Cellular covert communication network system and method realized by utilizing D2D (Device-to-Device) technology

Abstract

The embodiment of the invention discloses a cellular covert communication network system and method realized by utilizing a D2D (Device-to-Device) technology. The system comprises a base station BS, a transmitting device CT in a cellular network, a receiving device CR, a D2D communication pair and k collusion monitors Wk, wherein the D2D communication pair comprises a D2D transmitting device (DT) and a D2D receiving device (DR); the cellular sending device CT, the cellular receiving device CR, the D2D communication device pair and the k collusion monitors Wk are all single-antenna communication devices; the cellular transmitting device CT is used for transmitting an uplink hidden signal to the base station BS through a cellular uplink CT-BS; the base station BS is used for sending a cellular downlink signal to a cellular receiving device CR through a cellular downlink BS-CR; and the K collusion monitors are used for monitoring a cellular uplink when the K collusion monitors are interfered by the DT-Wk of the D2D link. The scheme is suitable for a scene of multiple non-collusion monitors, and can realize a non-zero concealment rate.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a cellular hidden communication network system and method implemented by using D2D technology. Background Art

[0002] The introduction of D2D (Device-to-Device) communication technology has brought significant changes to cellular networks. It allows devices within a certain range to communicate directly without forwarding through base stations. This combination of technologies forms a D2D cellular network, which has advantages including reducing base station load, improving spectrum utilization, increasing communication throughput, and reducing communication latency. In 5G cellular networks, D2D communication technology is considered to be a crucial link, and its widespread application will become a major trend in the future. Through D2D cellular networks, devices can communicate directly with each other, which not only improves the efficiency and performance of the network, but also provides a more flexible and reliable communication method for various application scenarios.

[0003] As more and more privacy-sensitive information is transmitted through D2D cellular networks, network security issues have become particularly prominent. Although traditional communication content security methods such as cryptography and physical layer security methods can protect communication content to a certain extent, for scenarios with special security requirements, such as banking and financial transactions and personal medical data sharing, simply protecting the communication content is obviously not enough. In these cases, it is necessary to ensure that the existence of the communication process is also protected. Therefore, what has attracted widespread attention is the covert communication technology that aims to hide the communication process. This technology not only focuses on data encryption and transmission security, but also focuses on hiding the fact of communication in communication, making the existence of communication difficult to detect. Through covert communication technology, users can transmit sensitive information in D2D cellular networks without being detected by criminals or eavesdroppers, thereby further ensuring the security and privacy of communication.

[0004] Most of the existing research focuses on realizing covert communication of D2D links in D2D cellular networks, and few studies focus on realizing covert communication of cellular links. In addition, current research mainly focuses on single monitor scenarios or multi-monitor non-collusion scenarios, but the cellular covert communication system based on D2D technology in multi-monitor collusion scenarios still needs in-depth research, which is helpful to evaluate the system's covert performance and covert rate in complex environments. Summary of the invention

[0005] Based on this, it is necessary to propose a cellular hidden communication network system and method using D2D technology to address the above problems.

[0006] To achieve the above objectives, the present application provides a cellular covert communication network system using D2D technology, the system comprising: a base station BS, a transmitting device CT in a cellular network, a receiving device CR, a D2D communication pair, and k collusion monitors W k ;

[0007] Wherein, the D2D communication pair includes a D2D transmitting device DT and a D2D receiving device DR;

[0008] The cellular transmitting device CT, the cellular receiving device CR, the D2D communication device pair and k collusion monitors W k All are single-antenna communication devices;

[0009] The cellular transmitting device CT is used to send an uplink concealed signal to the base station BS via a cellular uplink CT-BS;

[0010] The base station BS is used to send a cellular downlink signal to the cellular receiving device CR via a cellular downlink link BS-CR;

[0011] The K collusion monitors are used to monitor the D2D link DT-W. k While preventing interference, the cellular uplink is monitored.

[0012] In some embodiments, the cellular transmitting device CT has a fixed transmission power P c , the transmission power P of the D2D transmitting device DT d obey The uniform distribution on the time slot is constant within a time slot and varies randomly between different time slots. Its probability density function is expressed as

[0013] To achieve the above-mentioned purpose, the second aspect of the present application provides a cellular concealed communication method of a cellular concealed communication network system implemented by using D2D technology, the method comprising:

[0014] Establish a monitoring model for collusion monitors;

[0015] Through the monitoring model, the K collusion monitors are used to monitor whether the cellular uplink CT-BS transmits covert signals;

[0016] Based on the monitoring results, the average minimum detection error probability of the fusion center is determined by the equal gain merging method;

[0017] Based on the monitoring results, the average minimum detection error probability of the fusion center is determined by the maximum ratio combining method;

[0018] After determining that the cellular link can achieve covert communication according to the average minimum detection error probability of the fusion center, the covert rate is determined and optimized.

[0019] In some implementations, the establishing of a monitoring model for collusion monitors specifically includes:

[0020] The monitoring model of the collusion monitor is: Among them, τ FC is the detection threshold of the fusion center, D0 and D1 represent the decisions of accepting H0 and H1 respectively;

[0021] Analyze the monitoring process of the kth colluding monitor, k = 1, 2, ..., K, that is, the kth monitor collects the signal of a time slot and determines the average power of the signal received in the time slot;

[0022]

[0023] Among them, H0 means that the cellular device CT does not send a hidden signal to the base station BS, H1 means that the cellular device CT sends a hidden signal to the base station BS, and h DT,k is the channel coefficient between the D2D device and the kth listener, h CT,k is the channel coefficient between the cellular device and the kth listener;

[0024] The fusion center combines the average power of the signals collected from all K collusion monitors with equal gain. The binary hypothesis of the fusion center is expressed as

[0025]

[0026] Among them, ω k The weighting coefficient is used to perform the weighted summation of the power of the signals received by all colluding monitors.

[0027] In some embodiments, the determining the average minimum detection error probability of the fusion center by an equal gain merging method based on the monitoring results specifically includes:

[0028] The fusion center uses the equal gain combining method to sum the signal power received by all monitors to obtain the signal power of the fusion center:

[0029]

[0030] Determine the false alarm probability of the fusion center:

[0031]

[0032] in,

[0033] Determine the missed detection probability of the fusion center:

[0034]

[0035] in,

[0036] Determine the total detection error probability of the fusion center

[0037] The optimal detection threshold with the minimum probability of detection error in determining the fusion center is:

[0038]

[0039] Determine the minimum detection error probability corresponding to the fusion center:

[0040]

[0041] The average minimum detection error probability of determining the fusion center is:

[0042]

[0043] In some embodiments, the determining the average minimum detection error probability of the fusion center by the maximum ratio combining method based on the monitoring results specifically includes:

[0044] The fusion center uses the maximum ratio combining method to sum the signal power received by all collusion monitors to obtain the weighted coefficient where γ k represents the signal-to-interference ratio of the kth monitor, expressed as:

[0045] Let X k =|h CT,k | 2 ,λ x =λ CT,w , then X k Subject to the mean value λ X exponential distribution. Let Y k =|h DT,k | 2 ,λ Y =λ DT,W , then Y k Subject to the mean value λ Y The exponential distribution of determines the total signal power at the fusion center:

[0046]

[0047] Determine the false alarm probability of the fusion center:

[0048]

[0049] in, Determine the missed detection probability at the fusion center:

[0050]

[0051] in, Determine the total detection error probability of the fusion center The optimal detection threshold with the minimum probability of detection error in determining the fusion center is:

[0052]

[0053] Determine the minimum detection error probability corresponding to the fusion center:

[0054]

[0055] make The average minimum detection error probability of determining the fusion center is:

[0056]

[0057] Among them, f W (w) and F W (w) represent the probability density function and cumulative distribution function of the variable W respectively.

[0058] In some implementations, after determining that the cellular link can achieve covert communication according to the average minimum detection error probability of the fusion center, determining and optimizing the covert rate specifically includes:

[0059] Determine the communication interruption probability of the cellular link CT-BS and the D2D link DT-DR;

[0060] Determine the average covert transmission rate

[0061] In some implementations, the communication interruption probability of the cellular link CT-BS and the D2D link DT-DR specifically includes:

[0062] The interruption probability of the cellular link and the D2D link are defined as

[0063] P co =P{C c <R c =P{log2(1+SIR BS ) <R c}

[0064] P do =P{C d <R d =P{log2(1+SIR DR ) <Rd};

[0065] Where R c and R d The predefined transmission rates for the cellular link and the D2D link.

[0066] In some embodiments, the determining the average concealed transmission rate Specifically include:

[0067]

[0068] Determine the average covert transmission rate

[0069] In some implementations, after determining that the cellular link can achieve covert communication according to the average minimum detection error probability of the fusion center, optimizing the covert rate specifically includes:

[0070] When the fusion center adopts the equal gain merging method, the optimization problem of the average concealed transmission rate of the cellular link is expressed as:

[0071]

[0072] Wherein, Ω represents the maximum transmission power allowed by the D2D transmitting device DT;

[0073] When the fusion center adopts the maximum ratio combining method, the optimization problem of the average concealed transmission rate of the cellular link is expressed as

[0074]

[0075] The embodiments of the present invention have the following beneficial effects:

[0076] The present invention is applicable to the scenario of multiple non-colluding monitors. By calculating the concealment and concealment rate, it is proved that the model can achieve a non-zero concealment rate. In the monitoring model of this colluding monitor, the D2D link reuses the spectrum resources of the cellular link in the underlying mode, resulting in co-channel interference between the D2D link and the cellular link. However, the present invention finds that this interference can be regarded as a friendly auxiliary factor. By dynamically adjusting the power of the D2D sender, the present invention successfully introduces uncertainty, making it impossible for the monitor to accurately obtain the communication content of the cellular link, thereby achieving covert communication; this method significantly improves the concealment and concealment rate of the system. In terms of concealment calculation, the present invention considers that the monitor adopts a binary hypothesis and uses a threshold method to determine whether a covert communication behavior occurs, and its detection threshold is unknown to the covert communication sender. Therefore, the worst case is assumed, and the average minimum detection error probability is used as the detection performance measurement indicator of the monitor; in the scenario of multiple monitors colluding, the equal gain merging method and the maximum ratio merging method are used to analyze the detection performance of the monitor. For equal-gain combining, the fusion center sums the received signal powers of all monitors with the same weighting coefficient, while for maximum ratio combining, the weighting coefficient used by the fusion center is proportional to the signal-to-interference ratio of each monitor. For the above two combining methods, the average minimum detection error probability of the fusion center is derived respectively to measure its detection performance. In terms of performance analysis and optimization of covert communication of cellular links, the present invention first derives the transmission interruption probability of cellular links and D2D links respectively, and derives the average covert transmission rate of cellular links, which is used as a measure of the covert communication performance of cellular networks. Taking the detection performance of the monitors when using equal-gain combining and maximum ratio combining as constraints, the problem of maximizing the average covert transmission rate of cellular links is established. By solving this optimization problem, the maximization of the concealment performance of the cellular link is achieved under the premise of satisfying the concealment constraints, and an average concealment rate greater than 0 can be obtained by adjusting the power of the D2D sender. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0078] in:

[0079] Figure 1 It is a schematic diagram of a cellular hidden communication network system implemented by the present invention using D2D technology;

[0080] Figure 2It is an overall flow chart of a cellular concealed communication method of a cellular concealed communication network system implemented by using D2D technology in the present invention;

[0081] Figure 3 It is a performance analysis flow chart of a medium gain combined collusion monitoring model of a cellular covert communication method of a cellular covert communication network system implemented by the present invention using D2D technology;

[0082] Figure 4 It is a performance analysis flow chart of the maximum ratio combining collusion monitoring model in the cellular covert communication method of the cellular covert communication network system implemented by the present invention using the D2D technology;

[0083] Figure 5 It is a flow chart of concealed rate calculation of a cellular concealed communication network system implemented by the present invention using D2D technology;

[0084] Figure 6 It is a relationship diagram between the average minimum detection error probability at the fusion center and the maximum transmission power of the DT when the monitor adopts the equal gain merging method in the cellular covert communication network system implemented by the present invention using the D2D technology;

[0085] Figure 7 It is a relationship diagram between the average minimum detection error probability at the fusion center and the maximum transmission power of the DT when the monitor adopts the maximum ratio combining method in the cellular covert communication network system implemented by the present invention using the D2D technology;

[0086] Figure 8 It is a relationship diagram between the concealed communication rate and the maximum transmission power of the DT when the monitor adopts equal gain combining constraints in the cellular concealed communication network system implemented by the D2D technology of the present invention;

[0087] Fig. 9 It is a relationship diagram between the maximum average concealed transmission rate of a cellular link in a cellular concealed communication network system implemented by the present invention using D2D technology and the predefined transmission rate of the cellular link. DETAILED DESCRIPTION

[0088] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0089] To facilitate understanding, the relevant terms involved in this application are first introduced below.

[0090] Embodiment 1 of the present invention provides a cellular hidden communication network system implemented by using D2D technology, and its architecture diagram is as follows: Figure 1 As shown, the base station BS, the transmitting device CT in the cellular network, the receiving device CR, the D2D communication pair and k collusion monitors W k ;

[0091] Wherein, the D2D communication pair includes a D2D transmitting device DT and a D2D receiving device DR;

[0092] The cellular transmitting device CT, the cellular receiving device CR, the D2D communication device pair and k collusion monitors W k All are single-antenna communication devices;

[0093] The cellular transmitting device CT is used to send an uplink concealed signal to the base station BS via a cellular uplink CT-BS;

[0094] The base station BS is used to send a cellular downlink signal to the cellular receiving device CR via a cellular downlink link BS-CR;

[0095] The K collusion monitors are used to monitor the D2D link DT-W. k While preventing interference, the cellular uplink is monitored.

[0096] Use h i,j To represent the channel coefficient from node i to node j, where i∈{CT,DT},j∈{DR,BS,W1,...,W k Each communication link obeys block-independent quasi-static Rayleigh fading, and its channel coefficient is an independent cyclic symmetric complex Gaussian random variable, expressed as h i,j ~CN(0,λ i,j ); the channel coefficient remains unchanged within a time slot and changes randomly between time slots. Therefore, the square of its channel coefficient follows a mean of λ i,j , its probability density function can be expressed as

[0097] All nodes i will be affected by the variance The cellular transmitting device CT has a fixed transmission power P c , the transmission power P of the D2D transmitting device DT d obey The uniform distribution on the time slot is constant within a time slot and changes randomly between different time slots. Its probability density function can be expressed as:

[0098]

[0099] The monitor has mastered the channel state information CSI of the link associated with it, while the legitimate user only knows the channel distribution information CDI of the link related to the monitor.

[0100] In addition, the cellular link and the D2D link only know each other's CDI but not the specific channel status.

[0101] All monitors only know P d distribution information without knowing its exact value.

[0102] In addition, R c and R d are the predefined communication rates of the cellular uplink and D2D link respectively.

[0103] The embodiment of the present invention also provides a cellular concealed communication method for a cellular concealed communication network system implemented by using D2D technology and applied in the above embodiment, and its flow chart is as follows: Figure 2 As shown, the following steps are implemented:

[0104] Step 1, establish a monitoring model for collusion monitors;

[0105] Specifically, step 1.1 analyzes the monitoring process of the kth monitor, k = 1, 2, ..., K, that is, the kth monitor collects the signal of a time slot and calculates the average power of the signal received in the time slot:

[0106]

[0107] Step 1.2: The fusion center combines the average power of the signals collected from all K collusion monitors with equal gain, and the fusion center abstracts the judgment problem into a binary hypothesis. The null hypothesis H0 indicates that the cellular device CT does not send a covert signal to the base station BS, and the alternative hypothesis H1 indicates that the cellular device CT sends a covert signal to the base station BS. The binary hypothesis at the fusion center is expressed as:

[0108]

[0109] The fusion center performs a weighted summation of the power of the signals received by all monitors. The weighting coefficient is represented by ω k .

[0110] Step 1.3: The fusion center aggregates and combines the average power of the signals received by all monitors and compares it with the preset detection threshold. The comparison process is as follows, that is, the monitoring model of the monitor is as follows:

[0111]

[0112] Among them, τ FCis the detection threshold at the fusion center, D0 and D1 represent the decisions of accepting H0 and H1, respectively.

[0113] Step 2: Use the monitoring model to monitor whether the K collusion monitors transmit covert signals to the cellular uplink CT-BS;

[0114] Step 3, based on the monitoring results, determine the average minimum detection error probability of the fusion center through the equal gain merging method;

[0115] Specifically, if Figure 3 As shown, the detection performance analysis of the equal gain merging method is specifically implemented according to the following steps:

[0116] Step 4.1.1: The equal gain combining method is used at the fusion center to sum the signal powers received by all monitors. At this time, let Then the signal power at the fusion center can be obtained as follows:

[0117]

[0118] Step 4.1.2, according to the definition of false alarm rate, the false alarm probability of the fusion center is calculated as follows:

[0119]

[0120] in,

[0121] Step 4.1.3, similarly, according to the definition of missed detection rate, the missed detection probability at the fusion center is obtained as:

[0122]

[0123] in,

[0124] Step 4.1.4, the total detection error probability of the fusion center is

[0125] Step 4.1.5: In order to achieve covert communication of cellular links, the cellular transmitter CT needs to consider the worst case scenario, that is, it is assumed that the optimal detection threshold can be set at the fusion center to obtain the minimum detection error probability. Specifically:

[0126] The detection error probability at the fusion center is given in the following two cases:

[0127] when hour:

[0128]

[0129] when When EGC Get the minimum value 0.

[0130] when hour:

[0131]

[0132] In order to determine the optimal τ FC and the corresponding minimum ξ EGC , we need to determine EGC About τ FC The monotonicity of hour, This shows that at this time EGC With τ FC decreases with the increase of , so the optimal threshold is when hour, This means that within this interval EGC With τ FC increases with the increase of , so the optimal threshold Because EGC is τ FC is a continuous function, so ξ EGC In the interval Get the minimum value within

[0133] Therefore, the optimal detection threshold with the minimum detection error probability at the fusion center is:

[0134]

[0135] The corresponding minimum detection error probability is:

[0136]

[0137] Step 4.1.6: Since the CT does not know the CSI of the link monitored by the monitor, the worst case scenario needs to be considered from the perspective of the legitimate communication party, that is, the average minimum detection error probability of the fusion center needs to be calculated. According to formula (11), the average minimum detection error probability of the fusion center is:

[0138]

[0139] To do this, we must first find The probability density function of .

[0140] make Because |h CT,k | 2 Subject to the mean value λ CT,W According to the conversion relationship between exponential distribution and Gamma distribution, X follows the shape parameter K and the rate parameter is Gamma distribution, that is, X ~ Gamma (K, β1). Similarly, Y ~ Gamma (K, β2), the probability density functions of X and Y are given as follows

[0141]

[0142] Where Γ(·) represents the Gamma function.

[0143] make Then the probability density function of Z is calculated as follows:

[0144]

[0145] According to the above formula, the average minimum detection error probability of the fusion center can be rewritten as:

[0146]

[0147] The probability of the first term is calculated as follows:

[0148]

[0149] The integral of the second term is calculated as follows:

[0150]

[0151] Substituting formula (17) (18) into (16), we can get the average minimum detection error probability of the fusion center:

[0152]

[0153] Step 4, based on the monitoring results, determine the average minimum detection error probability of the fusion center through the maximum ratio combining method;

[0154] Specifically, if Figure 4 As shown in step 4.1.1, the fusion center uses the maximum ratio combining method to sum the signal powers received by all monitors. At this time, the weighted coefficient of the sum is proportional to the signal-to-interference ratio (SIR) of the monitor. At this time, let ω in formula (4) k It is expressed as follows:

[0155]

[0156] where γ k represents the signal-to-interference ratio of the kth monitor, expressed as:

[0157]

[0158] Let X k =|h CT,k | 2,λ X =λ CT,W , then X k Subject to the mean value λ X exponential distribution, let Y k =|h DT,k | 2 ,λ Y =λ DTW , then Y k Subject to the mean value λ Y The total signal power at the fusion center can be obtained as follows:

[0159]

[0160] Step 4.1.2, according to the definition of false alarm rate, the false alarm probability of the fusion center is calculated as follows:

[0161]

[0162] in,

[0163] Step 4.1.3, similarly, according to the definition of missed detection rate, the missed detection probability at the fusion center is obtained as:

[0164]

[0165] in,

[0166] Step 4.1.4, the total detection error probability of the fusion center is

[0167] Step 4.1.5: In order to achieve covert communication of cellular links, the cellular transmitter CT needs to consider the worst case scenario, that is, the fusion center can set the optimal detection threshold to obtain the minimum detection error probability. Specifically:

[0168] The detection error probability at the fusion center is given in the following two cases:

[0169] when hour,

[0170]

[0171] It can be seen that when When MRC Get the minimum value 0.

[0172] when hour,

[0173]

[0174] In order to determine the optimal τFC and the corresponding minimum ξ MRC , we need to determine MRC About τ FC The monotonicity of hour, Explain that this time MRC With τ FC decreases with the increase of , so the optimal threshold when hour, This means that within this interval MRC With τ FC increases with the increase of , so the optimal threshold Because MRC is τ FC is a continuous function, so ξ MRC In the interval Get the minimum value within

[0175] Therefore, the optimal detection threshold with the minimum detection error probability at the fusion center is:

[0176]

[0177] The corresponding minimum detection error probability is:

[0178]

[0179] In step 4.1.6, since the CT does not know the CSI of the monitor, it is necessary to calculate the average minimum detection error probability at the fusion center from the perspective of the legitimate party.

[0180] make And the probability density function of W is labeled as f W (w), according to formula (28), the average minimum detection error probability at the fusion center is:

[0181]

[0182] In order to seek We need to find the cumulative distribution function F of W W (w). However, due to the complexity of the random variable W, it is difficult to directly obtain the expression of its cumulative distribution function. Here, the empirical cumulative distribution function is used to estimate its cumulative distribution function.

[0183] Let the cumulative distribution function of W be The following algorithm gives the calculation Steps:

[0184] 4.1.6.1) For the sample set W = {w1, w2, ..., w n} Sort from small to large, and get the sorted sample set W′={w (1) , w (2) , ..., w (k)};

[0185] 4.1.6.2) For each sample point w after sorting (k) (from the first to the last sample point), the calculation is no greater than w (k) The proportion of sample points is:

[0186] 4.1.6.2) Return

[0187] Step 5, after determining that the cellular link can achieve covert communication according to the average minimum detection error probability of the fusion center, determine and optimize the covert rate.

[0188] Specifically, Figure 5 As shown: Calculate the communication interruption probability of the cellular link CT-BS and the D2D link DT-DR, specifically:

[0189] The transmission rate of the cellular link when the cellular link and the D2D link are not interrupted at the same time is defined as the average hidden transmission rate This indicator is used to measure the concealment performance of the cellular link. In order to calculate the average concealed transmission rate It is necessary to first calculate the interruption probability of the cellular link and the D2D link, which are defined as:

[0190] P co =P{C c <R c =P{log2(1+SIR BS ) <R c} (30)

[0191] P do =P{C d <R d =P{log2(1+SIR DR ) <R d} (31)

[0192] The outage probability of a cellular link is calculated as follows:

[0193]

[0194] The interruption probability of the D2D link is calculated as follows:

[0195]

[0196] According to the definition of the average covert transmission rate, we can get:

[0197]

[0198] When the fusion center adopts the equal gain merging method, the optimization problem of the average concealed transmission rate of the cellular link can be expressed as:

[0199]

[0200] The objective function is the average concealed transmission rate of the cellular link, which is given by formula (35). Formula (36) represents the concealment constraint, is the average minimum detection error probability of the fusion center given by formula (19), and ε is a small positive number. If the average minimum detection error probability of the fusion center can satisfy formula (36), it is considered that the cellular link can achieve covert communication. Formula (37) represents the range of the maximum transmission power of DT, and Ω is the upper limit of its transmission power.

[0201] The present invention adopts the (Karush–Kuhn–Tucker) condition to solve the optimization problem and defines the Lagrangian function as follows:

[0202]

[0203] Where λ1, λ2, λ3 are Lagrange multipliers.

[0204] The KKT conditions are given as follows

[0205]

[0206] λ i ≥0,i=1,2,3, (42)

[0207]

[0208] Among them, equations (43), (44), and (45) represent complementary relaxation conditions, which stipulate that the two product terms in the complementary relaxation conditions are not 0 at the same time. After solving the KKT conditions and analyzing the solutions, the following three candidate optimal solutions can be obtained, which constitute the candidate solution set:

[0209] 1. When λ1=0,λ2=0,λ3=0, we get from (39) Thus, we can solve

[0210] 2. When λ1=0,λ2>0,λ3=0, we get from (44) therefore

[0211] 3. When λ1>0,λ2=0,λ3=0, we can get from (43) So according to this formula we can get

[0212] Find the objective function value corresponding to each solution in the candidate solution set. The solution with the largest objective function value is the optimal solution to the optimization problem. However, due to and The complexity makes it difficult to find the optimal solution Therefore, the optimal solution can be obtained by numerical solution method.

[0213] When the fusion center adopts the maximum ratio combining method, the optimization problem of the average concealed transmission rate of the cellular link can be expressed as:

[0214]

[0215] The meanings of the formulas are the same as those in step 5.1.1, except that is the average minimum detection error probability when the fusion center adopts the maximum merging ratio, which is given by formula (29).

[0216] The KKT condition is used to solve the optimization problem and the Lagrangian function is defined as follows:

[0217]

[0218] The KKT conditions are given as follows:

[0219]

[0220] λ i ≥0,i=1,2,3, (53)

[0221]

[0222] After solving the KKT conditions and analyzing the solutions, we can get the following three candidate optimal solutions, which constitute the candidate solution set:

[0223] 1. When λ1=0,λ2=0,λ3=0, we get from (50) Thus, we can solve

[0224] 2. When λ1=0,λ2>0,λ3=0, from (55) we get therefore

[0225] 3. When λ1>0,λ2=0,λ3=0, we can get from (54) Thus, we can solve

[0226] Find the objective function value corresponding to each solution in the candidate solution set. The solution with the largest objective function value is the optimal solution to the optimization problem. However, due to and Due to the complexity of the problem, it is difficult to find a closed expression for the optimal solution. Therefore, a numerical optimal solution can be obtained by numerical solution.

[0227] In order to verify the performance of the method proposed in the present invention, the following simulation experiments are carried out:

[0228] like Figures 6 to 9 As shown in the figure, the simulation environment is as follows: Unless otherwise specified, all communication links are Rayleigh fading channels, and the channel coefficients obey a complex Gaussian distribution with a mean of 0 and a variance of 1. The ambient noise power at each node is Concealment requirement ε = 0.05, the predefined communication rate of the cellular link and the predefined communication rate of the D2D link are R c =R d =0.1Mbps, the experimental result is after 2×10 4 obtained by Monte Carlo simulation.

[0229] Figure 6 It is given that when the monitor adopts the equal gain merging method, K={1,3},P c ={1,5}dBm, the average minimum detection error probability of the fusion center About the maximum transmission power of DT As can be seen from the figure, for a specific number of monitors K and hidden signal transmission power P_c, along with This is because the increase in DT's transmission power will impose greater interference on the monitor, which will lead to an increase in the monitor's detection error probability, and ultimately lead to the average minimum detection error probability of the fusion center. It can also be seen from the figure that for a given K and With P c The phenomenon can be explained as follows: c The decrease in leads to a decrease in the received power at the monitor, which in turn leads to a decrease in the difference between H0 and H1, thereby increasing the probability of detection error at the monitor. In addition, it is also observed in the figure that when P c =1dBm and When K = 3, the average minimum detection error probability at the fusion center is smaller than that when K = 1, indicating that multiple colluding monitors have stronger detection performance than a single monitor. Finally, the theoretical value and the simulation value have a high degree of agreement, which proves that for the average minimum detection error probability The correctness of the theoretical analysis.

[0230] Figure 7 It shows that when the monitor adopts the maximum ratio combining method, K={1,3},P c={1,5}dBm, the average minimum detection error probability of the fusion center Maximum transmit power with DT The figure shows that for a specific hidden signal transmission power P_c and the number of monitors K, along with For a given K and It decreases with the increase of K. This shows that when the collusion monitors use the maximum ratio merging method, the more monitors there are, the better the detection performance.

[0231] Figure 8 The covert communication rate under the equal gain merging constraint is given About the maximum transmission power of DT As can be seen from the figure, with increase, Initially it remains at 0, then reaches a maximum value and then decreases. The reason for this phenomenon can be explained as follows: for smaller The hidden constraint cannot be satisfied, so along with As the hidden constraint is satisfied, increase, reaches its maximum value. But continues to increase DT also increases the interference to the cellular link, resulting in The figure also shows that as P C The increase requires the use of a larger To achieve the maximum This is because the concealed transmission power P C The larger the interference is, the greater the interference is needed to confuse the monitor in order to meet the concealment constraint, so a larger transmission power is required.

[0232] Fig. 9 Shown in P c =5dBm and K = {1,2,3}, the maximum average concealed transmission rate of the cellular link With the preset transmission rate R c It can be observed that, given K, as R c Increase, It rises first and then falls. This is because when R c When smaller, Mainly affected by R c The influence of R c When R c When it increases to a certain extent, the transmission interruption probability P of the cellular link co Start to increase and Produce a greater impact, leading to With R c further increase and decrease.

[0233] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0234] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A cellular hidden communication network system implemented using D2D technology, characterized in that: The system includes: a base station BS, a transmitting device CT in a cellular network, a receiving device CR, a D2D communication pair, and k collusion monitors W k ; Wherein, the D2D communication pair includes a D2D transmitting device DT and a D2D receiving device DR; The cellular transmitting device CT, the cellular receiving device CR, the D2D communication device pair and k collusion monitors W k All are single-antenna communication devices; The cellular transmitting device CT is used to send an uplink concealed signal to the base station BS via a cellular uplink CT-BS; The base station BS is used to send a cellular downlink signal to the cellular receiving device CR via a cellular downlink link BS-CR; The K collusion monitors are used to monitor the D2D link DT-W. k While preventing interference, the cellular uplink is monitored.

2. The cellular hidden communication network system implemented by using D2D technology according to claim 1, characterized in that: The cellular transmitting device CT has a fixed transmission power P c , the transmission power P of the D2D transmitting device DT d obey The uniform distribution on the time slot is constant within a time slot and varies randomly between different time slots. Its probability density function is expressed as 3. A cellular covert communication method applied to a cellular covert communication network system implemented by D2D technology as described in any one of claims 1-2, characterized in that: The method is: Establish a monitoring model for collusion monitors; Through the monitoring model, the K collusion monitors are used to monitor whether the cellular uplink CT-BS transmits covert signals; Based on the monitoring results, the average minimum detection error probability of the fusion center is determined by the equal gain merging method; Based on the monitoring results, the average minimum detection error probability of the fusion center is determined by the maximum ratio combining method; After determining that the cellular link can achieve covert communication according to the average minimum detection error probability of the fusion center, the covert rate is determined and optimized.

4. The cellular covert communication method according to claim 3, characterized in that: The monitoring model for establishing collusion monitors specifically includes: The monitoring model of the collusion monitor is: Among them, Y FC represents the average power after the fusion center fuses the received power of all monitors, τ FC is the detection threshold of the fusion center, D0 and D1 represent the decisions of accepting H0 and H1 respectively; Analyze the monitoring process of the kth collusion monitor, k = 1, 2, ..., K, that is, the kth monitor collects the signal of a time slot and determines the average power of the signal received in the time slot. Among them, H0 means that the cellular device CT does not send a hidden signal to the base station BS, H1 means that the cellular device CT sends a hidden signal to the base station BS, and h DT,k is the channel coefficient between the D2D device and the kth listener, h CT,k is the channel coefficient between the cellular device and the kth listener; The fusion center combines the average power of the signals collected from all K collusion monitors with equal gain. The binary hypothesis of the fusion center is expressed as: Among them, ω k The weighting coefficient is used to perform the weighted summation of the power of the signals received by all colluding monitors.

5. The cellular covert communication method according to claim 3 or 4, characterized in that: The method of determining the average minimum detection error probability of the fusion center based on the monitoring results by using the equal gain merging method specifically includes: The fusion center uses the equal gain combining method to sum the signal power received by all monitors to obtain the signal power of the fusion center: Determine the false alarm probability of the fusion center as: in, Determine the missed detection probability of the fusion center as: in, Determine the total detection error probability of the fusion center The optimal detection threshold with the minimum probability of detection error in determining the fusion center is: Determine the minimum detection error probability corresponding to the fusion center: The average minimum detection error probability of determining the fusion center is: in Γ(·) represents the gamma function, λ is the mean of the exponential distribution.

6. The cellular covert communication method according to claim 5, characterized in that: The method of determining the average minimum detection error probability of the fusion center based on the monitoring results by the maximum ratio combining method specifically includes: The fusion center uses the maximum ratio combining method to sum the signal power received by all collusion monitors to obtain the weighted coefficient where γ k represents the signal-to-interference ratio of the kth monitor, expressed as: Let X k =|h CT，k | 2 ,λ X =λ CT，W , then X k Subject to the mean value λ x exponential distribution, let Y k =|h DT，k | 2 ,λ Y =λ DT，W , then Y k Subject to the mean value λ Y The exponential distribution of determines the total signal power at the fusion center: Determine the false alarm probability of the fusion center: in, Determine the missed detection probability at the fusion center: in, Determine the total detection error probability of the fusion center The optimal detection threshold with the minimum probability of detection error in determining the fusion center is: Determine the minimum detection error probability corresponding to the fusion center: make The average minimum detection error probability of determining the fusion center is: Among them, f W (w) and F W (w) represent the probability density function and cumulative distribution function of the variable W respectively.

7. The cellular covert communication method according to claim 6, characterized in that: After determining that the cellular link can achieve concealed communication according to the average minimum detection error probability of the fusion center, determining and optimizing the concealed rate specifically includes: Determine the communication interruption probability of the cellular link CT-BS and the D2D link DT-DR; Determine the average covert transmission rate 8. The cellular covert communication method according to claim 7, characterized in that: The communication interruption probability of the cellular link CT-BS and the D2D link DT-DR specifically includes: The interruption probability of the cellular link and the D2D link are defined as P co =P{C c <R c }=P{log2(1+SIR BS )<R c } P do =P{C d <R d }=P{log2(1+SIR DR )<R d }; Where R c and R d The predefined transmission rates for the cellular link and the D2D link.

9. The cellular covert communication method according to claim 8, characterized in that: Determining the average concealed transmission rate Specifically include: Determine the average covert transmission rate 10. The cellular covert communication method according to claim 9, characterized in that: After determining that the cellular link can achieve concealed communication according to the average minimum detection error probability of the fusion center, optimizing the concealed rate specifically includes: When the fusion center adopts the equal gain merging method, the optimization problem of the average concealed transmission rate of the cellular link is expressed as: Wherein, Ω represents the maximum transmission power allowed by the D2D transmitting device DT; When the fusion center adopts the maximum ratio combining method, the optimization problem of the average concealed transmission rate of the cellular link is expressed as:

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