and is The probability expressions for each event in this case are as follows:

[0080]

[0081] Similarly, substitute Equation (21) and Equation (22) into Equation (29) and Equation (30) respectively, and it can be calculated that and

[0082] Case 3: The detection error probability of S is expressed as:

[0083]

[0084] where,

[0085]

[0086] The probability expression of this event is as follows:

[0087]

[0088] Similarly, substituting formula (21) and formula (22) into formula (32) respectively, it can be calculated that

[0089] Combining formula (23), formula (28) and formula (31), the total detection error probability of S is determined to be:

[0090] ξ = ξ 1 + ξ 2 + ξ 3 (33)

[0091] The optimal detection threshold that minimizes the total detection error probability is expressed as:

[0092]

[0093] The optimal detection threshold and the total detection error probability ξ are determined by numerical search solution opt .

[0094] Furthermore, the specific steps of step S5 include:

[0095] Under the condition of meeting the concealment requirement, given a fixed transmission power P C , the effective average covert transmission rate that can be achieved in a system equipped with N relay nodes is expressed as

[0096]

[0097] where, is the exponential integral function.

[0098] The present invention provides a covert communication system based on expired channel state information and relay selection. The system includes a network interface, a memory, and a processor; where

[0099] The network interface is used to realize signal reception and transmission during the process of receiving and sending information with other external network elements;

[0100] The memory is used to store computer program instructions that can run on the processor;

[0101] The processor is used to execute the steps of a covert communication method based on expired channel state information and relay selection when running the computer program instructions.

[0102] Advantageous effects: Compared with the prior art, the present invention has the following advantages:

[0103] 1. Due to the time-varying characteristics of the channel and the delay of the communication system, the estimated value of the channel state information is often an expired version of the actual channel state information. The expired channel state information will cause the attenuation of the transmission performance and have a negative effect on covert communication. Based on the non-ideal condition of the expired channel state information faced in actual communication, the present invention provides an effective covert communication method for a relay selection-based covert communication system configured with greedy relays, which can better meet the requirements of covert communication in actual applications.

[0104] 2. Based on the application scenario of the expired channel state information, the present invention provides a method for determining the optimal detection threshold that minimizes the total detection error probability for a relay selection-based covert communication system configured with greedy relays, and proves that a positive covert transmission rate can be achieved in this network.

[0105] 3. Based on the application scenario of the expired channel state information, the present invention provides an evaluation method for the performance of covert communication for a relay selection-based covert communication system configured with greedy relays. Description of the Drawings

[0106] Figure 1 is the specific flowchart of the method of the present invention;

[0107] Figure 2 is the schematic diagram of the composition of the covert communication system of the present invention;

[0108] Figure 3 is the simulation result diagram of the total detection error probability of the present invention;

[0109] Figure 4 is the simulation result diagram of the effective average covert transmission rate of the present invention when the correlation coefficient ranges from 0 to 0.9;

[0110] Figure 5 is the simulation result diagram of the effective average covert transmission rate of the present invention when the fixed transmission rate ranges from 0.2 (bits) to 1 (bits). Detailed Embodiments

[0111] The present invention will be further illustrated below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. After reading the present invention, various equivalent modifications made by those skilled in the art fall within the scope defined by the appended claims of this application.

[0112] Embodiment 1:

[0113] This embodiment provides a covert communication method based on expired channel state information and relay selection. As Figure 1 shown, it includes the following steps:

[0114] S1: Construct a transmission model of a covert communication system based on expired channel state information;

[0115] As Figure 2 shown, this embodiment considers a multi-relay network containing a source S, a destination D, and N half-duplex decode-and-forward relays, denoted as R i , where i = 1,..., N represents the index of each channel use; each node is equipped with a single antenna. Given the deep fading situation, there is no direct link between S and D; in this system, S also acts as a listener to detect whether R i transmits its covert information to D; the channel coefficient of the link a → b (a, b ∈ {S, R i , D}) is represented by h ab , which is an independent zero-mean circularly symmetric complex Gaussian random variable with variance ; the estimated value of h ab is denoted as Due to the time-varying and delay characteristics of the channel, is an expired version of h ab ; the communication is divided into two phases. In the first phase, S communicates with R i , and in the second phase, R i communicates with D. S detects whether R i and D are conducting covert communication.

[0116] S2: Determine the selected relay node, the non-interruption condition of legitimate communication, and the necessary condition for the relay node to send a covert message according to the transmission model;

[0117] Determining the selected relay node includes:

[0118] Adopt partial relay selection to determine the selected relay R k ; in the relay selection phase, each relay starts a timer, which is an inverse function of , and the relay whose timer expires first is the selected relay R k , which notifies other nodes through a flag signal, expressed as:

[0119]

[0120] h ab The estimated value of is expressed as For communication transmission and detection; due to the time-varying nature and delay of the channel, is the outdated version of h ab and their relationship is expressed as:

[0121]

[0122] where, and is a circularly symmetric complex Gaussian random variable, ρ ab is h ab and The correlation coefficient between; according to Jakes' autocorrelation model ρ ab = J 0 (2πf ab τ d ), where f ab is the maximum Doppler frequency of the link a→b, τ d is the delay, and J 0 (·) represents the Bessel function of the first kind of order zero.

[0123] The communication transmission is divided into two stages:

[0124] In the first stage, S sends its message x SD to R k at a fixed rate r S , and the received signal at R k is expressed as:

[0125]

[0126] where, P S is the transmit power of S, x S (i) is the normalized signal transmitted by S, satisfying E{|x S (i)| 2} = 1, is the additive white Gaussian noise at R k ;

[0127] In the second stage, when R k starts to transmit, the received signal at D is expressed as:

[0128]

[0129] where, and P CThey are the transmission power of the legitimate message and the fixed transmission power of the covert message respectively. I = 0 means that R k does not transmit its covert message, and I = 1 means that R k transmits its covert message, x R (i) and x C (i) represent the signals of the legitimate message and the covert message respectively, satisfying E{|x R (i)| 2} = 1 and E{|x C (i)| 2} = 1, is the additive white Gaussian noise at D.

[0130] The non - interruption condition for legitimate communication and the necessary condition for the relay node to send a covert message are specifically:

[0131] Based on the expired channel state information, whether R k transmits depends on two necessary conditions: one is that R k can successfully decode x S ; the other is that D can also successfully decode. The specific conditions are expressed as:

[0132]

[0133] Among them, represents the received signal - to - noise ratio at R k , represents the maximum received signal - to - noise ratio at D, represents the signal - to - noise ratio threshold, P M is the maximum transmit power of R k , is the noise power at D;

[0134] Similarly, based on the actual channel state information, whether R k transmits depends on two necessary conditions: one is that R k can successfully decode x S ; the other is that D can also successfully decode. The specific conditions are expressed as:

[0135]

[0136] Among them, represents the received signal - to - noise ratio at R k , γ D,I represents the received signal - to - noise ratio at D;

[0137] The signal - to - interference - plus - noise ratio for decoding x R is expressed as:

[0138]

[0139] To ensure that D can successfully decode the message, let It follows that:

[0140]

[0141]

[0142] Consider the maximum power constraint at R k The necessary condition for covert transmission is expressed as: R k After decoding x

[0143]

[0144] After decoding x R subtract it from the received signal at D, so the signal-to-noise ratio for decoding x C is given by:

[0145]

[0146] S3: According to the non-interruption condition of legitimate communication and the necessary condition for the relay node to send a covert message, determine the communication interruption mechanism and three detection error cases for the detector to judge whether the relay node sends a covert message;

[0147] Determine a communication interruption mechanism. Once the communication is interrupted, the detector determines that R k sends a covert message. Subsequently, determine three cases of detection errors, specifically including:

[0148] Case 1: The actual communication is not interrupted and is further divided into three events, respectively represented as:

[0149]

[0150] Among them, represents the event that satisfies and R k does not send a covert message, represents the event that satisfies and R k sends a covert message;

[0151] Case 2: The actual communication between R k and D is interrupted and is further divided into two events, respectively represented as:

[0152]

[0153] Among them, represents the event that satisfies and R k does not send a covert message;

[0154] Case 3: S and R k The actual communication between them is interrupted, that is,

[0155]

[0156] wherein, represents the event that R k does not send a message.

[0157] S4: Determine the detection error probabilities in the three detection error cases, and the optimal detection threshold that minimizes the total detection error probability;

[0158] First, when R k starts to transmit, S will detect whether R k transmits its covert information. The binary hypothesis of the received signal at S is expressed as:

[0159]

[0160] wherein, is the additive white Gaussian noise at S, and H 1 and H 0 respectively represent the hypotheses that R k has or has no transmitted covert message; the optimal detection scheme is a radiometer and is expressed as:

[0161]

[0162] where τ is the decision threshold, and D 1 and D 0 are binary decisions, corresponding to R k transmitting with or without a covert message; due to channel reciprocity assuming that the block length is infinite, n→∞, T(n) is expressed as:

[0163]

[0164] In the high signal-to-noise ratio region, the expression of the conditional cumulative distribution function of is:

[0165]

[0166] where L is a constant,

[0167] the expression of the joint probability density function of the expired channel state information and the actual channel state information:

[0168]

[0169] Among them,

[0170] Case 1: Assume that when the necessary conditions are met R k sends a covert message with probability φ. Given the decision threshold τ, the detection error probability of S is expressed as:

[0171]

[0172] where Pr(H 1 ) = φ, Pr(H 0 ) = 1 - φ,

[0173]

[0174] j 1 = min(t 1 , t 3 ), j 2 = max(t 1 , t 3 ),

[0175] For a given τ, the detection error probability of S consists of two parts: the false alarm probability and the miss detection probability. Then, the false alarm probability conditioned on is expressed as:

[0176]

[0177] Similarly, the false alarm probability conditioned on The false alarm probability The miss detection probability conditioned on is expressed as:

[0178]

[0179] Substitute Equation (8) and Equation (9) into Equation (20) to determine the lower bound t 1 and the upper bound t 2 ; then, substitute Equation (21) into Equation (25) and Equation (26) respectively, and the calculated results are and The probability expressions for each event in this case are as follows:

[0180]

[0181] Substitute Equation (22) and Equation (23) into Equation (27) and Equation (28) respectively, and the calculated results are and

[0182] Case 2: The detection error probability of S is expressed as:

[0183]

[0184] where

[0185]

[0186] Then, and the false alarm probability The probability expression for each event in this case is as follows:

[0187]

[0188] Similarly, substituting formula (22) and formula (23) into formula (30) and formula (31) respectively, the calculation gives and

[0189] Case 3: The detection error probability of S is expressed as:

[0190]

[0191] where

[0192]

[0193] The probability expression for this event in this case is as follows:

[0194]

[0195] Similarly, substituting formula (22) and formula (23) into formula (33), the calculation gives

[0196] Combining formula (24), formula (29) and formula (32), the total detection error probability of S is determined as:

[0197] ξ = ξ 1 + ξ 2 + ξ 3 (34)

[0198] The optimal detection threshold that minimizes the total detection error probability is expressed as:

[0199]

[0200] The optimal detection threshold and the total detection error probability ξ are determined by numerical search opt .

[0201] S5: Determine the average covert transmission rate on the premise of meeting the covert requirement;

[0202] Under the condition of meeting the covert requirement, given a fixed transmit power P C , the covert transmission rate is defined as R C = log 2 (1 + γ C ). Combining with formula (11), the effective average covert transmission rate that can be achieved in a system equipped with N relay nodes is expressed as

[0203]

[0204] where is the exponential integral function.

[0205] Example 2:

[0206] For the method provided in Example 1, this example provides a covert communication system based on expired channel state information and relay selection. The system includes a network interface, a memory, and a processor. Among them, the network interface is used to realize the reception and transmission of signals during the process of receiving and sending information with other external network elements; the memory is used to store computer program instructions that can run on the processor; the processor is used to execute the steps of the above consensus method when running the computer program instructions.

[0207] This example also provides a computer storage medium. The computer storage medium stores a computer program, and the above-described method can be realized when the processor executes the computer program. The computer-readable medium can be considered tangible and non-transitory. Non-limiting examples of non-transitory tangible computer-readable media include non-volatile memory circuits (such as flash memory circuits, erasable programmable read-only memory circuits, or mask read-only memory circuits), volatile memory circuits (such as static random access memory circuits or dynamic random access memory circuits), magnetic storage media (such as analog or digital tapes or hard disk drives), and optical storage media (such as CDs, DVDs, or Blu-ray discs), etc. The computer program includes processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer program may also include or rely on stored data. The computer program may include a basic input / output system (BIOS) that interacts with the hardware of a dedicated computer, device drivers that interact with specific devices of a dedicated computer, one or more operating systems, user applications, background services, background applications, etc.

[0208] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) that contain computer-usable program code.

[0209] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in one Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0210] Embodiment 3:

[0211] Based on Embodiments 1 and 2, in order to verify the effectiveness and effects of the present invention, this embodiment verifies the performance of the covert communication system provided by the present invention through experiments, specifically as follows:

[0212] The experimental results are as Figures 3 to 5 shown, and the numerical results are given as follows: P M = 10dB, P S = 10dB, P C = -10dB,, φ = 0.5, r SD = 1bits,

[0213] It can be seen from Figure 3 that: as the value of the correlation coefficient increases, the total detection error probability decreases, indicating that the expired channel state information leads to an increase in the total detection error probability, which is beneficial to covert communication. When the value of the correlation coefficient is low, as the number of relays increases, the total detection error probability increases significantly, indicating that the application of relay selection will also cause an increase in the total detection error probability.

[0214] It can be seen from Figure 4 that: as the value of the correlation coefficient increases, the effective average covert transmission rate decreases. On the other hand, we can also observe that when the fixed transmission rate r of the source SDWhen ρ = 0.8, applying relay selection can improve the effective average covert transmission rate in the case of outdated channel state information.

[0215] It can be seen from Figure 5 that when the fixed transmission rate of the source is low, the effective average covert transmission rate decreases as the number of relays increases. However, when the fixed transmission rate of the source is high, the effective average covert transmission rate increases as the number of relays increases, which indicates that applying relay selection can provide a gain in the effective average covert transmission rate as the fixed transmission rate of the source increases.

[0216] Combining Figure 3 , Figure 4 and Figure 5 , the method proposed by the present invention is that when the correlation coefficient value between the actual channel state information and the outdated channel state information is small, applying relay selection can also cause an increase in the total detection error probability, and when the fixed transmission rate of the source increases, it can provide a gain in the effective average covert transmission rate.

Claims

1. A covert communication method based on expired channel state information and relay selection, characterized in that: The steps include: S1: Construct a transmission model for a covert communication system based on outdated channel state information; S2: Determine the selected relay node, the uninterrupted conditions of legitimate communication and the necessary conditions for the relay node to send covert messages according to the transmission model; S3: According to the uninterrupted conditions of legitimate communication and the necessary conditions for the relay node to send covert messages, determine the communication interruption mechanism and the three detection error situations in which the detector determines whether the relay node sends a covert message; S4: determining the detection error probabilities under three detection error conditions and the optimal detection threshold that minimizes the total detection error probability; S5: Determine the average concealed transmission rate while meeting the concealment requirements.

2. A covert communication method based on expired channel state information and relay selection according to claim 1, characterized in that: The construction of the transmission model in step S1 specifically includes: considering a multi-relay network, including a source S, a destination D and N half-duplex decoding and forwarding relays, denoted as R i , where i = 1, ..., N, represents the index used by each channel; each node is equipped with a single antenna, and due to deep fading, there is no direct link between S and D; in this system, S also acts as a listener to detect R i Whether to transmit its own hidden information to D; link a→b(a,b∈{S,R i ,D}) is represented by h ab It means that it has variance independent zero-mean cyclically symmetric complex Gaussian random variables; h ab The estimated value of is expressed as Due to the time variability and delay of the channel, Yes ab The communication is divided into two phases. In the first phase, S and R i Communicate, Phase II R i Communicate with D, S detects R i Whether to communicate covertly with D.

3. A covert communication method based on expired channel state information and relay selection according to claim 2, characterized in that: Determining the selected relay node in step S2 includes: Partial relay selection To determine the selected relay R k ; During the relay selection phase, each relay starts a timer, which is Inversely proportional function, the relay whose timer expires first is the selected relay R k , which notifies other nodes through a flag signal, expressed as: h ab The estimated value of is expressed as Used for communication transmission and detection; due to the time variability and delay of the channel, Yes ab The outdated version of them is expressed as: in, and is a circularly symmetric complex Gaussian random variable, ρ ab Yes ab and The correlation coefficient between them; According to Jakes' autocorrelation model ρ ab =J0(2πf ab τ d ), where f ab is the maximum Doppler frequency of link a→b, τ d is the delay, and J0(·) represents the zero-order Bessel function of the first kind.

4. A covert communication method based on expired channel state information and relay selection according to claim 2, characterized in that: The communication transmission in step S2 is divided into two stages: In the first stage, S moves at a fixed rate r SD To R k Send its message x S , in R k The received signal at is expressed as: Among them, P S is the transmission power of S, x S (i) is the normalized signal emitted by S, satisfying E{|x S (i)| 2 }=1, YesR k Additive Gaussian white noise; The second stage, R k Start transmission, then the received signal at D is expressed as: in, and P C are the transmission power of legitimate messages and the fixed transmission power of concealed messages, respectively. I = 0 means R k No hidden message is transmitted, I = 1 means R k Transmit its covert message, x R (i) and x C (i) The signals representing the legitimate message and the concealed message respectively satisfy E{|x R (i)| 2 }=1 and E{|x C (i)| 2 }=1, is the additive white Gaussian noise at D.

5. A covert communication method based on expired channel state information and relay selection according to claim 4, characterized in that: The conditions for uninterrupted legitimate communication and the necessary conditions for the relay node to send a covert message in step S2 are specifically: Based on the outdated channel state information, R k Whether to transmit depends on two necessary conditions: one is R k can successfully decode x S ; Second, D can also be successfully decoded. The specific conditions are expressed as: in, Represents R k The received signal-to-noise ratio at represents the maximum received signal-to-noise ratio at D, represents the signal-to-noise ratio threshold, P M YesR k The maximum transmit power, is the noise power at D; Based on the actual channel state information, R k Whether to transmit depends on two necessary conditions: one is R k can successfully decode x S ; Second, D can also be successfully decoded. The specific conditions are expressed as: in, Represents R k The received signal-to-noise ratio at D,I represents the received signal-to-noise ratio at D; For decoding x R The signal to interference plus noise ratio is expressed as: To ensure that D can successfully decode the message, let It turns out that: Consider R k The maximum power constraint at R k The necessary conditions for covert transmission are expressed as:

6. A covert communication method based on expired channel state information and relay selection according to claim 5, characterized in that: In step S3, a communication interruption mechanism is determined. Once the communication is interrupted, the detector determines R k Send covert information and then determine three situations of detection errors, including: Case 1: The actual communication is uninterrupted and is divided into three events, which are represented as follows: in, Express satisfaction And R k Do not send hidden messages. Express satisfaction And R k Events that send covert messages; Case 2: R k The actual communication interruption between and D is divided into two events, represented as: in, Express satisfaction And R k Events that do not send covert messages; Case 3: S and R k The actual communication between in, Represents R k Events that do not send messages.

7. A covert communication method based on expired channel state information and relay selection according to claim 6, characterized in that: The step S4 specifically includes: First R k When transmission starts, S will detect R k Whether to transmit its hidden information, the binary hypothesis of the received signal of S is expressed as: in, is the additive Gaussian white noise at S, H1 and H0 represent the assumptions R k With or without the transmission of covert messages; the best detection scheme is the radiometer, which is expressed as: Among them, τ is the decision threshold, D1 and D0 are binary decisions, corresponding to R k Transmitted with or without covert message; due to channel reciprocity Assuming the block length is infinite, n→∞, T(n) is expressed as: In high signal-to-noise ratio regions, The conditional cumulative distribution function expression is: Where L is a constant, The joint probability density function expression of the outdated channel state information and the actual channel state information is: in, Case 1: Assuming that the necessary conditions are met When R k Sending a covert message with probability φ, given a decision threshold τ, the probability of false detection of S is expressed as: Among them, Pr(H1)=φ, Pr(H0)=1-φ, j1=min(t1,t3), j2=max(t1,t3), For a given τ, the detection error probability of S consists of two parts: the false alarm probability and the missed detection probability. The false alarm probability under the condition is expressed as: by The false alarm probability under the condition by The probability of missed detection under the condition is expressed as: Substitute formula (8) and formula (9) into formula (19) to determine the lower bound t1 and upper bound t2 of τ; then substitute formula (20) into formula (24) and formula (25) respectively to obtain and The probability expression for each event in this case is as follows: Substituting formula (21) and formula (22) into formula (26) and formula (27) respectively, we can get and Case 2: The detection error probability of S is expressed as: in, Then and The false alarm probability under the condition The probability expression for each event in this case is as follows: Substituting formula (21) and formula (22) into formula (29) and formula (30) respectively, we can get and Case 3: The probability of S's detection error is expressed as: in, In this case, the probability expression of this event is as follows: Substituting formula (21) and formula (22) into formula (32), we can get Combining formula (23), formula (28) and formula (31), the total detection error probability of S is determined as: ξ=ξ1+ξ2+ξ3(33) The optimal detection threshold that minimizes the total detection error probability is expressed as: Determine the optimal detection threshold and total detection error probability ξ by numerical search opt .

8. A covert communication method based on expired channel state information and relay selection according to claim 7, characterized in that: The step S5 specifically includes: Under the condition of meeting the concealment requirements, a fixed transmission power P is given C , the effective average covert transmission rate that can be achieved in a system equipped with N relay nodes is expressed as in, is the exponential integral function.

9. A covert communication system based on expired channel state information and relay selection, characterized in that: The system includes a network interface, a memory and a processor; wherein, The network interface is used to receive and send signals during the process of sending and receiving information with other external network elements; The memory is used to store computer program instructions that can be executed on the processor; The processor is configured to execute the steps of a covert communication method based on expired channel state information and relay selection according to any one of claims 1 to 8 when running the computer program instructions.

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