A covert communication method suitable for a NOMA visible light communication system

Abstract

The application discloses a kind of covert communication methods suitable for NOMA visible light communication system, the method is first according to the channel model of visible light communication, builds out including 4 nodes of visible light communication system: one LED transmitter, two NOMA users (one public user and one covert user) and one monitor who attempts to detect whether the transmitter and covert user carry out covert transmission between;Then, by designing random sending power strategy to increase the detection uncertainty of monitor, to enhance the covert performance of system;Then, the error detection probability of monitor and the information transmission interruption probability of NOMA user are analyzed;Finally, this is used as the constraint condition of covert communication, the sending power distribution ratio of LED transmitter is optimized, so that the effective covert rate of covert user is maximized.Simulation results verify the covert performance of system, and provide a theoretical basis for the covert communication research of multi-user visible light communication system.

Description

Technical Field

[0001] This invention relates to the fields of visible light communication and covert communication technology, specifically a covert communication method applicable to NOMA visible light communication systems. Background Technology

[0002] In recent years, the rapid growth of data traffic has prompted researchers to seek new spectrum and technologies to meet communication demands. Visible Light Communications (VLC) uses light-emitting diodes (LEDs) as transmitters, serving both lighting and communication functions to send light and communication signals to users. With its advantages of not requiring specific spectrum applications, immunity to electromagnetic interference, and high transmission rates, it is considered one of the most promising communication technologies for the future 6G era and has attracted widespread attention from researchers.

[0003] On the other hand, the rapid development of wireless communication technology has led to an increasing reliance on wireless devices for information transmission. Simultaneously, people are paying more attention to the security and privacy of their information, and they urgently need a more secure communication environment. While the inability of light signals to penetrate opaque objects provides a degree of confidentiality for visible light communication, secure communication remains compromised when users are in public areas due to the open broadcast nature of wireless communication. Traditional encryption technologies are no longer reliable against new attacks on the wireless physical layer. Although researchers have studied this issue from the perspective of Physical Layer Security (PLS), PLS primarily focuses on protecting the content of communication. In certain scenarios (such as military and commercial activities), protecting only the content is clearly insufficient; protection of the communication behavior itself is also necessary. Therefore, a new secure communication model has emerged in recent years—covert communication. Covert communication is a low-probability-of-detection communication approach studied from an information theory perspective, aiming to prevent unauthorized users from detecting the existence of communication behavior, thereby achieving secure and reliable covert communication.

[0004] However, current research on covert communication largely focuses on radio frequency (RF) systems, with very little research on visible light communication (VLC) systems. Existing covert VLC research primarily addresses the limitations of covert transmission performance in visible light communication systems. Furthermore, due to significant differences in channel characteristics between VLC and RF systems—VLC channels are mainly dependent on the distance and angle between the transmitter and receiver and remain stable most of the time, while RF channels experience fading—this fading introduces uncertainty into the detection process for malicious monitors. Therefore, research on covert VLC often focuses on introducing uncertainty factors. However, while artificially created detection uncertainty can interfere with the detection results of malicious monitors, it can also affect the information reception of legitimate users to some extent. Non-Orthogonal Multiple Access (NOMA) technology, on the other hand, can simultaneously transmit superimposed signals to different users. Utilizing this characteristic and combining it with a random transmission power strategy, occasionally transmitted secret information can be hidden by continuously transmitting public, legitimate information, thus achieving secure transmission of secret information. In conclusion, research on covert communication within NOMA visible light communication systems is of great significance. Summary of the Invention

[0005] The purpose of this invention is to provide a covert communication method suitable for NOMA visible light communication systems.

[0006] The technical solution to achieve the objective of this invention is:

[0007] A covert communication method suitable for NOMA visible light communication systems includes the following steps:

[0008] 1) Assume that in a covert visible light communication system, there is an LED transmitter Alice, two NOMA users, and a monitor Willie who attempts to detect covert communication behavior in the system; among the two NOMA users, Bob, who is closer to the user, is the covert user, and Roy, who is farther from the user, is the public user.

[0009] 2) Construct a covert visible light communication channel model that includes the visible light communication system equipment in step 1). Under the Lambertian radiation mode of Alice's illumination model, express the channel gain from Alice to the covert user Bob and the public user Roy respectively.

[0010] 3) Based on step 2) and the basic principle of power domain-NOMA, analyze the covert visible light communication process based on NOMA, and obtain the received signal-to-noise ratio expression for NOMA users, namely covert user Bob and public user Roy.

[0011] 4) To ensure the concealment of secret information transmission, a random transmission power strategy is designed;

[0012] 5) Based on the visible light communication process in step 3) and the random transmission power strategy in step 4), analyze Willie's detection process, detect whether Alice sends covert information to the covert user Bob, and obtain the expression for Willie's false detection probability. Then, by analyzing the optimal threshold value and Willie's minimum false detection probability, obtain the covert constraints of visible light communication.

[0013] 6) According to the random transmission power strategy in step 4), the uncertainty of transmission power may cause the information transmission between Alice and the covert user Bob and the public user Roy to be interrupted. By analyzing the received signals of the covert user Bob and the public user Roy under the random transmission power, the transmission interruption probability expression of the public user Roy and the covert user Bob is obtained, and the interruption constraint condition of visible light communication is obtained.

[0014] 7) In order to better realize covert communication between Alice and covert user Bob, based on the covert constraints obtained in step 5) and the interruption constraints obtained in step 6), the effective covert rate maximization problem of covert user is formed by optimizing Alice's transmission power allocation ratio.

[0015] In step 1), each of the concealed user Bob, the public user Roy, and the monitor Willie has a single photodetector PD to receive or detect signals.

[0016] In step 2), the specific process of building the covert visible light communication channel model is as follows:

[0017] 2-1) Alice's lighting model is modeled as a Lambertian radiation mode and is installed on the ceiling at a height L above the ground. Based on the propagation characteristics of light, the receiving illumination area is circular, with the center point being Alice's mapping point on the ground. It is assumed that this model is based on a polar coordinate system (r...). k ,θ k The design is as follows: where k∈K, K={B,R,W} represents the receiver set, B, R, and W correspond to receivers Bob, Roy, and Willie, respectively. k It is the distance from k to the center of the circle, θ k The angle between k and the polar axis is given by the Euclidean distance from Alice to k.

[0018] 2-2) Assume that the locations of the covert user Bob and the public user Roy within Alice's illuminated cell are known; Alice publicly transmits information to Roy, and secretly transmits information with Bob under Willie's surveillance, and can obtain the Channel State Information (CSI) of users Bob and Roy, while Willie is in a silent state, and Alice can only obtain statistical CSI about Willie; assume the system is in the worst case, that is, Willie can obtain instantaneous CSI about Alice;

[0019] 2-3) Based on the channel modeling in step 2-1), the channel gain h between Alice and k, k∈K is... k for:

[0020]

[0021] In formula (1), A is the physical area of ​​the photodetector PD at point k, and R... p It is the PD response rate, m = -ln2 / ln[cos(Φ 12 )] represents the Lambert emission order, Φ 12 For half-power half-angle, d k It is the Euclidean distance φ between the LED and k. k It is the launch angle of the transmitter with respect to k. It is the angle of incidence perpendicular to the k-receiver. For the gain of the receiver filter, Let η be the gain of the optical concentrator, where η is the refractive index and ψ is the gain of the optical concentrator. c The field of view (FOV) of the receiving end;

[0022] Where φ k and The following relationship exists: Therefore, the channel gain h k Simplified to:

[0023]

[0024] In formula (2), b = m + 3.

[0025] In step 3), the covert visible light communication process is as follows:

[0026] 3-1) The transmitter Alice can transmit two types of information: one is the continuously transmitted public information s R One type is the occasional transmission of hidden information. BTherefore, Alice has two transmission scenarios: H0, where she transmits public information to Roy but not hidden information to Bob; and H1, where she uses superposition coding to superimpose public and hidden information, transmitting public information to Roy while simultaneously transmitting hidden information to Bob. The electrical signal s[n] sent by Alice in the nth symbol period can then be represented as:

[0027]

[0028] In formula (3), n = 1, 2, ..., N, where N represents the total number of symbols in a communication block, n represents the nth symbol, and P is the power P that Alice sends to public user Roy. R and the power P sent to the covert user Bob B ,satisfy:

[0029]

[0030] In formula (4), Alice assigns the power allocation factor β to the public user Roy. R And the power allocation factor β that Alice assigns to the covert user Bob. B Power domain-NOMA protocol requires β to be satisfied. R >β B ,β R +β B =1;

[0031] After electro-optical conversion, the electrical signal s[n] becomes the optical signal X[n]:

[0032]

[0033] In formula (5), Let B represent the electro-optical conversion factor, and B be the DC bias to ensure that the optical signal X[n] is non-negative, assuming that the distribution of X[n] is exponential;

[0034] 3-2) In cases H0 and H1, the optical signal X[n] reaches the receiver through the VLC link, undergoes photoelectric conversion in the PD receiver, and after the DC bias B is removed by the DC blocking circuit in the receiver, the electrical signal y received by the receiver k,k∈K is... k [n] is represented as:

[0035]

[0036] In formula (6), μ is the photo-to-electric conversion factor, and z k [n] is additive white Gaussian noise in the channel, with a mean of 0 and a variance of .

[0037] 3-3) Since no covert information is transmitted in case H0, the analysis mainly focuses on the decoding in case H1, where covert information is transmitted to Bob while public information is transmitted to Roy: Bob uses continuous interference cancellation technology to decode s sequentially. R [n] and s B [n], decoding s R The signal-to-interference-plus-noise ratio γ at [n] B→R and decoding B Signal-to-noise ratio γ at [n] B They are represented as follows:

[0038]

[0039]

[0040] Roy Decodes R The signal-to-interference-plus-noise ratio γ at [n] R for:

[0041]

[0042] In step 4), the transmit power strategy is as follows: the public transmission between Alice and public user Roy adopts a random transmit power strategy, that is, the transmit power is within a certain range. The probability density function follows a continuous uniform distribution. Represented as:

[0043]

[0044] in, This is the maximum power Alice sends to the public user Roy; the purpose of introducing randomness in the transmission power is to prevent the monitor Willie from distinguishing whether the power change is caused by the occurrence of secret information transmission or by random power transmission, thereby ensuring the secure transmission of secret information.

[0045] In step 5), based on the random transmission power strategy of step 4) and the reception status of monitor Willie in step 3-2), Willie's detection results are modeled as a binary hypothesis testing problem; Willie, based on its observations... To determine whether Alice transmitted secret information to the covert user Bob, Willie's detection process is as follows:

[0046] 5-1) Willie uses a power detector for detection, and the decision rule is:

[0047]

[0048] In formula (11), PW This represents Willie's average received power within a communication block. and Let represent Willie's decisions of "Alice transmitted the secret information" and "Alice did not transmit the secret information," respectively, and λ be the decision threshold. When N→∞, according to the strong number theorem, P can be further obtained from formula (6). W The expression is:

[0049]

[0050] 5-2) Willie uses the false detection probability to evaluate its detection performance; when the prior probabilities of H0 and H1 are equal, Willie's false detection probability is expressed as:

[0051]

[0052] In formula (13), is the false alarm probability, indicating that Willie judged Alice to have transmitted secret information, but Alice did not actually transmit it. Pr(·) represents the probability of a certain event occurring. Let be the false alarm probability, representing Willie's judgment that Alice did not transmit the secret information, when in fact Alice did; according to formulas (11), (12) and step 4), the false alarm probabilities are obtained respectively. and the probability of missed detection The expression is:

[0053]

[0054]

[0055] In formulas (14) and (15), Substituting formulas (14) and (15) into formula (13), we obtain the expression for the Willie error detection probability as follows:

[0056]

[0057] 5-3) In covert communication, it is common to... As a hidden constraint, among which It is Willie's minimum false detection probability, and ∈ is an arbitrarily small positive number that determines the concealment level; concealment constraints This indicates that when Willie's minimum error detection probability is sufficiently large, covert transmission can be achieved between Alice and Bob; according to the analysis of formula (16), the decision threshold λ is... When the value is within the range, Willie's false detection probability ξW Regarding the monotonically decreasing nature of λ; λ in When taking values ​​within the range, ξ W The threshold λ is monotonically increasing; therefore, there exists an optimal threshold value λ. * Make ξ W To reach the minimum, that is At that time, Willie's minimum false detection probability

[0058] In step 6), the transmission interruption probability expressions for public user Roy and covert user Bob, as well as the corresponding interruption constraints, are obtained in the following specific process:

[0059] 6-1) The probability of transmission interruption for public user Roy is Ξ R The expression is:

[0060]

[0061] in It is the target communication rate value set by the public user Roy, and

[0062] Substituting equations (9) and (10) into equation (17) and performing variable substitution, we obtain the transmission interruption probability Ξ of Roy. R The expression is:

[0063]

[0064] In formula (18), ρ is the Alice transmit power allocation ratio, and its value is ρ = β. B / β R Because of β R >β B If ρ∈[0,1);

[0065] 6-2) The probability of transmission interruption for the covert user Bob Ξ B The expression is:

[0066]

[0067] in It is the target communication rate value set by the hidden user Bob, and

[0068] Substituting equations (7), (8), and (10) into equation (19) and performing variable substitution, we obtain Bob's transmission interruption probability Ξ. B The expression is:

[0069]

[0070] 6-3) In NOMA communication, to ensure the normal transmission of information by the public user Roy, it is necessary to... R ≤Ξ th As an interruption constraint, Ξ th This is the maximum probability of transmission interruption allowed by the public user Roy.

[0071] In step 7), to better achieve covert communication between Alice and the covert user Bob, based on the covert constraints obtained in step 5) and the interruption constraints obtained in step 6), the effective covert rate R of the covert user is formed by optimizing Alice's transmit power allocation ratio ρ. c The maximization problem, specifically the optimization problem, is as follows:

[0072]

[0073] stC1:

[0074] C2:Ξ R ≤Ξ th

[0075] In the optimization problem (21), constraint C1 is a concealment constraint to ensure the concealed transmission of information between Alice and the concealed user Bob; constraint C2 is a reliability constraint to ensure that Roy's information transmission can proceed normally; based on the effective concealment rate... It can be known that R c It concerns the probability of transmission interruption for the covert user Bob. B A monotonically decreasing function, when Ξ B When the minimum value is taken, R c It is the maximum value; according to formula (20), in Ξ B When the minimum value is reached, ρ = α B / (α R +α R α B Meanwhile, considering whether the constraints of optimization problem (21) hold, the constraints of optimization problem (21) are transformed into expressions related to ρ. The specific steps are as follows:

[0076] 7-1) For the implicit constraint C1 of formula (21), according to step 5-3), we obtain Constraint C1 is β R ≥1-∈; according to the setting in step 3-1), β R =1-β B Therefore, constraint C1 is transformed into β. B The form ≤∈; and because β B +β R =1, therefore we get ρ = β B / (1-βB The final constraint C1 is transformed into:

[0077]

[0078] 7-2) For the reliability constraint C2 in formula (21), it can be seen from formula (18) that when ρ=0, Ξ R Taking the minimum value, however, ρ = 0 means that the power allocated by the transmitter Alice to the covert user Bob is zero. In this case, it is obviously impossible to conduct covert communication between the transmitter Alice and the covert user Bob. Therefore, ρ = 0 is obviously not valid. Therefore, in formula (18), 0 ≤ ρ < 1 / α R The probability of transmission interruption of Roy within the range Ξ R Substituting constraint C2 and rearranging, constraint C2 is finally transformed into:

[0079]

[0080] 7-3) Combining steps 7-1) and 7-2), we can obtain:

[0081]

[0082] min(·) means returning the minimum value in a set of values;

[0083] Substituting formula (24) into formula (20), and further analyzing the optimization problem (21): when 0≤min(∈ / (1-∈), At that time, R c With ρ increasing monotonically, Alice's optimal power allocation ratio ρ is... * for when At that time, R c As ρ is monotonically decreasing, Alice's optimal power allocation ratio is ρ. * =α B / (α R +α R α B Based on the above, the optimal power allocation ratio ρ for Alice is obtained. * The expression is:

[0084]

[0085] Based on the Alice optimal power allocation ratio ρ obtained in step 7-3), * This enables the effective concealment rate R of the concealed user Bob. c To achieve maximum coverage, this scheme not only utilizes a random transmission power strategy to improve the concealment performance of visible light communication systems, but also comprehensively considers the information transmission interruption problem for NOMA users.

[0086] This invention provides a covert communication method suitable for NOMA visible light communication systems, which has the following advantages:

[0087] 1. Improve the covert communication performance of NOMA visible light communication system by designing a random transmission power strategy and optimizing the transmission power allocation ratio of LED transmitter;

[0088] 2. It provides a theoretical basis for the research on covert communication in multi-user visible light communication systems;

[0089] 3. Promote the application of covert visible light communication technology in military and emergency communications. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of covert visible light communication based on NOMA.

[0091] Figure 2 The maximum probability of transmission interruption allowed for the concealment level ∈ and the public user Roy is Ξ. th A schematic diagram illustrating the impact on the maximum effective concealment rate of the concealed user Bob.

[0092] Figure 3 A schematic diagram illustrating the effect of LED installation height L on the maximum effective concealment rate of concealed user Bob.

[0093] Figure 4 This is a schematic diagram illustrating the effect of LED half-power half-angle on the maximum effective concealment rate of concealed user Bob. Detailed Implementation

[0094] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this is not intended to limit the scope of the invention.

[0095] Example:

[0096] A covert communication method suitable for NOMA visible light communication systems includes the following steps:

[0097] 1) Assume a covert visible light communication system with one LED transmitter Alice, two NOMA users (Bob, the near-end user, is the covert user, and Roy, the far-end user, is the public user), and a monitor Willie attempting to detect covert communication activities within the system; each of the covert user Bob, the public user Roy, and the monitor Willie has a single photodetector (PD) to receive or detect signals, such as... Figure 1 As shown;

[0098] 2) Construct a covert visible light communication channel model that includes the visible light communication system equipment from step 1):

[0099] 2-1) Alice's lighting model is modeled as a Lambertian radiation mode and is installed on the ceiling at a height L above the ground. Based on the propagation characteristics of light, the receiving illumination area is circular, with the center point being Alice's mapping point on the ground. It is assumed that this model is based on a polar coordinate system (r...). k ,θ k The design is as follows: where k∈K, K={B,R,W} represents the receiver set, B, R, and W correspond to receivers Bob, Roy, and Willie, respectively. k It is the distance from k to the center of the circle, θ k The angle between k and the polar axis is given by the Euclidean distance from Alice to k.

[0100] 2-2) Assume that the locations of the covert user Bob and the public user Roy within Alice's illuminated cell are known; Alice publicly transmits information to Roy, and secretly transmits information with Bob under Willie's surveillance, and can obtain the Channel State Information (CSI) of users Bob and Roy, while Willie is in a silent state, and Alice can only obtain statistical CSI about Willie; assume the system is in the worst case, that is, Willie can obtain instantaneous CSI about Alice;

[0101] 2-3) Based on the channel modeling in step 2-1), the channel gain h between Alice and k, k∈K is... k for:

[0102]

[0103] In formula (1), A is the physical area of ​​the photodetector PD at point k, and R... p It is the PD response rate, m = -ln2 / ln[cos(Φ 1 / 2 )] represents the Lambert emission order, Φ 1 / 2 For half-power half-angle, d k It is the Euclidean distance φ between the LED and k. k It is the launch angle of the transmitter with respect to k. It is the angle of incidence perpendicular to the k-receiver. For the gain of the receiver filter, Let η be the gain of the optical concentrator, where η is the refractive index and ψ is the gain of the optical concentrator. c The field of view (FOV) of the receiving end;

[0104]

[0105]

[0106] In formula (2), b = m + 3;

[0107] 3) Based on step 2) and the theoretical knowledge of power domain-NOMA, the steps of the covert visible light communication process are as follows:

[0108] 3-1) The transmitter Alice can transmit two types of information: one is the continuously transmitted public information s R One type is the occasional transmission of hidden information. B Therefore, Alice has two transmission scenarios: scenario H0, where she transmits public information to Roy but not hidden information to Bob; and scenario H1, where she uses superposition coding to superimpose public and hidden information, transmitting public information to Roy while simultaneously transmitting hidden information to Bob. Thus, the electrical signal s[n] transmitted by Alice in the nth symbol period is represented as:

[0109]

[0110] In formula (3), n = 1, 2, ..., N, where N represents the total number of symbols in a communication block, n represents the nth symbol, and P is the power P that Alice sends to public user Roy. R and the power P sent to the covert user Bob B ,satisfy:

[0111]

[0112] In formula (4), Alice assigns the power allocation factor β to the public user Roy. R And the power allocation factor β that Alice assigns to the covert user Bob. B Power domain-NOMA protocol requires β to be satisfied. R >β B ,β R +β B =1;

[0113] After electro-optical conversion, the electrical signal s[n] becomes the optical signal X[n]:

[0114]

[0115] In formula (5), Let B represent the electro-optical conversion factor, and B be the DC bias to ensure that the optical signal X[n] is non-negative, assuming that the distribution of X[n] is exponential;

[0116] 3-2) In cases H0 and H1, the optical signal X[n] reaches the receiver through the VLC link, undergoes photoelectric conversion in the PD receiver, and after the DC bias B is removed by the DC blocking circuit in the receiver, the electrical signal y received by the receiver k,k∈K is... k[n] is represented as:

[0117]

[0118] In formula (6), μ is the photo-to-electric conversion factor, and z k [n] is additive white Gaussian noise in the channel, with a mean of 0 and a variance of .

[0119] 3-3) Since no covert information is transmitted in case H0, the analysis mainly focuses on the decoding in case H1, where covert information is transmitted to Bob while public information is transmitted to Roy: Bob uses continuous interference cancellation technology to decode s sequentially. R [n] and s B [n], decoding s R The signal-to-interference-plus-noise ratio γ at [n] B→R and decoding B Signal-to-noise ratio γ at [n] B They are represented as follows:

[0120]

[0121]

[0122] Roy Decodes R The signal-to-interference-plus-noise ratio γ at [n] R for:

[0123]

[0124] 4) To ensure the confidentiality of secret information transmission, a transmission power strategy is designed: the public transmission between Alice and public user Roy adopts a random transmission power strategy, that is, the transmission power is within a certain range. The probability density function follows a continuous uniform distribution. Represented as:

[0125]

[0126] in, This is the maximum power Alice sends to public user Roy; the purpose of introducing randomness in the transmission power is to prevent the monitor Willie from distinguishing whether the power change is caused by the occurrence of secret information transmission or by the transmission of random power, thereby ensuring the secure transmission of secret information.

[0127] 5) Based on the random transmission power strategy in step 4) and the reception status of monitor Willie in step 3-2), Willie's detection results can be modeled as a binary hypothesis testing problem; Willie, based on its observations... To determine whether Alice transmitted secret information to the covert user Bob, Willie's detection process involves the following steps:

[0128] 5-1) Willie uses a power detector for detection, and the decision rule is:

[0129]

[0130] In formula (11), P W This represents Willie's average received power within a communication block. and Let represent Willie's decisions of "Alice transmitted the secret information" and "Alice did not transmit the secret information," respectively, and λ be the decision threshold. When N→∞, according to the strong number theorem, P can be further obtained from formula (6). W The expression is:

[0131]

[0132] 5-2) Willie uses the false detection probability to evaluate its detection performance; when the prior probabilities of H0 and H1 are equal, Willie's false detection probability can be expressed as:

[0133]

[0134] In formula (13), is the false alarm probability, indicating that Willie judged Alice to have transmitted secret information, but Alice did not actually transmit it. Pr(·) represents the probability of a certain event occurring. Let be the false alarm probability, indicating that Willie judged Alice not to have transmitted the secret information, but Alice actually did; according to formulas (11), (12) and step 4), the false alarm probabilities can be obtained respectively. and the probability of missed detection The expression is:

[0135]

[0136]

[0137] In formulas (14) and (15),

[0138] Next, substituting formulas (14) and (15) into formula (13), we can obtain the expression for the Willie error detection probability as follows:

[0139]

[0140] 5-3) In covert communication, it is common to... As a hidden constraint, among which It is Willie's minimum false detection probability, and ∈ is an arbitrarily small positive number that determines the concealment level; concealment constraints This indicates that when Willie's minimum error detection probability is sufficiently large, covert transmission can be achieved between Alice and Bob; according to formula (16), it can be analyzed that the decision threshold λ is... When the value is within the range, Willie's false detection probability ξ W Regarding the monotonically decreasing nature of λ; λ in When taking values ​​within the range, ξ W The threshold λ is monotonically increasing; therefore, there exists an optimal threshold value λ. * Make ξ W To reach the minimum, that is At that time, Willie's minimum false detection probability

[0141] 6) While the random transmission power strategy in step 4) can enhance the system's stealth performance, the uncertainty of the transmission power may cause interruptions in information transmission between Alice and the covert user Bob, and between the public user Roy. The transmission interruption probability expression for the public user Roy and the covert user Bob, as well as the corresponding interruption constraints, are analyzed in detail below:

[0142] 6-1) The probability of transmission interruption for public user Roy is Ξ R The expression is:

[0143]

[0144] in It is the target communication rate value set by the public user Roy, and

[0145] Substituting equations (9) and (10) into equation (17) and performing variable substitution, we obtain the transmission interruption probability Ξ of Roy. R The expression is:

[0146]

[0147] In formula (18), ρ is the Alice transmit power allocation ratio, and its value is ρ = β. B / β R Because of β R >β B If ρ∈[0,1);

[0148] 6-2) The probability of transmission interruption for the covert user Bob Ξ BThe expression is:

[0149]

[0150] in, It is the target communication rate value set by the hidden user Bob, and

[0151] Substituting equations (7), (8), and (10) into equation (19) and performing variable substitution, we obtain Bob's transmission interruption probability Ξ. B The expression is:

[0152]

[0153] 6-3) In NOMA communication, to ensure the normal transmission of information by the public user Roy, it is necessary to... R ≤Ξ th As an interruption constraint, Ξ th This is the maximum probability of transmission interruption allowed by the public user Roy.

[0154] 7) To better achieve covert communication between Alice and the covert user Bob, based on the covert constraints obtained in step 5) and the interruption constraints obtained in step 6), the effective covert rate R of the covert user is formed by optimizing Alice's transmit power allocation ratio ρ. c The maximization problem, specifically the optimization problem, is as follows:

[0155]

[0156] stC1:

[0157] C2:Ξ R ≤Ξ th

[0158] In the optimization problem (21), constraint C1 is a concealment constraint to ensure the concealed transmission of information between Alice and the concealed user Bob; constraint C2 is a reliability constraint to ensure that Roy's information transmission can proceed normally; note the effective concealment rate. It can be known that R c It concerns the probability of transmission interruption for the covert user Bob. B A monotonically decreasing function, when Ξ B When the minimum value is taken, R c It is the maximum value; according to formula (20), in Ξ B When the minimum value is reached, ρ = α B / (α R +α R α BHowever, since we also need to consider whether the constraints of optimization problem (21) are valid, we need to convert the constraints of optimization problem (21) into expressions related to ρ. The specific steps are as follows:

[0159] 7-1) For the implicit constraint C1 of formula (21), according to step 5-3), we can obtain Constraint C1 is β R ≥1-∈; according to the setting in step 3-1), β R =1-β B Therefore, constraint C1 can be transformed into β. B The form ≤∈; and because β B +β R =1, therefore we can obtain ρ = β B / (1-β B The final constraint C1 is transformed into:

[0160]

[0161] 7-2) For the reliability constraint C2 in formula (21), it can be seen from formula (18) that when ρ=0, Ξ R Taking the minimum value, however, ρ = 0 means that the power allocated by the transmitter Alice to the covert user Bob is zero. In this case, it is obviously impossible to carry out covert communication between the transmitter Alice and the covert user Bob. Therefore, ρ = 0 is obviously not valid. Therefore, it is necessary to reduce 0 ≤ ρ < 1 / α in formula (18). R The probability of transmission interruption of Roy within the range Ξ R Substituting constraint C2 and rearranging, constraint C2 is finally transformed into:

[0162]

[0163] 7-3) Combining steps 7-1) and 7-2), we can obtain:

[0164]

[0165] min(·) means returning the minimum value in a set of values;

[0166] Substituting formula (24) into formula (20), and further analyzing the optimization problem (21): when 0≤min(∈ / (1-∈), At that time, R c With ρ increasing monotonically, Alice's optimal power allocation ratio ρ is... * for when At that time, R c As ρ is monotonically decreasing, Alice's optimal power allocation ratio is ρ.* =α B / (α R +α R α B Based on the above, Alice's optimal power allocation ratio ρ can be obtained. * The expression is:

[0167]

[0168] Based on the Alice optimal power allocation ratio ρ obtained in step 7-3), * This can increase the effective concealment rate R of the concealed user Bob. c To achieve maximum coverage, this scheme not only utilizes a random transmission power strategy to improve the concealment performance of visible light communication systems, but also comprehensively considers the information transmission interruption problem for NOMA users.

[0169] The method described above was used to verify this method, as detailed below:

[0170] Appendix Figure 2 The analysis examined the concealment level ∈ and the maximum interruption probability value Ξ allowed by the public user Roy. th The impact on the maximum effective concealment rate of the concealed user Bob. From Figure 2 It can be observed that the maximum effective concealment rate of the concealed user Bob varies with the concealment level ∈ and the maximum interruption probability value Ξ allowed by the public user Roy. th The value increases with the increase of ∈, and eventually remains unchanged. This is because the increase of ∈ reduces the requirements of the concealment constraint, making the concealment constraint easier to satisfy, which means that more concealed information can be transmitted; Ξ th The increase in the power allocation ratio indicates a lower reliability constraint on the public user. Alice can allocate more power to the covert user, thus allowing more covert information to be transmitted and increasing Bob's maximum effective covert rate. However, considering the reliable transmission of the public user Roy, the power Alice allocates to Bob will not increase indefinitely. Changes in the parameters of Alice's optimal power allocation ratio expression no longer alter the optimal power allocation ratio. Therefore, at a certain value, Alice's optimal power allocation ratio will remain constant, and Bob's maximum effective covert rate will also remain constant. These conclusions verify that optimizing Alice's power allocation ratio can improve the system's covert performance to a certain extent.

[0171] Appendix Figure 3 The impact of LED installation height L on the maximum effective concealment rate for concealed user Bob was analyzed. From Figure 3It can be observed that the maximum effective covert rate of the concealed user Bob decreases as L increases. This is because the larger the height L, the greater the Euclidean distance between the LED and the concealed user Bob, resulting in a weakening of the received signal strength by the concealed user Bob, and therefore a smaller maximum effective covert rate for the concealed user Bob. This indicates that when designing the LED installation height, the height should not be designed too high to ensure effective covert communication.

[0172] Appendix Figure 4 The impact of LED half-power half-angle on the maximum effective concealment rate of concealed user Bob was analyzed. From Figure 4 It can be observed that Bob's maximum effective concealment rate decreases as the LED half-power half-angle increases. This is because increasing the LED half-power half-angle indicates a broadening of the LED transmission beam, increasing the coverage probability and making the concealed information easier for Willie to detect. This makes the concealment constraints more stringent, resulting in less concealed information being transmitted, thus reducing Bob's maximum effective concealment rate. This suggests that the LED half-power half-angle should not be designed too large when Alice and Bob are conducting covert communication.

Claims

1. A covert communication method suitable for NOMA visible light communication systems, characterized in that, Includes the following steps: 1) Assume that in a covert visible light communication system, there is an LED transmitter Alice, two NOMA users, and a monitor Willie who attempts to detect covert communication behavior in the system; among the two NOMA users, Bob, who is closer to the user, is the covert user, and Roy, who is farther from the user, is the public user; 2) Construct a covert visible light communication channel model that includes the visible light communication system equipment in step 1). Under the Lambertian radiation mode of Alice's illumination model, express the channel gain from Alice to the covert user Bob and the public user Roy respectively. 3) Based on step 2) and the basic principles of power domain-NOMA, analyze the covert visible light communication process based on NOMA, and obtain the received signal-to-noise ratio expression for NOMA users, namely covert user Bob and public user Roy. 4) To ensure the concealment of secret information transmission, a random transmission power strategy is designed; The aforementioned transmit power strategy is as follows: the public transmission between Alice and public user Roy adopts a random transmit power strategy, that is, the transmit power is within a certain range. The probability density function follows a continuous uniform distribution. for: ,in This is the maximum power Alice sends to the public user Roy; 5) Based on the visible light communication process in step 3) and the random transmission power scheme in step 4), analyze Willie's detection process, detect whether Alice sends covert information to the covert user Bob, and obtain the expression for Willie's false detection probability. Then, by analyzing the optimal threshold value and Willie's minimum false detection probability, obtain the covert constraints of visible light communication. 6) According to the random transmission power strategy in step 4), the uncertainty of transmission power may cause the information transmission between Alice and the covert user Bob and the public user Roy to be interrupted. By analyzing the received signals of the covert user Bob and the public user Roy under the random transmission power, the transmission interruption probability expression of the public user Roy and the covert user Bob is obtained, and the interruption constraint condition of visible light communication is obtained. 7) In order to better realize covert communication between Alice and covert user Bob, based on the covert constraints obtained in step 5) and the interruption constraints obtained in step 6), the effective covert rate maximization problem of covert user is formed by optimizing Alice's transmission power allocation ratio. In step 3), the covert visible light communication process is as follows: 3-1) The transmitter Alice can transmit two types of information: one is public information that is always transmitted. One type is the occasionally transmitted hidden information. Therefore, Alice has two possible transmission scenarios: transmitting public information to Roy but not transmitting hidden information to Bob. The application of overlay coding technology combines public and hidden information, transmitting public information to Roy while simultaneously transmitting hidden information to Bob. Then Alice is in the th... Electrical signals transmitted per symbol period Represented as: （3） In formula (3), N represents the total number of symbols contained in a communication block. Indicates the first The symbol, the power Alice sent to public user Roy. and the power sent to the covert user Bob ,satisfy: （4） The power allocation factor that Alice assigns to public user Roy in formula (4) And the power allocation factor that Alice assigns to the covert user Bob. The power domain-NOMA protocol needs to meet the following requirements. , ; electric signal After electro-optical conversion, it becomes an optical signal. : （5） In formula (5), Indicates the electro-optical conversion factor. DC bias is used to ensure the optical signal. Yes / no negative, assuming The distribution of is an exponential distribution; 3-2) In and In both cases, the optical signal The signal reaches the receiver via a VLC link, where it undergoes photoelectric conversion in the PD receiver and DC bias is removed by a DC blocking circuit within the receiver. Afterwards, the recipient Received electrical signals Represented as: （6） In formula (6), It is the photo-to-electric conversion factor. It is additive white Gaussian noise in the channel, with a mean of 0 and a variance of . ; 3-3) Because Since no covert information was transmitted under these circumstances, the main analysis focuses on the transmission of covert information to Bob simultaneously with the transmission of public information to Roy. Decoding under these conditions: Bob uses sequential decoding with continuous interference cancellation technology. and ,decoding Signal-to-interference-to-noise ratio and decoding Signal-to-noise ratio They are represented as follows: （7） （8） Roy Decoding Signal-to-interference-to-noise ratio for: （9）。 2. The covert communication method for NOMA visible light communication systems according to claim 1, characterized in that, In step 1), each of the concealed user Bob, the public user Roy, and the monitor Willie has a single photodetector PD to receive or detect signals.

3. The covert communication method for NOMA visible light communication systems according to claim 1, characterized in that, In step 2), the specific process of building the covert visible light communication channel model is as follows: 2-1) Alice's lighting model is modeled as a Lambertian radiation mode and is installed at a height of [height missing] above the ground. On the ceiling; based on the propagation characteristics of light, the shape of the receiving light area is circular, and the center point is Alice's mapping point on the ground. This model is assumed to be based on a polar coordinate system. Designed, among which Let B, R, and W represent the set of receivers, where B, R, and W correspond to receivers Bob, Roy, and Willie, respectively. yes Distance to the center of the circle, yes The angle between Alice and the polar axis, Alice to The Euclidean distance is ; 2-2) Assume that the locations of covert user Bob and public user Roy within Alice's illuminated cell are known; Alice publicly transmits information to Roy, and secretly transmits information with Bob under Willie's surveillance, and can obtain the Channel State Information (CSI) of users Bob and Roy, while Willie is in a silent state, and Alice can only obtain statistical CSI about Willie; assume the system is in the worst case, that is, Willie can obtain instantaneous CSI about Alice; 2-3) Based on the channel modeling in step 2-1), Alice and Channel gain between for: （1） In formula (1), yes The physical area of ​​the photodetector PD. It is the PD response rate. Let the Lambertian emission order be . It is half power and half angle. It is LED to The Euclidean distance between them It is about the transmitter The angle of departure, It is perpendicular to The angle of incidence of the receiver, For the gain of the receiver filter, The gain of the optical concentrator is where For refractive index, The field of view (FOV) of the receiving end; in and The following relationship exists: Therefore, channel gain Simplified to: （2） In formula (2), , .

4. The covert communication method for NOMA visible light communication systems according to claim 1, characterized in that, In step 5), based on the random transmission power strategy of step 4) and the reception status of monitor Willie in step 3-2), Willie's detection results are modeled as a binary hypothesis testing problem; Willie, based on its observations... To determine whether Alice transmitted secret information to the covert user Bob, Willie's detection process is as follows: 5-1) Willie uses a power detector for detection, and the decision rule is: （10） in, This represents Willie's average received power within a communication block. and These represent Willie's judgments: "Alice transmitted the secret message" and "Alice did not transmit the secret message." It is the judgment threshold; when At that time, according to the strong number theorem, we can further obtain from formula (6) The expression is: （11） 5-2) Willie uses the false detection probability to evaluate its detection performance; in and Given equal prior probabilities, Willie's false detection probability is expressed as: （12） in, denoted as False Alarm Probability, representing Willie's judgment that Alice transmitted secret information when Alice did not. This indicates the calculation of the probability of an event occurring. The false alarm probability is denoted as , which means Willie judged Alice not to have transmitted the secret information, but Alice actually did. The false alarm probabilities are obtained according to formulas (10), (11), and step 4. and the probability of missed detection The expression is: （13） （14） In formulas (13) and (14), , Substituting formulas (13) and (14) into formula (12), we obtain the expression for the Willie false detection probability as follows: （15） 5-3) In covert communication, it is common to... As a hidden constraint, among which It is Willie's minimum false detection probability. It is an arbitrarily small positive number that determines the concealment level; concealment constraints This indicates that when Willie's minimum error detection probability is sufficiently large, covert transmission can be achieved between Alice and Bob; based on the analysis of formula (15), the decision threshold is: exist When the value is within the range, Willie's false detection probability about Monotonically decreasing; exist When taking values ​​within a range, about Monotonically increasing; therefore, there exists an optimal threshold value. Make To reach the minimum, that is When, Willie's minimum false detection probability .

5. A covert communication method for NOMA visible light communication systems according to claim 1, characterized in that, In step 6), the transmission interruption constraint probability expressions for public user Roy and covert user Bob, as well as the corresponding interruption constraints, are obtained through the following process: 6-1) Probability of transmission interruption for public user Roy The expression is: （16） in It is the target communication rate value set by the public user Roy, and ; Substituting equations (9) and (10) into equation (16) and performing variable substitution, we obtain the transmission interruption probability of Roy. The expression is: （17） in, This is Alice's transmit power allocation ratio, and its value is... ,because ,but ; 6-2) Probability of transmission interruption for covert user Bob The expression is: （18） in It is the target communication rate value set by the hidden user Bob, and ; Substituting equations (7), (8), and (10) into equation (18) and performing variable substitution, we obtain Bob's transmission interruption probability. The expression is: （19）； 6-3) In NOMA communication, to ensure the normal transmission of information by the public user Roy, the following measures will be taken: As an interruption constraint, This is the maximum probability of transmission interruption allowed by the public user Roy.

6. A covert communication method for NOMA visible light communication systems according to claim 1, characterized in that, In step 7), to better achieve covert communication between Alice and the covert user Bob, based on the covert constraints obtained in step 5) and the interruption constraints obtained in step 6), the transmit power allocation ratio of Alice is optimized. This forms an effective concealment rate for hidden users. The maximization problem, specifically the optimization problem, is as follows: （20） In the optimization problem (20), constraint C1 is a concealment constraint to ensure the concealed transmission of information between Alice and the concealed user Bob; constraint C2 is a reliability constraint to ensure that Roy's information transmission can proceed normally; based on the effective concealment rate... It can be known that It concerns the probability of transmission interruption for the covert user Bob. A monotonically decreasing function, when When taking the minimum value, It is the maximum value; according to formula (19), in When taking the minimum value, Meanwhile, considering whether the constraints of optimization problem (20) hold, the constraints of optimization problem (20) are transformed into relevant... The expression, and the specific steps are as follows: 7-1) For the implicit constraint C1 of formula (20), according to step 5-3), we get Constraint C1 is ; According to the settings in step 3-1), Therefore, constraint C1 is transformed into The form; and because Therefore, we get The final constraint C1 is transformed into: （21） 7-2) For the reliability constraint C2 in formula (20), it can be seen from formula (17) that when hour Take the minimum value, however This means that Alice, the transmitter, allocates zero power to Bob, the covert user. Under these circumstances, covert communication between Alice and Bob is clearly impossible. This is clearly not true; therefore, in formula (17) Probability of transmission interruption of Roy within range Substituting constraint C2 and rearranging, constraint C2 is finally transformed into: （22） 7-3) Combining steps 7-1) and 7-2), we can obtain: （23） in This indicates that the minimum value in a set of values ​​is returned. Substituting formula (23) into formula (19), and further analyzing the optimization problem (20): when hour, about Monotonically increasing, this is Alice's optimal power allocation ratio. for ;when hour, about Monotonically decreasing, Alice's optimal power allocation ratio is then... Based on the above, the optimal power allocation ratio for Alice is obtained. The expression is: （24） Based on the Alice optimal power allocation ratio obtained in step 7-3) This enables Bob, the hidden user, to achieve an effective concealment rate. Reach the maximum.

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