Interferer-assisted hidden visible light communication performance improvement method

Abstract

The invention relates to the technical field of visible light communication, in particular to a jammer-assisted hidden visible light communication performance improvement method, which comprises the following steps of: adding a cooperative jammer to an indoor visible light communication network consisting of a transmitter, a legal receiver and a monitor; receiving signals of a legal receiver and a monitor are determined according to distribution of sent useful signals and interference signals and a designed interference strategy, the minimum detection error probability of the monitor is determined according to a power detection criterion, the minimum detection error probability serves as a constraint condition of covert communication, the average information rate of a system is maximized, and the system reliability is improved. By maximizing the upper and lower bounds of the average information rate of the system, the maximum average optical power of the transmitter under the constraint condition and the optimal values of the upper and lower bounds of the average information rate at the moment are obtained. According to the method provided by the invention, the effect of improving the hidden visible light communication performance is obvious, especially when the channel use times approach to infinity, the limitation of zero asymptotic rate is broken, and hidden information transmission at positive rate is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of visible light communication, and particularly to a method for improving the performance of covert visible light communication assisted by a jammer. Background Art

[0002] Visible Light Communications (VLC), as a new type of wireless communication technology developed relying on Light Emitting Diode (LED) technology, has significant advantages of short distance and high-speed transmission. It uses an LED as both a light source and a signal source, transmits information by emitting visible light signals that are imperceptible to the naked eye and flicker rapidly, and at the receiving end, a photodiode (PD) is used to complete photoelectric conversion, and then the received, regenerated, and demodulated electrical signals are used to achieve information transmission.

[0003] Since it was proposed in 1999, VLC has achieved rapid development. Currently, the research focus of VLC is gradually shifting from link-level communication to networking. In future indoor VLC network scenarios, the privacy and confidentiality of user data will become particularly important. Although VLC has the characteristic of line-of-sight propagation, it still has a broadcast characteristic. While this broadcast characteristic facilitates data transmission, it also provides an opportunity for eavesdropping users to access the network and eavesdrop on information, posing a potential security risk to the data transmission of legitimate users.

[0004] From the perspective of information theory, the earliest technology to solve the security problem of wireless communication networks was the encryption technology based on computational complexity, mainly including communication information encryption, key management, secure communication protocols, etc. However, these technologies all solve network security problems from the upper layer of the protocol stack through access control, password protection, and end-to-end encryption, etc. Their security is based on the limited computing power of eavesdropping users. Currently, their security faces many problems. On the one hand, due to the mobility of users and the limited resources in wireless networks, traditional encryption algorithms, key distribution, and management will become extremely complex. On the other hand, with the rapid development of high-performance computing, especially the emergence of quantum computers, the security of encryption mechanisms based on computational complexity is challenged, and it is easy to cause the leakage of security information. Therefore, traditional encryption technologies based on computational complexity can no longer meet the security requirements of future communications, and domestic and foreign scholars have begun to seek new network security technologies.

[0005] In the process of the development of network security technology, the physical layer in the protocol stack has been ignored. As the bottom layer of the protocol stack, the physical layer is the foundation of the entire network. How to make full use of the transmission characteristics of the wireless channel and turn seemingly unfavorable factors into factors conducive to improving the security performance of the communication network has become an important direction in the development of wireless communication technology in recent years. Against this background, physical layer security has gradually received wide attention. However, physical layer security only protects the transmitted content and does not provide protection for transmission detection. In recent years, a new secure transmission technology - covert communication has been proposed. It not only protects the transmitted content, but also emphasizes that the transmission behavior of legitimate users is difficult to detect.

[0006] At present, many achievements have been made in covert communication in the radio frequency field. However, there are significant differences between covert VLC and radio frequency covert communication in terms of signal characteristics, channel characteristics, input distribution, etc., resulting in the achievements in radio frequency covert communication not being directly applicable to covert VLC. Through our previous research on the basic performance limit of covert VLC, it is found that when the number of channel uses approaches infinity, the average covert information transmission rate of the VLC system approaches zero. However, this zero asymptotic rate transmission greatly limits the practicality of the covert VLC system. Therefore, improving the covert transmission performance of the covert VLC system has become a key problem to be solved urgently. Aiming at the problem of limited covert transmission performance of covert VLC, the present invention provides a method for improving the performance of interference-assisted covert VLC, which breaks this zero asymptotic rate limit and realizes positive-rate covert information transmission. Summary of the Invention

[0007] The purpose of the present invention is to overcome the above problems or at least partially solve the above problems, and propose a method for improving the performance of interference-assisted covert visible light communication. An indoor visible light communication network composed of a transmitter, a legitimate receiver and a monitor is added with a cooperative jammer. According to the distribution of the useful signal and the interference signal sent and the designed interference strategy, the received signals of the legitimate receiver and the monitor are determined. According to the power detection criterion, the minimum detection error probability of the monitor is determined, and this is used as a constraint condition for covert communication. The average information rate of the system is maximized, and the optimal values of the maximum average optical power of the transmitter and the upper and lower bounds of the average information rate at this time under the constraint conditions are obtained by maximizing the upper and lower bounds of the average information rate of the system. The method proposed by the present invention has an obvious effect on improving the performance of covert visible light communication. Especially when the number of channel uses approaches infinity, it breaks the zero asymptotic rate limit and realizes positive-rate covert information transmission.

[0008] To achieve the above object, the present invention provides the following technical solution: A method for improving the performance of interference-assisted covert visible light communication, comprising the following steps:

[0009] S1: Consider a covert visible light communication system consisting of a transmitter (denoted as Alice), a cooperative jammer (denoted as Dave), a legitimate receiver (denoted as Bob), and a monitor (denoted as Willie); construct a three-dimensional Cartesian coordinate system, set the coordinates of Alice, Dave, Bob, and Willie; use the Lambert radiation model to construct a channel gain model; consider the non-negativity of the signal and the average optical power constraint to construct a signal constraint model;

[0010] S2: According to the signal constraint model constructed in step S1, determine the distributions of the useful signal transmitted by Alice and the interfering signal transmitted by Dave as exponential distributions, and let the average optical power \(P\) of the interfering signal J follow a uniform distribution on \([0, P]\) Jmax ;

[0011] S3: Consider the additive white Gaussian noise independent of the signal and the channel gain model constructed in step S1, determine the expression of the received signal of Bob on the communication channel; Willie observes the usage of the channel \(n\) times, constructs a binary hypothesis test, and determines the expression of the received signal on its detection channel;

[0012] S4: Willie determines the minimum detection error probability \(\zeta\) min according to the power detection criterion, and uses this as an evaluation index to characterize Willie's detection performance, and constructs a covertness constraint \(\zeta\) min \(\geq 1 - \varepsilon\), where \(\varepsilon>0\) represents a pre-agreed covertness constraint threshold. To ensure that Alice's communication behavior is sufficiently covert, \(\varepsilon\) needs to be small enough;

[0013] S5: Since the average optical power \(P\) of the interfering signal J follows a uniform distribution on \([0, P]\) Jmax , take the average information transmission rate between Alice and Bob as an evaluation index of the system's communication performance;

[0014] S6: Comprehensively consider the detection performance and communication performance, construct an optimization problem, that is, maximize the average information transmission rate under the condition of ensuring the system's covertness constraint to obtain the optimal value of the average optical power \(P\) A of Alice;

[0015] S7: Considering that the optimization problem in step S6 is very complex, further simplify the objective function and constraint conditions; first, according to the entropy power inequality and the principle that the differential entropy of any random variable is not greater than the differential entropy of a Gaussian random variable with the same variance, obtain the upper and lower bounds of the instantaneous information transmission rate \(R\) of the system; then, according to the distribution of the average optical power of the interfering signal, obtain the upper bound of the average information transmission rate ; and the lower bound ; then, set the Willie detection threshold to minimize the detection error probability and simplify the concealment constraint.

[0016] S8: According to the upper bound and the lower bound obtained in step S7, transform the original optimization problem into maximizing the upper bound of the average information transmission rate while ensuring the system concealment constraint conditions and the lower bound

[0017] S9: Utilize the and monotonic relationship with respect to P A to determine the optimal value of P A as well as and and optimal values and

[0018] S10: When the number of channel uses n approaches infinity, the upper and lower bounds of the average covert information transmission rate are independent of n. Therefore, after adding interfering nodes, the asymptotic covert transmission rate is no longer zero but a positive value, achieving positive-rate covert optical information transmission.

[0019] In a preferred embodiment, in step S1, the channel gain between the transmitter v (v = A represents Alice, v = J represents Dave) and the receiver k (k = B represents Bob, k = W represents Willie) is modeled as:

[0020]

[0021] where m is the Lambert radiation order; A r is the physical area of the photodiode in the receiver; D vk , and ψ vk respectively represent the distance from the transmitter v to the receiver k, the irradiation exit angle, and the irradiation incident angle; T s and g respectively represent the gain of the optical filter and the gain of the optical concentrator; Ψ represents the field of view angle of the photodiode in the receiver; the non-negativity and average optical power constraint of the signal x v,i transmitted by the transmitter v through the i-th (i = 1, 2,..., n) channel are modeled as:

[0022]

[0023] where E(·) represents the expectation operation, P vDenotes the average optical power of the light-emitting diode at transmitter v, ξ A ∈(0, 1] represents the dimming target at Alice, which can be adjusted according to different user requirements. The dimming target at Dave is a fixed value, i.e., ξ J = 1.

[0024] In a preferred embodiment, in the step S2, the useful signal x sent by Alice through the i-th (i = 1, 2,..., n) channel A,i and the interference signal x sent by Dave through the i-th channel J,i both follow an exponential distribution. The probability density functions of x A,i and x J,i are respectively expressed as:

[0025]

[0026]

[0027] where P A denotes the average optical power of the useful signal sent by Alice, ξ A ∈(0, 1] represents the dimming target of Alice, P J denotes the average optical power of the interference signal sent by Dave, and P J follows a uniform distribution on [0, P Jmax , and P Jmax denotes the maximum average optical power of Dave.

[0028] In a preferred embodiment, in the step S3, the signals y received by Bob and Willie through the i-th channel k,i are respectively expressed as:

[0029] y B,i = r B h AB x A,i + r B h JB x J,i + n B,i , i = 1, 2,..., n

[0030]

[0031] where r k represents the optoelectronic conversion factor of the photodiode at receiver k; denotes the Gaussian white noise with a mean of 0 and a variance of received by receiver k using the i-th channel; H 0 represents the null hypothesis, i.e., Alice did not send information; H 1Denote the alternative hypothesis, i.e., Alice sent a message.

[0032] In a preferred embodiment, in the step S4, it specifically includes the following steps:

[0033] Define signal independence: In n channel uses, the symbols sent by Alice are independent of each other, the transmitted symbols and the ambient noise are also independent of each other, and since the channel gain of visible light communication follows the Lambert radiation model, the channel gain is also fixed, making the signals received by Willie independent of each other;

[0034] Calculate the average electric power of the received signal: When the number of channel uses approaches infinity, according to the weak law of large numbers, the average electric power Ω of the signal received by Willie is expressed as:

[0035]

[0036] Since the average optical power P of the jammer Dave J obeys the uniform distribution on [0, P Jmax , the average electric power of the signal received by Willie is a randomly varying value;

[0037] Determine the detection decision method: Willie makes a decision through power detection, expressed as:

[0038]

[0039] where τ represents the detection threshold set by Willie. When Ω > τ, Willie determines it as D 1 , that is, it is determined that Alice sent a signal; when Ω < τ, Willie determines it as D 0 , that is, it is determined that Alice did not send a signal;

[0040] Analyze the minimum detection error probability: The minimum detection error probability ζ min There are two cases: When P Jmax ≤h AW ξ A P A / h JW ), Willie sets the detection threshold to any value within the range of to achieve the minimum detection error probability ζ min = 0; when P Jmax > h AW ξ A P A / h JW ), Willie sets the detection threshold to to achieve the minimum detection error probability ζ min = 1 - hAW ξ A P A / (h JW P Jmax )。

[0041] In a preferred embodiment, in the step S5, the average information transmission rate is expressed as:

[0042]

[0043] where R represents the instantaneous information transmission rate of the system, P J and P Jmax are the average optical power and the maximum average optical power of Dave, respectively.

[0044] In a preferred embodiment, in the step S6, the optimization problem is modeled as:

[0045]

[0046] In a preferred embodiment, in the step S7, the upper bound and the lower bound of the average information transmission rate are respectively:

[0047]

[0048] Set the detection threshold of Willie to Then the concealment constraint is reformulated as:

[0049]

[0050] In a preferred embodiment, in the step S8, the transformed optimization problem is expressed as:

[0051]

[0052] where is the lower bound of the average information rate, is the upper bound of the average information rate.

[0053] In a preferred embodiment, in the step S9, the upper bound and the lower bound are both monotonically increasing functions of P A , and the optimal value of P A is and the maximum value of and are respectively expressed as:

[0054]

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1. By introducing a jammer that emits interference signals with random average optical power, the present invention effectively disrupts the detection of the monitor and provides cover for communication. With this assistance, the covert VLC successfully breaks the limit of zero asymptotic rate (i.e., lim n→∞ nR / n = 0), realizes the transmission of covert optical information with positive rate, and significantly improves the feasibility and effectiveness of the covert VLC system in practical applications;

[0057] 2. The present invention determines the upper and lower bounds of the maximum average optical power and average information transmission rate of the transmitter in covert VLC. Specifically, the present invention constructs an optimization problem for the jammer-assisted covert VLC system, that is, to maximize the average transmission rate of the system under the condition of ensuring the covertness constraint of the system Maximize the average information transmission rate by problem transformation of the upper bound and the lower bound to obtain the maximum average optical power of the transmitter that satisfies the covert condition of the system and the average information transmission rate at this time of the upper bound and the lower bound of the maximum value and provide a theoretical basis for evaluating the performance of the covert VLC system, and help researchers and engineers better design and optimize the covert VLC system;

[0058] 3. The present invention expands the application scope of covert communication. According to the characteristics of covert VLC, effective methods for performance improvement are determined, and the application scope of covert communication is successfully extended to the field of visible light communication. This not only enriches the research content of covert communication, but also has important guiding significance for the indoor coverage and networking of future 6G, and provides a new solution for realizing secure and efficient information transmission by 6G communication technology in complex indoor environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a schematic diagram of the indoor covert VLC network of the present invention;

[0060] Figure 2 is a comparison diagram of the relationship between the minimum detection error probability ζ min of Willie with the change of P A when there is or without the assistance of a jamming node in the present invention;

[0061] Figure 3For the present invention at different average optical powers P A under the conditions, the minimum detection error probability ζ of Willie min varies with the maximum average optical power P of the interference signal Jmax ;

[0062] Figure 4 For the present invention when h JW / h JB = 100, the maximum value of the lower bound of the average information transmission rate and the maximum value of the upper bound vary with the covert constraint value ε;

[0063] Figure 5 For the present invention when ε = 0.1, under different h JW JB / h JB conditions, the maximum value of the lower bound of the average information transmission rate and the maximum value of the upper bound vary with the maximum average optical power P of the interference signal ; Jmax Specific embodiments

[0064] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0065] Please refer to Figures 1 - 5 , the present invention provides a technical solution: a method for improving the performance of covert visible light communication assisted by a jammer, including the following steps:

[0066] S1: System modeling: As Figure 1 shown, consider a covert VLC system composed of a transmitter (Alice), a cooperative jammer (Dave), a legitimate receiver (Bob), and a monitor (Willie). Among them, both Alice and Dave are equipped with a single light-emitting diode and deployed on the ceiling in the room, and both Bob and Willie equipped with a single photodiode are located on the ground. Alice sends a useful signal to Bob and hopes that this communication process will not be detected by Willie. The cooperative jammer Dave disrupts Willie's detection by transmitting interference signals. Model the channel gain between the transmitter v (v = A represents Alice, v = J represents Dave) and the receiver k (k = B represents Bob, k = W represents Willie) as:

[0067]

[0068] where m is the Lambert radiation order; A r is the physical area of the photodiode in the receiver; D vk , and ψ vk respectively represent the distance from transmitter v to receiver k, the irradiation exit angle, and the irradiation incident angle; T s and g respectively represent the gain of the optical filter and the gain of the optical concentrator; Ψ represents the field of view angle of the photodiode in the receiver. The non-negativity and average optical power constraints of the signal x v,i transmitted by transmitter v through the i-th (i = 1, 2,..., n) channel are modeled as:

[0069]

[0070] where E(·) represents the expectation operation, P v represents the average optical power of the light-emitting diode at transmitter v, ξ A ∈(0, 1] represents the dimming target at Alice, which can be adjusted according to different user requirements, and the dimming target at Dave is a fixed value, i.e., ξ J = 1.

[0071] S2: Determine the distributions of the useful signal and the interference signal: According to the signal constraint model constructed in step S1, the distributions of the useful signal transmitted by Alice and the interference signal transmitted by Dave are determined to be exponential distributions, and the average optical power P J of the interference signal is made to follow a uniform distribution on [0, P Jmax . Specifically, the probability density functions of the useful signal x A,i transmitted by Alice through the i-th (i = 1, 2,..., n) channel and the interference signal x J，i transmitted by Dave through the i-th channel are respectively expressed as:

[0072]

[0073]

[0074] where P A represents the average optical power of the useful signal transmitted by Alice, ξ A ∈(0, 1] represents the dimming target of Alice, P J represents the average optical power of the interference signal transmitted by Dave, and P J follows a uniform distribution on [0, P Jmax , P JmaxRepresents the maximum average optical power of Dave.

[0075] S3: Determine the received signals of Bob and Willie: Considering the additive white Gaussian noise independent of the signal and the channel gain model constructed in step S1, the signal y received by Bob for the i-th time on the communication channel B,i and the signal y received by Willie for the i-th time on the detection channel W,i are respectively expressed as:

[0076] y B,i = r B h AB x A,i + r B h JB x J,i + n B,i , i = 1, 2, …, n (6)

[0077]

[0078] where r k represents the optoelectronic conversion factor of the photodiode at receiver k; represents the Gaussian white noise with a mean of 0 and a variance of received by receiver k using the i-th channel; H 0 represents the null hypothesis, i.e., Alice did not send information; H 1 represents the alternative hypothesis, i.e., Alice sent information.

[0079] S4: Determine Willie's detection performance: In n channel uses, the symbols sent by Alice are independent of each other, the transmitted symbols and the environmental noise are also independent of each other, and since the channel gain of VLC follows the Lambert radiation model, the channel gain is also fixed. Therefore, the signals received by Willie are also independent of each other. According to the weak law of large numbers, when the number of channel uses tends to infinity, the average electrical power Ω of the signals received by Willie is expressed as:

[0080]

[0081] Since the average optical power P J of the jammer Dave follows a uniform distribution on [0, P Jmax , the average electrical power of the signals received by Willie is a randomly varying value. Therefore, it is necessary to analyze the detection error probability at Willie. Willie makes a determination through power detection, which is specifically expressed as:

[0082]

[0083] Among them, τ represents the detection threshold set by Willie. When Ω > τ, Willie determines it as D 1 , that is, it is determined that Alice has sent a signal; when Ω < τ, Willie determines it as D 0 , that is, it is determined that Alice has not sent a signal. When Alice sends a signal with equal probability, the minimum detection error probability ζ of Willie through power detection min There are the following two cases:

[0084] When P Jmax ≤h AW ξ A P A / h JW , Willie sets the detection threshold τ * to be any value within the range, so as to achieve the minimum detection error probability ζ min = 0.

[0085] When P Jmax > h AW ξ A P A / h JW , Willie sets the detection threshold so as to achieve the minimum detection error probability ζ min = 1 - h AW ξ A P A / (h JW P Jmax ).

[0086] In covert communication, the minimum detection error probability ζ of Willie min can measure the covert performance of the communication system. Generally speaking, the larger the minimum detection error probability ζ of Willie min , the better the covert performance of the system. Therefore, ζ min ≥ 1 - ε is used as the covertness constraint condition, where ε > 0 represents the pre-agreed covert constraint threshold. To ensure that Alice's communication behavior is sufficiently covert, ε needs to be small enough.

[0087] S5: Determine Bob's communication performance: Since the average optical power P of the interference signal J obeys a uniform distribution on [0, P Jmax , the average information transmission rate between Alice and Bob is used as an evaluation index of the system communication performance. Specifically, the average information transmission rate

[0088]

[0089] Among them, R represents the instantaneous information transmission rate of the system.

[0090] S6: Construct an optimization problem to improve the covert transmission performance: Considering both the detection performance and the communication performance, construct an optimization problem, that is, maximize the average information transmission rate under the condition of ensuring the covert constraint of the system to obtain the optimal value of the average optical power P of Alice A . Mathematically, the optimization problem can be modeled as:

[0091]

[0092] S7: Problem simplification: Since the signals observed by Bob through each channel transmission are independent and identically distributed, without loss of generality, the situation of the i-th channel transmission can be analyzed. For the sake of convenience of representation, x A,i , x J,i , y B,i and n B,i are abbreviated as x A , x J , y B and n B . According to the relevant knowledge of information theory, the information transmission rate R represents the amount of information that can be transmitted per symbol on average in the channel, that is, the average mutual information. Therefore, there is

[0093]

[0094] where I(x A ; y B ) represents the average mutual information of each channel use between Alice and Bob.

[0095] Since the distribution forms of the input signal, interference signal, and noise signal are different, the signal distribution received by the legitimate receiver Bob is very complex. In addition, P J obeys a uniform distribution on [0, P Jmax , which causes R to change with the change of P J . This makes it difficult to analyze the specific expressions of the output entropy H(y B ) and the conditional entropy H(y B |x A ). Therefore, consider deriving the upper and lower bounds of the average information transmission rate .

[0096] (1) Lower bound of the average information transmission rate : Obtained by applying the entropy power inequality

[0097]

[0098] Based on the input signal distribution determined in step S2, we can obtain

[0099] H(x A ) = log 2 (ξ A P A e) (14)

[0100] H(x J ) = log 2 (P J e) (15)

[0101] H(r B h JB x J +n B ) can be upper-bounded by the differential entropy of a Gaussian random variable with variance var(r B h JB x J +n B ), i.e.,

[0102]

[0103] According to equations (17)-(18), the lower bound of R is expressed as:

[0104]

[0105] Therefore, according to formula (20), the lower bound of the average information transmission rate can be expressed as:

[0106]

[0107] (2) Upper bound of the average information transmission rate : Similarly, the upper bound of R can be expressed as:

[0108]

[0109] Therefore, according to formula (23), the upper bound of the average information transmission rate can be expressed as:

[0110]

[0111] According to S6, when Willie sets the detection threshold to , the detection error probability of Willie reaches the minimum value of ζ min = 1 - h AW ξ A P A / (h JW P​Jmax ) Then the concealment constraint can be reformulated as:

[0112]

[0113] S8: Problem transformation: According to the upper bound and the lower bound expressions obtained in step S7, transform the original optimization problem into maximizing the upper bound and the lower bound of the average information transmission rate under the condition of ensuring the system concealment constraint.

[0114]

[0115] S9: Problem solving: According to equations (28) and (29), it can be known that the upper bound and the lower bound of the average information transmission rate are both monotonically increasing functions of P A . Therefore, the optimal value of P A at this time and and both achieve the maximum value, and the maximum values and are respectively:

[0116]

[0117] S10: Verify performance improvement: When the number of channel uses n approaches infinity, the upper and lower bounds of the average covert information transmission rate are independent of n. Therefore, after adding interference nodes, the asymptotic covert transmission rate is no longer zero but a positive value, realizing positive-rate covert optical information transmission.

[0118] The effectiveness of the present invention in improving the performance of covert VLC is further verified through Matlab simulation below.

[0119] Consider Figure 1 the covert VLC scenario shown. Without special instructions, set the noise power at Bob and the noise power at Willie to be both normalized to 1, and the photoelectric conversion factors r B and r W of the photodiodes at Bob and Willie are both 1, the channel gain h AW between Alice and Willie, the channel gain h AB between Alice and Bob, the channel gain h JW between Dave and Willie, and the channel gain hJB are all 1, i.e., h AW = h AB = h JW = h JB = 1, the dimming target ξ A has a value of 1, and the number of channel uses n is sufficiently large.

[0120] Figure 2 gives the minimum detection error probability ζ of Willie with or without the assistance of interfering nodes min versus the average optical power P of Alice A . It can be seen from the figure that when there is no interfering signal, ζ min is constantly 0, which means that when Alice communicates with any P A , Willie can detect the communication behavior between Alice and Bob without error; when Dave sends an interfering signal, as P A increases, ζ min gradually decreases from 1 to 0. When P A increases to more than 10 W, ζ min is constantly 0. Therefore, when Dave sends interference, a smaller P A can make ζ min sufficiently large. This shows that compared with the interference-free case, the addition of interfering signals can increase Willie's detection error probability, thereby increasing the interfering node can improve the concealment of Alice and Bob's communication.

[0121] Figure 3 shows that when Dave sends an interfering signal, under different average optical power P A conditions, the minimum detection error probability ζ of Willie min versus the maximum average optical power P of Dave Jmax . It can be seen from the figure that as P Jmax increases, ζ min is first fixed at zero, but when P Jmax increases to a certain value, ζ min begins to increase with the increase of P Jmax . This shows that when the maximum average optical power P of Dave Jmax is small, Willie can achieve error-free detection, and at this time, covert communication cannot be carried out. From the perspective of the two legitimate communication parties, the maximum average optical power P of Dave must be Jmax increased to a certain value so that Willie's detection error probability is large enough to achieve covert communication. In addition, according to Figure 3 it can also be seen that under the same P Jmax conditions, when the average optical power P of AliceA The larger, the minimum detection error probability ζ of Willie min The smaller. Therefore, when P Jmax is fixed, increasing P A will increase the probability that the communication behaviors of the legitimate parties are detected by Willie, thus degrading the covert performance of the VLC system.

[0122] Figure 4 Shows that Dave sends interference signals, h JW / h JB = 100, the maximum value of the lower bound of the average information transmission rate and the maximum value of the upper bound versus the change of the covert constraint value ε. It can be seen from the figure that as the covert constraint value ε increases, and both increase, indicating that the covert performance and communication performance of the system will affect each other. When the covert performance of the system is worse, the communication performance of the system is better. Therefore, in order to make the detection error probability of Willie large enough, it is necessary to sacrifice part of the communication performance of the system to maintain the covertness of the VLC system.

[0123] Figure 5 Shows that Dave sends interference signals, when the covert constraint value ε = 0.1, under different ratios h JW / h JB of the channel gains between Dave - Willie and Dave - Bob, the maximum value of the lower bound of the average information transmission rate and the maximum value of the upper bound versus the change of the maximum average optical power P Jmax of Dave. Jmax From the figure, it can be seen that when increasing P and both increase, indicating that increasing the maximum average optical power P Jmax of Dave is beneficial to the communication between Alice and Bob. However, when P Jmax increases to a certain value, and the change curves gradually flatten out, indicating that when P Jmax is large enough, further increasing P Jmax has little effect on improving the communication performance of the system. Therefore, in an actual system, when adding a jammer, it is necessary to reasonably set P Jmax to save resources. In addition, according to Figure 5 it can also be seen that as h JW / h JB increases, and both increase. This shows that when hJW / h JB The larger the and are non - zero positive values. Therefore, the average information transmission rate The maximum value of is no longer zero, but a positive value between , which proves that the addition of interference breaks the limit of the zero asymptotic rate of the covert VLC and realizes the covert optical information transmission with a positive rate.

[0124] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A jammer-assisted covert visible light communication performance improvement method, characterized in that: The following steps are involved: S1: Construct a covert visible light communication system including transmitter Alice, cooperative jammer Dave, legitimate receiver Bob and monitor Willie; and construct a channel gain model and signal constraint model; S2: The distribution of the useful signal transmitted by Alice and the interference signal transmitted by Dave is determined to be an exponential distribution, and the average optical power P of the interference signal is set to J Obey [0,P Jmax ] uniform distribution on ; S3: Considering the noise in the signal transmission process and the constructed channel gain model, determine the expression of Bob's received signal on the communication channel; Willie observes the use of the channel n times, makes detection judgments, and determines the expression of his received signal on the detection channel; S4: Willie determines the minimum detection error probability ζ according to the power detection criterion min , which is used as the evaluation index to characterize the Willie detection performance, and the concealment constraint ζ is constructed min ≥1-ε; S5: The average information transmission rate between Alice and Bob As an evaluation index of system communication performance; S6: Construct an optimization problem to maximize the average information transmission rate while ensuring the system's hidden constraints To obtain Alice's average optical power P A The optimal value of S7: Use mathematical methods to simplify the objective function and constraints of the optimization problem in step S6 to obtain the upper and lower bounds of the instantaneous information transmission rate R of the system; then, according to the distribution of the average optical power of the interference signal, obtain the average information transmission rate The upper bound of and lower bound , and simplify the implicit constraints; S8: Transform the original optimization problem into maximizing the upper bound of the average information transmission rate under the constraint of ensuring system concealment. and the lower bound S9: Exploitation and About P A The monotonicity relationship of P A The optimal value of as well as and The optimal value of and S10: Average hidden information transmission rate when the number of channel usage n approaches infinity The upper and lower bounds of are both positive values, realizing the positive rate of covert optical information transmission.

2. According to claim 1, a method for improving the performance of a jammer-assisted covert visible light communication is characterized in that: In step S1, the transmitter v, v=A represents Alice, v=J represents Dave, the receiver k, k=B represents Bob, k=W represents Willie, and the channel gain between the transmitter v and the receiver k is modeled as: Where m is the Lambertian radiation order; A r is the physical area of ​​the photodiode in the receiver; D vk , and ψ vk represent the distance from the transmitter v to the receiver k, the radiation exit angle and the radiation incident angle respectively; T s and g represent the gain of the optical filter and the gain of the optical concentrator respectively; Ψ represents the field of view of the photodiode in the receiver; the signal x sent by the transmitter v through the i-th (i=1,2,…,n) channel v,i The non-negativity and average optical power constraints are modeled as: Among them, E(·) represents the expectation operation, P v represents the average optical power of the light-emitting diode at the transmitter v, ξ A ∈(0,1] represents the dimming target at Alice, and the dimming target at Dave is a fixed value, that is, ξ J =1.

3. According to claim 1, a jammer-assisted covert visible light communication performance improvement method is characterized in that: In step S2, Alice sends a useful signal x through the i-th (i=1, 2, ..., n) channel. A,i and the interference signal x sent by Dave through the i-th channel J,i All obey exponential distribution, x A,i and x J,i The probability density functions can be expressed as: Among them, P A represents the average optical power of the useful signal sent by Alice, ξ A ∈(0,1] represents Alice’s dimming target, P J represents the average optical power of the interference signal sent by Dave, and P J Obey [0,P Jmax ] is uniformly distributed, P Jmax Indicates Dave’s maximum average optical power.

4. According to claim 1, a jammer-assisted covert visible light communication performance improvement method is characterized in that: In step S3, Bob and Willie receive the signal y through the i-th channel k,i Respectively expressed as: y B,i =r B h AB x A,i +r B h JB x J,i +n B,i ,i=1,2,…,n Among them, r k represents the photoelectric conversion factor of the photodiode at receiver k; It means that the mean value received by receiver k using the i-th channel is 0 and the variance is Gaussian white noise; H0 represents the null hypothesis, that is, Alice did not send information; H1 represents the alternative hypothesis, that is, Alice sent information.

5. According to claim 1, a jammer-assisted covert visible light communication performance improvement method is characterized in that: In the step S4, the following steps are specifically included: Clear signal independence: In the n-time channel usage, the symbols sent by Alice are independent of each other, and the transmission symbols and environmental noise are also independent of each other. In addition, since the channel gain of visible light communication obeys the Lambertian radiation model, the channel gain is also fixed, so the signals received by Willie are also independent of each other. Calculate the average electric power of the received signal: When the number of channel usages tends to infinity, according to the weak law of large numbers, the average electric power Ω of the Willie received signal is expressed as: Since the average optical power P of the jammer Dave J Obey [0,P Jmax ] is uniformly distributed, so the average electric power of the signal received by Willie is a randomly changing value; Determine the detection and judgment method: Willie makes judgments through power detection, which is expressed as: Wherein, τ represents the detection threshold set by Willie. When Ω>τ, Willie determines it as D1, that is, it determines that Alice has sent a signal; when Ω<τ, Willie determines it as D0, that is, it determines that Alice has not sent a signal; Analysis of the minimum detection error probability: Minimum detection error probability ζ min There are two situations: when P Jmax ≤h AW ξ A P A / h JW When Willie sets the detection threshold to Any value within the range can achieve the minimum detection error probability ζ min =0; when P Jmax >h AW ξ A P A / h JW When Willie sets the detection threshold to The minimum detection error probability ζ can be achieved min =1-h AW ξ A P A / (h JW P Jmax ).

6. According to claim 1, a jammer-assisted covert visible light communication performance improvement method is characterized in that: In step S5, the average information transmission rate It is expressed as: Among them, R represents the instantaneous information transmission rate of the system, P J and P Jmax are Dave’s average optical power and maximum average optical power respectively.

7. According to claim 1, a jammer-assisted covert visible light communication performance improvement method is characterized in that: In step S6, the optimization problem is modeled as:

8. According to claim 7, a jammer-assisted covert visible light communication performance improvement method is characterized in that: In step S7, the average information transmission rate The upper bound of and lower bound They are: Set Willie's detection threshold to The hidden constraint can be restated as:

9. According to claim 1, a method for improving the performance of a jammer-assisted covert visible light communication is characterized in that: In step S8, the converted optimization problem is expressed as: in, is the lower bound of the average information rate, is the upper bound of the average information rate.

10. The method for improving the performance of a jammer-assisted covert visible light communication according to claim 1, characterized in that: In step S9, the upper bound and the lower bound All about P A A monotonically increasing function, P A The optimal value is and The maximum value of and Respectively expressed as:

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