Joint optimization method for realizing average information age minimization in wireless covert communication

Abstract

The invention discloses a joint optimization method for realizing average information age minimization in wireless covert communication, and aims to improve the freshness of information transmitted from Alice to box and ensure the communication concealment. The joint optimization method comprises the following steps: modeling channels in wireless covert communication as wireless discrete time slot channels obeying independent quasi-static Rayleigh fading channels to obtain a communication system model; based on the model established in the system modeling, calculating a transmission interruption probability and an effective concealment rate in an information transmission process from the sending device to the full duplex receiver, and determining constraint conditions; minimizing the average information age at the full-duplex receiver as a target function, and determining constraint conditions according to the transmission outage probability and the concealment rate in the information transmission process from the sending device to the full-duplex receiver, the transmission block length, the transmitting power and the prior transmission probability in the information transmission process from the transmitting device to the full duplex receiver are optimized respectively.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of mobile communication technology, and in particular to a joint optimization method for minimizing average information age in wireless covert communication. Background Art

[0002] As an advanced wireless communication technology, a key part of the fifth generation (5G) and future sixth generation (6G) communication technology, wireless covert communication systems have attracted extensive attention and research. Due to the large number of mobile terminals accessing wireless transmission and the broadcast characteristics of wireless channels, information security transmission faces huge challenges. Although traditional encryption methods are effective in ensuring information security transmission, their high computational complexity and applicability to restricted devices in wireless systems are limited.

[0003] Covert communications are increasingly used in military communications, public security, medical privacy, smart transportation, and other fields, where information has high requirements for information freshness (i.e., information age). Information age refers to the time since the latest state update observed at the destination node was generated, that is, the younger the information age, the higher the information freshness.

[0004] Realizing covert communication without being detected by illegal users under the constraints of information age and ensuring the secure transmission of information are issues that need to be urgently addressed for the widespread application of covert communication. Summary of the invention

[0005] In order to overcome the above technical defects, an embodiment of the present application provides a joint optimization method for minimizing the average information age in wireless covert communication, and its specific scheme is as follows:

[0006] The joint optimization method is used in a short packet wireless communication system with a full-duplex receiver. The full-duplex receiver is equipped with a jammer antenna in addition to a single receiving antenna for transmitting artificial jammer noise. The power transmitted by the jammer antenna is the jammer power. The short packet wireless communication system also includes a transmitting device and a monitoring device.

[0007] The joint optimization method includes:

[0008] S1. System modeling: The channels in wireless covert communication are modeled as wireless discrete time slot channels that obey independent quasi-static Rayleigh fading channels to obtain the communication system model. Based on the established communication system model, the information transmission process from the sending device to the full-duplex receiver, the detection performance of the monitoring device, and the average information age at the full-duplex receiver are modeled respectively;

[0009] S2. Determine the constraint conditions: Based on the model established in the above system modeling, calculate the transmission interruption probability and effective concealment rate during the information transmission process from the sending device to the full-duplex receiver and determine the constraint conditions;

[0010] S3. Joint optimization: Minimizing the average information age at the full-duplex receiver is taken as the objective function, and the constraints are determined by the transmission interruption probability and concealment rate during the information transmission from the sending device to the full-duplex receiver. The transmission block length, transmission power and prior transmission probability during the information transmission from the sending device to the full-duplex receiver are optimized respectively.

[0011] Optionally, in a possible implementation manner, in S3, optimizing the transmission block length specifically includes:

[0012] Under given transmission power, interference power and prior transmission probability, the optimization problem of minimizing the average information age is solved to obtain the optimal transmission block length:

[0013] n2 is the root of f′(n)=0, n up The upper limit of the block length.

[0014] Optionally, in a possible implementation manner, in S3, optimizing the transmit power specifically includes:

[0015] For a given transmission block length, interference power and prior transmission probability, the optimization problem of minimizing the average information age is solved to obtain the optimal transmission power:

[0016] Where D is the amount of information contained in a short data packet, in units of nat, n is the block length, ε is the concealment constraint, Pb is the transmit power at the full-duplex receiver, |Hij|2 is the channel gain, λ1 is the prior transmission probability at the transmitter, λ0=1-λ1, σ2 is the variance of the Gaussian distribution, α and η are respectively the algebraic, and

[0017] Optionally, in a possible implementation manner, in S3, optimizing the priori transmission probability specifically includes:

[0018] For a given transmit power, interference power and transmission block length, the optimization problem of minimizing the average information age is solved to obtain the highest a priori transmission probability:

[0019] Where n is the block length, ε is the hidden constraint, is algebraic,

[0020] Optionally, in a possible implementation, in S1, the channels in the wireless covert communication include the channels corresponding to the wireless link from the transmitting device to the full-duplex receiver, the wireless link from the transmitting device to the monitoring device, the wireless link from the full-duplex receiver to the monitoring device, and the wireless link in which the full-duplex receiver generates artificial noise through an antenna.

[0021] Optionally, in a possible implementation manner, in S1, modeling the information transmission process from the sending device to the full-duplex receiver specifically includes:

[0022] The message received by the full-duplex receiver, the observation signal monitored by the monitoring device and the signal-to-interference-noise ratio of the full-duplex receiver during the information transmission process from the sending device to the full-duplex receiver are calculated.

[0023] Optionally, in a possible implementation, in S1, the detection performance of the monitoring device is modeled specifically through the total detection probability and concealment constraint at the monitoring device willie, the total detection probability is determined by the false alarm probability and the missed detection probability, and the concealment constraint is determined using the generalized bound of the total variation distance.

[0024] Optionally, in a possible implementation, in S1, the expression of the average information age is:

[0025] Where λ1 is the a priori transmission probability at the sending device, n is the block length, Pcop is the outage probability, Pbe is the packet error probability, and W is the system bandwidth.

[0026] Optionally, in a possible implementation, the hidden constraint is expressed as P cop ≤∈, where P cop represents the probability of covert communication interruption, that is, the probability of not satisfying the concealment constraint; P cop The upper bound of is:

[0027] λ1 is the a priori transmission probability at the transmitting device, λ0=1-λ1, n is the block length, is algebraic,

[0028] For a given transmission rate R, the effective concealment rate C is expressed as: C = λ1WR(1-P cop )(1-P be ). λ1 is the a priori transmission probability at the transmitting device, Pcop is the outage probability, Pbe is the packet error probability, and W is the system bandwidth.

[0029] Optionally, in a possible implementation manner, the total detection probability is recorded as P WE , its expression is: WE=λ0P FA +λ1P MD , where P FA is the false alarm probability, P MD is the missed detection probability, λ1 is the prior transmission probability at the sending device, and λ0=1-λ1.

[0030] The above technical solution can achieve the following technical effects in the embodiments of the present application:

[0031] (1) High-level secure communication: The present invention provides a higher-level secure communication method, which makes it difficult for a third party to detect the existence of the communication behavior itself through signal hiding and camouflage technology of covert communication, so it is impossible to decrypt the intercepted information. This transmission method of protecting sensitive information and confidential data is particularly suitable for scenarios such as military and security fields that have strict requirements for the transmission of sensitive information.

[0032] (2) Improving the freshness of information: The present invention utilizes the characteristics of short packet communication and optimizes the block length to minimize the average information age of the communication, thereby improving the timeliness of communication.

[0033] (3) Flexible use of full-duplex receiver: The present invention utilizes the characteristics of the full-duplex receiver, uses the artificial noise generated to interfere with the detection of the eavesdropper Willie, and uses the self-interference elimination technology to reduce the impact on the received signal itself. This allows the communication signal to be optimized in a complex environment and improves the concealment of the transmission.

[0034] In summary, the advantages of the present invention include high-level secure communication, improved information freshness, and flexible use of full-duplex receivers, which has brought important technological breakthroughs to the field of modern communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The accompanying drawings exemplarily illustrate the embodiments and constitute a part of the specification, and together with the text description of the specification, are used to explain the exemplary implementation of the embodiments. The embodiments shown are for illustrative purposes only and do not limit the scope of the claims. In all drawings, the same reference numerals refer to similar but not necessarily identical elements.

[0036] Figure 1 A schematic diagram of a system architecture for wireless covert communication in this application;

[0037] Figure 2 A flowchart of a joint optimization method for minimizing the average information age in wireless covert communications;

[0038] Figure 3 This is a comparison chart of the average hidden information age changing with the transmission block length n in three situations in this application;

[0039] Figure 4 is the average hidden information age in the three cases in this application. ab | 2 Change comparison chart;

[0040] Figure 5 This is a comparison diagram of the average hidden information age changing with the transmitting power Pa of the transmitting end in three cases in this application;

[0041] Figure 6 This is a comparison diagram of the effective concealment rate C changing with the transmission block length n in three cases in this application;

[0042] Figure 7 Here is the maximum effective concealment rate C with the maximum block length n in three cases in this application: max Change comparison chart;

[0043] Figure 8 This is a comparison diagram of the effective concealment rate C changing with the prior transmission probability λ1 in three cases in this application;

[0044] Fig. 9 The maximum effective concealment rate C in three cases in this application varies with the prior transmission probability Change comparison chart;

[0045] Fig.10 This is a comparison diagram of the average effective concealment rate C versus the transmitting end power Pa in three cases in this application;

[0046] Fig.11 The maximum effective concealment rate C in three cases in this application varies with the maximum transmitting end transmission power Change comparison chart;

[0047] Fig.12 The maximum effective concealment rate C in three cases in this application varies with the maximum receiving end transmission power Change comparison chart. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.

[0049] It should be noted that the descriptions involving "first", "second", etc. in the embodiments of the present application are only for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by this application.

[0050] In the description of the present application, it should be understood that the numerical labels before the steps do not indicate the order in which the steps are executed, but are only used to facilitate the description of the present application and to distinguish each step, and therefore should not be understood as a limitation on the present application.

[0051] First, the following terms are explained:

[0052] Information age CAoI: refers to the time elapsed since the latest state update observed at the destination node was generated. In other words, the younger the information age, the higher the information freshness;

[0053] Signal-to-interference-plus-noise ratio (SINR): refers to the ratio of the strength of the received useful signal to the strength of the received interference signal (noise and interference);

[0054] Additive White Gaussian Noise (AWGN): It is the most basic noise and interference model. Its amplitude distribution obeys Gaussian distribution, while its power spectrum density is uniformly distributed.

[0055] Secondly, in order to facilitate those skilled in the art to understand the technical solutions provided in the embodiments of the present application, the relevant technologies are described below:

[0056] The technical solution of the present application is applicable to wireless covert communication, specifically to a system for implementing covert communication by assisting the detection of an eavesdropper (Willie) through artificial noise generated by a full-duplex receiver in short packet covert communication based on wireless transmission.

[0057] like Figure 1 As shown in Figure 1, the system model includes: a legitimate user (i.e., a sending device), an eavesdropper (i.e., a monitoring device), and a full-duplex receiver, a total of three system units. Figure 1 Alice is shown in the figure, and the monitoring device is Figure 1 As shown in Willie, the full-duplex receiver is Figure 1 Bob shown in .

[0058] Figure 1 It is also shown that the three system units are connected by four wireless links, namely: the wireless link from the legitimate user Alice to the full-duplex receiver Bob, denoted by H ab (Right now Figure 1 H shown in ar ), the wireless link from the legitimate user alice to the monitoring device willie, denoted as H aw (, the wireless link from the full-duplex receiver Bob to the monitoring device Willie is denoted by H bw , and Bob generates artificial noise through the wireless link antenna, denoted by H bb (Right now Figure 1 H shown in rr ).

[0059] In this system model, Alice wants to send confidential information to Bob in a hidden way, while Willie tries to monitor whether Alice is transmitting confidential information to Bob. At the same time, the artificial noise generated by the full-duplex receiver Bob interferes with Willie's detection.

[0060] In order to achieve timely information transmission under the condition of ensuring communication security, the present application provides a short packet covert communication information age scheme for a wireless transmission system based on a full-duplex receiver in wireless communication. Among them, the transmitter attempts to hide its transmission to the full-duplex receiver, and the listening device will detect this covert transmission. Specifically, under the condition of fading channel, we characterize the freshness of the state information by the closed form of the average age of covert information (CAoI), and by jointly optimizing the user's transmit power, the power at the full-duplex receiver, and the packet length and prior transmission probability of the information transmission, we can solve the proposed short packet covert communication average information age minimization problem while meeting the concealment requirements and ensuring the normal communication between cellular mobile users and base stations.

[0061] Specifically, the present application discloses a joint optimization method for minimizing the average information age in wireless covert communication while ensuring covert communication of mobile users in a wireless transmission system. The method is applicable to a short packet wireless communication system with a full-duplex receiver. In addition to a single receiving antenna, the full-duplex receiver is also deployed with an interference antenna for sending artificial interference noise. The power emitted by the interference antenna is the interference power of the receiving end. The short packet wireless communication system also includes a sending device and a monitoring device.

[0062] The above joint optimization method includes the following steps:

[0063] S1. System modeling: The channels in wireless covert communication are modeled as wireless discrete time slot channels obeying independent quasi-static Rayleigh fading channels to obtain the communication system model; and based on the established communication system model, the information transmission process from the sending device to the full-duplex receiver, the detection performance of the monitoring device and the average information age at the full-duplex receiver Bob are modeled respectively.

[0064] The details are as follows:

[0065] S1.1. Model all channels in wireless covert communication as wireless discrete time slot channels obeying independent quasi-static Rayleigh fading channels to obtain the communication system model.

[0066] The channels in wireless covert communication include the channels corresponding to the wireless link from the transmitting device to the full-duplex receiver, the wireless link from the transmitting device to the monitoring device, the wireless link from the full-duplex receiver to the monitoring device, and the wireless link in which the full-duplex receiver generates artificial noise through the antenna.

[0067] Specifically, the above channel is: the wireless link H from the legitimate user Alice to the full-duplex receiver Bob ab , the wireless link H from the legitimate user alice to the monitoring device willie aw , the wireless link H from the full-duplex receiver Bob to the monitoring device Willie bw , and the full-duplex receiver Bob generates artificial noise through the antenna wireless link H bb The corresponding channels. Wireless link H rr It can also be called a self-interference channel.

[0068] like Figure 1 As shown, the sender (Alice) tries to secretly send a message to the FD receiver (Bob) under the supervision of the monitor (Willie), who is detecting whether Alice is communicating with Bob. Assume that Alice and Willie are each equipped with an antenna, and in addition to the single receiving antenna, Bob also uses an additional antenna to transmit an (artificial noise), which may introduce uncertainty to Willie. We consider that each channel is modeled as a wireless discrete time slot channel, subject to an independent quasi-static Rayleigh fading channel. Each time slot contains N channels used, where N is large enough (N→∞). This means that the channel gain remains unchanged within a transmission period and changes independently from one transmission period to another. The channel between any two nodes i and j is denoted as H ij, the channels from alice to Bob, alice to willie, and Bob to willie are denoted by ab, aw, and bw, respectively. The self-interference channel is denoted by bb, which is also modeled as a Rayleigh fading channel. In order to ensure the confidentiality and timeliness of communication at the same time, we assume that Alice transmits a short data packet containing D nats information in each time slot with a priori transmission probability λ0. Alice encodes her hidden message M into a codeword x=(x (1) , ..., x (n) ) and sends it to the channel. Bob receives y = (y (1) , ..., y (n) ), and restore the message to M. x (n) Indicates the information carried by the nth channel. Willie observes y = (y (1) , ..., y (n) , and perform statistical hypothesis testing to determine whether Alice is active. The null hypothesis H0 indicates that Alice is not active, while the alternative hypothesis H1 indicates that Alice is active. In this paper, we assume that Bob works in full-duplex mode, so he continuously transmits a signal v = (v (1) , ..., v (n) ) Even when receiving signals, we assume that the wireless channel is subject to independent quasi-static Rayleigh fading, where the channel coefficient n remains constant within a communication time slot used by the channel and varies independently between different time slots. Represents the variance of the Gaussian white noise power received by i, and is expressed as It represents the variance of Gaussian white noise power on the wireless channel from i to j.

[0069] S1.2. Based on the established communication system model, the information transmission process from the legitimate user Alice to the full-duplex receiver Bob is modeled.

[0070] Specifically, modeling the above information transmission process specifically involves calculating the message received by the full-duplex receiver Bob, the observation signal monitored by the monitoring device Willie, and the signal-to-interference-noise ratio of the full-duplex receiver Bob during the information transmission process from the legitimate user Alice to the full-duplex receiver Bob.

[0071] Specifically, the transmission powers of Alice and Bob are defined as: P a and P b , when Alice sends a signal, according to the communication system model, the signal y received by Bob in any time slot m b (t), which is expressed as follows:

[0072]

[0073] Where φ∈[0,1] is the self-interference cancellation coefficient, φ=0 corresponds to complete self-interference cancellation, and φ=1 corresponds to no self-interference cancellation. The transmit power is represented by Pa, and the artificial noise (AN) power is represented by Pb. t=1,..,n means using more than n channels, Indicates n b (Channel coefficient) obeys AWGN (adding Gaussian white noise to the channel on the signal), its mean is 0 and its variance is

[0074] Willie's observation signal is shown in formula (3) below.

[0075] According to formula (1), the signal-to-interference-noise ratio γ of the signal received at Bob is obtained b for:

[0076]

[0077] S1.3. Based on the established communication system model, the detection performance of the monitoring device willie is modeled.

[0078] Specifically, the detection performance is modeled by the total detection probability and the concealment constraint at the monitoring device willie. The total detection probability is determined by the false alarm probability and the missed detection probability, and the concealment constraint is determined using the generalized bound of the total variation distance.

[0079] Specifically, when Alice sends a signal, the signal detected by Willie in any time slot m can be expressed by formula (3):

[0080] Where n w (t) represents the Gaussian white noise received by willlie in any time slot m, Indicates n w It obeys AWGN, its mean is 0 and its variance is When H0 is true (A is inactive), willie receives power P b , the interference signal from Bob, and Gaussian white noise. When H1 is true, willie receives a signal with a power of P a , the signal and power sent from Alice is P b , the interference signal sent from bob, and Gaussian white noise.

[0081] Furthermore, P0 and P1 are used to represent the probability distribution of Willie channel observations under H0 and H1, respectively. In order to determine the probability of detection error in Willie, we define two types of errors in covert communication, namely false alarm and missed detection. The former means that Willie makes a decision in favor of H1, while H0 is true; the latter means that Willie makes a decision in favor of H0, while H1 is true. The false alarm probability and missed detection probability are respectively denoted by P FA and P MD Then, determine the total detection probability P at Willie WE for:

[0082] P WE =λ0P FA +λ1P MD (4), where λ1 is the prior transmission probability at Alice, and λ0 = 1-λ1.

[0083] In this application, a generalized bound of the total variation distance is used to ensure the implicitness constraint, and then the total detection probability P WE Can be transformed into: P WE ≥maxλ0,λ1-minλ0,λ1V(P0,P1)≥1-∈(5), where V(P0,P1) is the total distance between P0 and P1.

[0084] According to Pinsker's inequality, the relative entropy D(P0||P1) between P0 and P1 can be expressed as:

[0085] Furthermore, according to the above equations (5) and (6), it can be deduced that:

[0086]

[0087] Moreover, the relative entropy D(P0||P1) between P0 and P1 can be transformed into:

[0088] Where X is the support set of P1(x), P0(x) and P0(x) are the densities of p0 and p1 respectively. Equation (7) is the concealment requirement or the concealment constraint.

[0089] Furthermore, we need to derive the relative entropy D(P0||P1) between P0 and P1 based on equation (7). Specifically, we first need to derive the probability density functions P0(x) and P1(x) of the symbols received at Willie when Alice does not send or sends the signal. Assume that the signals received at Willie in equations (7) and (8) correspond to the cases where H0 is true and H1 is true, respectively, and have a mean of zero and a variance of and Rayleigh distribution, then P0(x) and P1(x) are:

[0090]

[0091] and,

[0092] Substituting (9) and (10) into (8), we obtain:

[0093] In the formula, To make the optimization problem (13) mathematically tractable, we adopt the following approximation. When x approaches 0, ln(1+x)~x. In covert communication, the transmission power is usually small, which leads to a low signal-to-noise ratio. Therefore, the stealth constraint can be simplified to:

[0094] Finally, the detection performance of Willie can be determined based on the calculated total detection probability and concealment constraint. The total detection probability here refers to the total detection error probability of the monitoring device willie. The higher the probability, the smaller the possibility of monitoring and the higher the security. The constraint condition is equal to (1-total detection error probability).

[0095] S1.4. Based on the established communication system model, the average information age, i.e., average CAoI, at the full-duplex receiver Bob is modeled.

[0096] Among them, the average CAoI at the full-duplex receiver Bob is a key indicator for evaluating the freshness and concealment of information during the information transmission process from the legitimate user Alice to the full-duplex receiver Bob.

[0097] Specifically, in any time slot of the transmission phase, Alice needs to send the newly generated state information to Bob for timely status update. However, in order to achieve covert communication, Alice transmits the state information with a certain probability. Among them, CAoI is a key indicator for evaluating the freshness and concealment of information. In this case, some state information generated by Alice cannot be delivered to Bob in time, which is equivalent to adding a generation rate limit to the state information at Alie. In addition, for the timeliness of communication, we do not consider the retransmission mechanism. Therefore, due to the influence of decoding failure, Bob may not be able to successfully receive the state update. Therefore, we define valid state information to characterize the state information transmitted by Alice and successfully decoded by Bob. During the transmission of state information, each state information carries a generation timestamp. CAoI is defined as the time elapsed since the latest valid state information was generated. Let the latest valid state information received by Bob at time τ be the kth valid state information, which he received at time a kThe instantaneous Δ(τ) is: Δ(τ) = τ-a k (12).

[0098] CAoI increases linearly with time, and when Bob receives new valid state information, it will be reset to the age of the current valid state information. Figure 2 As shown in , we consider an example of CAoI evolving over time. When Alice does not send state information (i.e., null state information) or Alice sends state information but Bob fails to decode it (i.e., wrong state information), the CAoI curve increases linearly over time until Bob successfully receives valid state information. We define the generation time and reception time of the kth valid state information as a k and a k The residence time of the kth valid state information can be expressed as U k =a k -a k , which is fixed and equal to the original age of the valid data packet at Bob, that is, ( U k=T). Due to the control of the transmission probability and the failure of decoding the state information, there may be multiple time slots (denoted by N) between the consecutive valid state information received by bob. k represents the time interval between when Bob receives the (k-1)th and kth valid status information, that is, N k =a′ k -a′ k-1 For the time interval (0, τ), the average CAoI is: From formula (13), we can see that the average CAoI is equal to the area under the CAoI curve divided by the total time. k-1 and a k The shaded area between is denoted as Sk, therefore, the average CAoI can be expressed as:

[0099] Where K(T) represents the number of valid status messages received by bob in the time interval (0, T); E(S) represents the number of valid status messages received by S in the time interval (0, T). k The average value of It can be understood as the average arrival rate of valid state information at Bob. Therefore, the average CAoI can be transformed into:

[0100] S2. Determine the constraint conditions: Based on the model established in the above system modeling, calculate the transmission interruption probability and effective concealment rate during the information transmission process from the legitimate user Alice to the full-duplex receiver Bob.

[0101] Specifically, the packet error probability is calculated for a given transmission rate R, where δ is the decoding error probability. For a fixed R, the decoding error probability P be for:

[0102] Where, the SINR at Bob is given by equation (2) above, and the Q function is:

[0103] According to (13), (14) and (15), the approximate value of the packet error probability f(x) can be derived as follows:

[0104]

[0105] The hidden constraint can also be expressed as P cop ≤∈, where P cop represents the probability of covert communication interruption, that is, the probability of not satisfying the concealment constraint. P can be obtained by formula (6): cop The upper bound of is:

[0106] For a given transmission rate R (R = D / n), the effective concealment rate C can be expressed as: C = λ1WR (1-P cop )(1-P be )(20).

[0107] The purpose of this application is to improve the freshness of information transmitted from Alice to Bob while ensuring its communication concealment. Specifically, we first formulate the optimization problem of minimizing information age by optimizing the transmission probability and transmission power of state information and the burst length. Then, in order to solve this optimization problem, we design an effective transmission scheme as follows:

[0108] S3, joint optimization: Minimize the average information age at the full-duplex receiver Bob as the objective function, determine the constraints based on the transmission interruption probability and effective concealment rate during the information transmission from the legitimate user Alice to the full-duplex receiver Bob, and respectively optimize the transmission block length n and the transmission power P during the information transmission from the legitimate user Alice to the full-duplex receiver Bob. a and the prior transmission probability λ1 are optimized.

[0109] First, the above optimization of the transmission block length n specifically includes: for a given transmission power P a , interference power P b Under the condition of prior transmission probability λ1, the optimization problem of minimizing the average CAoI is solved to obtain the optimal transmission block length n * for: Where n2 is the root of f′(n)=0, n upThe upper limit of the block length.

[0110] Specifically, we first consider the significant impact of block length on the average CAoI, because it largely determines the probability of packet error, communication delay, and the probability of covert communication interruption. In this paper, we only consider 0≤P be ≤1, for a given transmit power P a Interference power P b The objective function f(n) of the optimization problem of minimizing the average CAoI with the prior transmission probability λ1 can be expressed as:

[0111] The constraints C1, C2 and C3 are:

[0112] C1:

[0113] C2:

[0114] Taking the derivative of the function f(n), that is, f′(n)=0, we can get two roots n1 and n2:

[0115]

[0116] and,

[0117] Based on constraints C1, C2 and C3, the transport block length n is restricted to a region n low ≤n≤n up , where n low is the lower limit of block length, n up is the upper limit of the block length, and its values ​​are:

[0118] and,

[0119]

[0120] We can further deduce the optimal transmission block length n in this case: * for:

[0121] Secondly, the above transmission power P a The optimization specifically includes: for a given transmission block length n, interference power P b Under the condition of prior transmission probability λ1, the optimization problem of minimizing the average CAoI is solved to obtain the optimal transmission power for:

[0122] Specifically, the larger the transmit power P aThis can ensure a low probability of packet error, but it will also lead to a high probability of covert communication interruption. For a given transmission block length n, interference power P b The objective function f(P a ) can be expressed as:

[0123] Its constraints C4, C5 and C6 are:

[0124] C4:

[0125] C5: 0<P a <P max ,

[0126] C6: Here Because f(P a )>0, so the optimal transmission power can be obtained for:

[0127]

[0128] Finally, the above optimization of the prior transmission probability λ1 specifically includes: for a given transmission power P a , interference power P b In the case of transmission block length n, the optimization problem of minimizing the average CAoI is solved to obtain the highest priority transmission probability for:

[0129]

[0130] Specifically, a higher prior transmission probability λ1 allows Alice to send more packets to Bob in a timely manner, but this makes it difficult to meet the concealment constraint. Therefore, there is an optimal prior transmission probability λ that minimizes the age of the hidden information. For a given transmission power P a , interference power P b The objective function f(λ1) of the optimization problem of minimizing the average CAoI under the condition of and transport block length n can be expressed as:

[0131] Its constraints C7 and C8 are:

[0132] C7:

[0133] C8:n min <n<n max n∈N + , the highest priority transmission probability can be obtained by calculation for:

[0134]

[0135] In order to facilitate those skilled in the art to understand the specific implementation of the present invention, the following embodiments and numerical results are provided to explore the influence of various system parameters on the age of hidden information. The minimum age of hidden information can be determined according to the optimization problems of equations (22), (24), and (26). The three cases described below correspond to the above three optimization problems respectively. Without affecting the generality, we set the transmission power of Alice and the interference power at Bob to 1mw, and the values ​​of other parameters are all 1 for the channel gain.

[0136] Let: W=1MHZ, D=10nats, σ b =σ w =σ a =0dbm, L max =1000,L min =100. The simulation results are explained as follows:

[0137] Figure 3 The results are consistent with correctness, and the optimal fast length strikes a balance between the concealment and timeliness of information. As shown in the figure, the block length has a positive impact on the average information age, and we can see that the smaller the block length, the better. This is because as the fast length increases, the probability of packet error decreases. At this time, the probability of packet error dominates, and the average information age decreases. When the fast length is greater than a certain value, the fast length dominates, and the average information age increases. So there is an optimal value.

[0138] Figure 4 The results are consistent with the correctness. As the channel gain from Alice to Bob increases, the average information age decreases. This is because as the channel gain increases, the channel enhancement experienced by the signal during transmission from the transmitter to the receiver decreases, so the average information age decreases. And we see that under the same channel gain, as the prior transmission probability increases, the average information age decreases.

[0139] Figure 5 The results are consistent with the correctness. As Alice's transmission power increases, the average information age decreases. This is because the transmission power increases, the signal is enhanced, and the information is updated in a faster manner, which leads to a decrease in the average information age. And we see that under the same transmission power, as the prior transmission probability increases, the average information age decreases. Figure 5Although the transmitting power Pa of the transmitter has a negative impact on the average information age, this is due to self-interference. We use self-interference technology. As the self-interference elimination coefficient decreases, the negative impact of power on the average information age becomes smaller and smaller, and can be almost ignored. Moreover, as the transmitting power Pa of the transmitter increases, the total detection error probability also increases, which improves the concealment of communication and helps to balance the timeliness and concealment of messages.

[0140] Figure 6 It summarizes how the effective concealment rate C changes with the block length under the conditions of Pa = 2 mW, Pb = 2 mW, and λ1 = 0.5. It can be observed from the figure that it increases with the increase of block length. The reason can be explained as follows: the effective concealment rate C is an increasing function of the block length. In addition, under the same block length, as the concealment constraint δ increases, the effective concealment rate C increases. Because the average CAoI is a decreasing function of the prior transmission probability. The effect of block length on CAoI is that it first decreases and then increases. At this time, the optimal block length that minimizes the average CAoI is not necessarily equal to the optimal block length that maximizes the effective transmission rate C.

[0141] Figure 7 In Settings The variation of the maximum effective concealment rate C with the maximum block length is summarized under the condition of . It can be observed from the figure that as the maximum block length increases, the maximum effective concealment rate C increases first, and then remains unchanged after reaching a certain value. The reason can be explained as follows: the effective concealment rate C increases with the increase of the block length, and as the maximum block length increases, the optimal block length is equal to the maximum block length, resulting in an increase in the effective concealment rate C. However, when the block length increases to a certain value, the further increase of the block length cannot meet the information freshness. Therefore, when the maximum block length increases further, the optimal block length remains unchanged. It is worth noting that when the concealment constraint is very small, in order to meet the information freshness, the transmitter needs to use a larger transmission power at a very small block length. However, this may lead to a decrease in concealment, so that the concealment constraint cannot be met. As a result, the maximum effective concealment rate C becomes a constant 0. Under the same maximum block length, as the concealment constraint increases, the optimal transmitter power may be larger, resulting in a greater maximum concealment energy efficiency.

[0142] Figure 8It summarizes how the effective concealment rate C varies with the prior transmission probability under the setting of Pa = 2 mW, Pb = 2 mW, and n = 100. It can be observed from the figure that it increases with the increase of the prior transmission probability. The reason can be explained as follows: the effective concealment rate C is an increasing function of the prior transmission probability. In addition, under the same prior transmission probability, as the concealment constraint δ increases, the effective concealment rate C increases. Because the average CAoI is a decreasing function of the prior transmission probability. The highest a priori transmission probability that minimizes the average CAoI is equal to the highest a priori transmission probability that maximizes the effective transmission rate C. Fig. 9 In Settings 0<n<n max How does the maximum effective concealment rate C change with the change of the maximum prior transmission probability under the condition of . It can be observed from the figure that as the prior transmission probability increases, C first increases, and then remains unchanged after reaching a certain value. The reason can be explained as follows: the concealment rate C is an increasing function of the prior transmission probability. As the prior transmission probability increases, the maximum prior transmission probability is equal to the maximum prior transmission probability, resulting in an increase in the effective concealment rate C. However, in order to ensure the concealment requirement, when the maximum prior transmission probability increases further, the optimal prior transmission probability remains unchanged. Under the same prior transmission probability, as the concealment constraint increases, the optimal prior transmission probability can become larger, resulting in an increase in the maximum effective concealment rate C.

[0143] Fig.10 It summarizes how the effective concealment rate C changes with the transmitter transmit power Pa under the conditions of λ1=0.5, Pb=2 mW, and n=100. It can be observed from the figure that it increases with the increase of the transmitter transmit power Pa. The reason can be explained as follows: the effective concealment rate C is an increasing function of the transmitter transmit power. In addition, under the same transmitter transmit power Pa, the effective concealment rate C increases with the increase of the concealment constraint δ. Because the average CAoI is a decreasing function of the prior transmission probability. The optimal transmitter transmit power Pa that minimizes the average CAoI is equal to the optimal transmitter transmit power Pa that maximizes the effective transmission rate C.

[0144] Fig.11 In Settings 0<n<n maxIt summarizes how the maximum effective concealment rate C changes with the change of the maximum transmitter transmit power under the condition of . It can be observed from the figure that as the maximum transmitter transmit power increases, the maximum effective concealment rate C first increases, and then remains unchanged after reaching a certain value. The reason can be explained as follows: the effective concealment rate C is an increasing function of the transmitter transmission power. As the maximum transmitter transmit power increases, the optimal transmitter transmit power is equal to the maximum transmitter transmit power, resulting in an increase in the maximum effective concealment rate C. However, to ensure the concealment requirement, when the maximum transmitter transmit power is further increased, the optimal transmitter transmit power remains unchanged. Under the same maximum transmitter transmit power, as the concealment constraint increases, the maximum priority transmission power may be larger, while the receiver's transmit power may be smaller, resulting in a larger maximum effective concealment rate C.

[0145] Fig.12 In Settings 0<n<n max The maximum effective concealment rate C is summarized as a function of the maximum receiver transmit power under the condition of . It can be observed from the figure that as the maximum receiver transmit power increases, the maximum effective concealment rate C is zero at first and then remains constant after reaching a certain value. This can be explained by the fact that when the concealment constraint is low, a higher receiver transmit power is required to meet the higher concealment requirement. Therefore, when the maximum receiver transmit power is low, it cannot meet the concealment requirement, resulting in the effective concealment rate C being zero. As the maximum receiver transmit power increases, the optimal receiver transmit power is equal to the maximum receiver transmit power when the concealment requirement is met, resulting in an increase in the maximum effective concealment rate C. When the maximum receiver transmit power increases further, since the receiver transmit power is a decreasing function of the effective concealment rate C, the optimal receiver transmit power is equal to a constant, resulting in a constant maximum effective concealment rate C. Under the same maximum receiver transmit power, as the concealment constraint increases, the optimal a priori transmission probability and transmitter transmit power may be larger, while the optimal receiver transmit power may be smaller, resulting in a larger maximum effective concealment rate C.

[0146] Obviously, those skilled in the art should understand that the modules or steps of the above-mentioned embodiments of the present application can be implemented by general-purpose computer devices, they can be concentrated on a single computer device, or distributed on a network composed of multiple computer devices, optionally, they can be implemented by executable program codes of computer devices, so that they can be stored in a storage device and executed by the computer device, and in some cases, the steps shown or described can be executed in a different order from that herein, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. In this way, the embodiments of the present application are not limited to any specific combination of hardware and software.

[0147] It should be noted that the above are only preferred embodiments of the present application, and the patent protection scope of the present application is not limited thereto. Any equivalent structure or equivalent process transformation made using the contents of the specification and drawings of the present application, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A joint optimization method for minimizing the average information age in wireless covert communication, characterized in that: The joint optimization method is used in a short packet wireless communication system with a full-duplex receiver, wherein the full-duplex receiver is equipped with an interference antenna in addition to a single receiving antenna, for transmitting artificial interference noise, and the power transmitted by the interference antenna is interference power, and the short packet wireless communication system also includes a transmitting device and a monitoring device; The joint optimization method comprises: S1. System modeling: The channels in wireless covert communication are modeled as wireless discrete time slot channels obeying independent quasi-static Rayleigh fading channels to obtain the communication system model. Based on the established communication system model, the information transmission process from the sending device to the full-duplex receiver, the detection performance of the monitoring device and the average information age at the full-duplex receiver are modeled respectively. S2. Determination of constraints: Based on the model established in the above system modeling, the transmission interruption probability and effective concealment rate in the information transmission process from the sending device to the full-duplex receiver are calculated and the constraint conditions are determined; S3, Joint Optimization: The objective function is to minimize the average information age at the full-duplex receiver, and the constraints are determined by the transmission interruption probability and concealment rate during the information transmission process from the sending device to the full-duplex receiver. The transmission block length, transmission power and prior transmission probability during the information transmission process from the sending device to the full-duplex receiver are optimized respectively.

2. The joint optimization method according to claim 1, characterized in that: In S3, the optimization of the transmission block length specifically includes: Under given transmission power, interference power and prior transmission probability, the optimization problem of minimizing the average information age is solved to obtain the optimal transmission block length n * for: Where n2 is the root of f′(n)=0, n up The upper limit of the block length.

3. The joint optimization method according to claim 1, characterized in that: In S3, the optimization of transmit power specifically includes: Given a transmission block length, interference power, and prior transmission probability, the optimization problem of minimizing the average information age is solved to obtain the optimal transmission power. for: Where D is the amount of information contained in a short data packet, in units of nat, n is the block length, ε is the concealment constraint, Pb is the transmit power at the full-duplex receiver, |H ij | 2 is the channel gain, λ1 is the a priori transmission probability at the transmitting device, λ0=1-λ1, σ 2 is the variance of the Gaussian distribution, α and η are respectively the algebraic and 4. The joint optimization method according to claim 1, characterized in that: In S3, the optimization of the prior transmission probability specifically includes: Given the transmission power, interference power and transmission block length, the optimization problem of minimizing the average information age is solved to obtain the highest a priori transmission probability. for: Where n is the block length, ε is the hidden constraint, is algebraic, 5. The joint optimization method according to claim 1, characterized in that: In S1, the channels in the wireless covert communication include the channels corresponding to the wireless link from the transmitting device to the full-duplex receiver, the wireless link from the transmitting device to the monitoring device, the wireless link from the full-duplex receiver to the monitoring device, and the wireless link in which the full-duplex receiver generates artificial noise through the antenna.

6. The joint optimization method according to claim 1, characterized in that: In S1, the information transmission process from the sending device to the full-duplex receiver is modeled specifically including: The message received by the full-duplex receiver, the observation signal monitored by the monitoring device and the signal-to-interference-noise ratio of the full-duplex receiver during the information transmission process from the sending device to the full-duplex receiver are calculated.

7. The joint optimization method according to claim 1, characterized in that: In S1, the detection performance of the monitoring device is modeled by the total detection probability and the concealment constraint at the monitoring device willie. The total detection probability is determined by the false alarm probability and the missed detection probability, and the concealment constraint is determined using the generalized bound of the total variation distance.

8. The joint optimization method according to claim 1, characterized in that: In S1, the expression of average information age is: Where λ1 is the a priori transmission probability at the sending device, n is the block length, Pcop is the outage probability, Pbe is the packet error probability, and W is the system bandwidth.

9. The joint optimization method according to claim 7, characterized in that: The hidden constraint is expressed as P cop ≤∈, where P cop represents the probability of covert communication interruption, that is, the probability of not satisfying the concealment constraint; P cop The upper bound of is: λ1 is the a priori transmission probability at the transmitting device, λ0=1-λ1, n is the block length, is algebraic, For a given transmission rate R, the effective concealment rate C is expressed as: C = λ1WR(1-P cop )(1-P be ), λ1 is the a priori transmission probability at the sending device, Pcop is the outage probability, Pbe is the packet error probability, and W is the system bandwidth.

10. The joint optimization method according to claim 7 or 9, characterized in that: The total detection probability is denoted as P WE , its expression is: WE =λ0P FA +λ1P MD , where P FA is the false alarm probability, P MD is the missed detection probability, λ1 is the prior transmission probability at the sending device, and λ0=1-λ1.

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