Transmission optimization method for joint hidden security time delay of physical layer

Abstract

The invention discloses a transmission optimization method for joint hidden security time delay of a physical layer. The method comprises the following steps: establishing a physical layer eavesdropping channel model based on short packet transmission; establishing new indexes of fusion reliability, low time delay and safety facing short packet communication, wherein the new indexes comprise effective safety probability ESP and average safety time delay SL; optimally designing a block length and a signal-to-noise ratio; determining a joint optimal parameter according to the optimal block length and the optimal signal-to-noise ratio; according to the method, resources such as the transmission signal-to-noise ratio and the data block length are optimally distributed, so that better transmission performance is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of communication physical layer transmission resource optimization, and particularly to a transmission optimization method for physical layer joint covert security delay. Background Art

[0002] It has been more than 80 years since Shannon first published "A Mathematical Theory of Communication". With the development of information technology, communication technology is changing with each passing day. Communication technology has gone through 2G, 3G, 4G, and even the fifth generation of communication technology is entering commercialization. And with the improvement of communication technology and the continuous development of chip technology, artificial intelligence has gradually emerged, and the development of Internet of Things technology is in full swing. According to McKinsey Digital Company statistics, the number of global Internet of Things devices has increased from 4.6 billion in 2016 to 15.14 billion in 2023, and is expected to continue to explode by 2030, reaching 29.42 billion. According to the Internet of Things and its derivative products, it is expected to reach 5.5-12.6 trillion US dollars, and the Internet of Things economy will have a huge impact on the world economy. Although there is no conclusion on the specific content of 6G, based on the current status of 5G, scholars generally believe that 6G is the overall vision of 6G, represented by ubiquitous Internet of Things, immersive communication-computing, artificial intelligence, and mission-critical communications. One of the key technologies for realizing the intelligent connection of all things, especially ensuring the reliability of control instructions in the Internet of Things, is short packet communication. Short packet communication refers to the data interaction of various types of Internet of Things engineering quality control, which is usually only a few bits to hundreds of bits. With the rapid development of the Internet of Things, users have more and more demands on the Internet of Things, and people's requirements for communication are also getting higher and higher. Short packet communication relies on the frequent interaction of effective short data such as control instructions, and has higher requirements for communication security, latency, and reliability. For example, in the automation control system of a smart factory, the reliability requirement is 99.999% and the latency is within 5ms; in the requirements of 5G, the reliability requirement is 99.999% and the latency reaches the millisecond level; and in the 6G Internet of Things, the reliability requirement is 99.99999% and the latency is less than 1ms. In the future intelligent Internet of Things scenarios of the sky and the earth, if the safety, reliability and low latency cannot be met, it may lead to serious consequences such as the instant paralysis of smart factories and smart cities and the instant change of battlefield situations. According to Shannon's second theorem: It points out that as long as the information transmission rate is less than the channel capacity, there is a type of coding that makes the error probability of information transmission arbitrarily small. This theorem was proposed a long time ago and has guiding significance for the design of channel coding in mobile communications. Traditional wireless communication networks have also developed rapidly based on the scenario of "big data" and "long code length", and are not specifically suitable for short packet transmission. Today, the limitations of classical Shannon information theory in short packet communication of the Internet of Things are becoming increasingly prominent. Its channel capacity, achievable information rate and coding theory can no longer support the analysis of capacity, delay and reliability in modern short packet communication of the Internet of Things. Because this theorem has a premise assumption: sufficiently long processing time and coding block length. However, in the face of short packet transmission scenarios in the Internet of Things, code length resources are scarce and do not meet the conditions of Shannon's second theorem, and transmission reliability will be reduced.

[0003] At present, the physical layer transmission relies on the HARQ mechanism. If the reception failure is caused by the retransmission mechanism, it is easy to lead to problems such as data leakage. In the rapidly developing Internet of Things (IoT) towards 6G, users' demand for data security is becoming increasingly prominent, and information security has received high attention and emphasis from the academic community, the industrial community, and the national government authorities. Once the reliability and security of the physical layer information in short-packet communication cannot be guaranteed, users' data will face serious leakage problems. However, in the traditional communication system, security measures mainly rely on increasing the complexity of keys and encryption algorithms in the network, which requires frequent interactive signaling such as key management, distribution, and update. It is more inclined to be "network"-centric rather than "data"-centric. Moreover, the current design of communication networks is oriented towards traditional mobile communications such as "big data" and "long packet lengths", and there is much room for performance optimization in the fields of modulation, coding, etc. for the system design of "short-packet transmission", and it cannot effectively solve the problems of reliability, low latency, and security of the physical layer in the IoT transmission scenario.

[0004] In 2010, Dr. Polyanskiy proposed based on the asymptotic analysis theory that in any communication system with a positive channel capacity, there exists a symbol rate with a finite packet length and a limited distortion range. Subsequently, in 2016, Professor Durisi ingeniously performed an inverse solution based on Polyanskiy's work and obtained the outage error probability with limited distortion and finite length. Since then, the research on the performance of short-packet communication has grown explosively. Feng Chen modeled the channel using the finite-length secure communication rate in 2021 and proposed a general framework for joint reliability and security analysis at the physical layer. Weiwei Yang first jointly analyzed the finite-length and limited-distortion channel capacity and communication with low detection probability. Professor Zhu Yao optimized the physical layer security problem based on the finite-length and limited-distortion channel capacity theory. Yixin Zhang combined RSMA with the finite-length channel coding theory for simulation analysis. Zhicheng Li combined the finite-length channel coding theory with MIMO for modeling analysis. Milad TatarMamaghani combined the finite-length channel coding theory with the UAV path optimization for modeling and simulation.

[0005] In terms of coding performance analysis, although there is currently much research based on the finite-distortion and finite-blocklength channel coding theory, it only focuses on the reliability or security of the physical layer and does not involve another key indicator of communication - low latency. As far as the research shows, there is currently no research on the joint analysis of the reliability, security, and low latency of short-packet communication. How to comprehensively evaluate the transmission performance of short-packet communication at the physical layer and how to allocate resources such as block length and power to achieve optimal performance are all problems that need to be explored and solved urgently. Summary of the Invention

[0006] To solve the problems existing in the prior art, the object of the present invention is to provide a transmission optimization method for jointly concealed secure delay in the physical layer. The present invention optimally allocates resources such as transmission signal-to-noise ratio and data block length to achieve better transmission performance.

[0007] To achieve the above object, the technical solution adopted by the present invention is: a transmission optimization method for jointly concealed secure delay in the physical layer, including the following steps:

[0008] Step 1, establish a physical layer wiretap channel model based on short-packet transmission;

[0009] Step 2, establish new metrics for short-packet communication that integrate reliability, low latency, and security, including effective security probability ESP and average security delay SL;

[0010] Step 3, optimize the design of block length and signal-to-noise ratio;

[0011] Step 4, determine the jointly optimal parameters according to the optimal block length and the optimal signal-to-noise ratio.

[0012] As a further improvement of the present invention, the specific content of the above Step 1 is as follows:

[0013] Assume that the legitimate user A transmits D bits of information to the legitimate user B, and represent the channel coefficient in the legitimate channel as h b , and define the channel coefficient between the legitimate user A and the illegal user E as h e ; then the signal-to-noise ratios of the received signals at the legitimate user B and the illegal user E are respectively and When the legitimate user A sends information with a block length of L to the legitimate user B in the dedicated time slot T, the signal received by the legitimate user B is:

[0014]

[0015] where i is the index of the block length, p represents the transmission power, x represents the transmitted signal, represents the channel noise between the legitimate user A and the legitimate user B; the illegal user E performs a statistical hypothesis test based on two cases during the time slot to determine whether the legitimate user A has transmitted a data packet; the observed signal of the illegal user E is as follows:

[0016]

[0017] where H 0 is the null hypothesis, H 1 represents the alternative hypothesis, represents the channel noise between the legitimate user A and the illegal user E;

[0018] For a given information rate R = D / L, the decoding error probability is:

[0019]

[0020] where is the Gaussian Q function, γ represents the signal-to-noise ratio, and C(γ) = log(1 + γ) represents the channel capacity, is the channel dispersion; combining the miss detection probability and the false alarm probability, the detection error probability when an illegal user E attempts to detect the transmission is expressed as:

[0021] P de = 1 - V T (H 0 , H 1 ), (4)

[0022] where is the total change probability for judging H 0 and H 1 , is the correct probability that the illegal user E is detected; when the detection error exceeds the illegal user E will make a misjudgment; according to the Pinsker inequality, is expressed as:

[0023]

[0024] where represents the relative entropy between H 0 and H 1 , and the probability that the illegal user E detects the propagation is expressed as:

[0025]

[0026] Adopting a retransmission mechanism, the legitimate user B simulates the detection of the illegal user E through a likelihood ratio test based on two hypotheses and the decoding situation of the illegal user E, and then provides a feedback signal.

[0027] As a further improvement of the present invention, step 2 is specifically as follows:

[0028] The effective security probability ESP is calculated as:

[0029] P ESP = (1 - P B )(1 - P d (1 - P E )), (7)

[0030] where P B defines the probability that the legitimate user B decodes the data packet incorrectly, and P E gives the probability that the illegal user E decodes the included data packet incorrectly, (1 - Pd (1 - P E )) indicates that illegal user E has detected an error in the transmission or failed to decode a data packet;

[0031] When communication fails, retransmission is triggered, and each transmission time is equal to the duration, given by T = 1 / W, where W represents the subcarrier spacing;

[0032] Let t i represent the time when the i-th short data packet starts transmission, (i = 1…n), and t′ i represent the time when the data packet is successfully transmitted to legitimate user B, and T Wi = t i - t′ i-1 represents the time the transmitter waits for the i-th packet after transmitting the (i - 1)-th packet, and λ is the probability of generating a short data packet in each time slot A i = t′ i - t i defines the SL of the i-th data packet, representing the time elapsed for the successful transmission of the data packet; if the transmission is successful, SL immediately returns 0 and waits for the next data packet to be transmitted, then at any time t, SL will be:

[0033]

[0034] where SL i,k represents the delay of the k-th transmission of the i-th data packet; the average SL is obtained by averaging SL over all time slots, representing the average time for legitimate user B to securely and reliably receive information; for an interval (0, τ), the average SL is calculated as:

[0035]

[0036] where S i is the area of the i-th triangle, N represents the number of valid data packets, and Λ represents the average arrival rate of data packets over all time slots; E(S i ) represents the average value of S i and is expressed as:

[0037]

[0038] Λ is expressed as:

[0039]

[0040] A i The average value of is calculated as:

[0041]

[0042] T WThe average value is calculated as:

[0043]

[0044] Combining (12) and (13), the average arrival rate of the data packet is obtained as:

[0045]

[0046] E(S i ) is derived as:

[0047]

[0048] Substituting (14) and (15) into (9), the average SL is:

[0049]

[0050] SNRγ, block length L, time slot T, and generation rate λ jointly affect the average SL. Compared with the SL in (12), the average SL includes a weighted proportion of the transmission time, that is which provides a measure of the system workload for the transmitter;

[0051] The optimization problem of minimizing the average SL is expressed as:

[0052]

[0053] where (17a) indicates that the positive integer L is restricted by the minimum value D and the maximum value L max constraint.

[0054] As a further improvement of the present invention, step 3 specifically includes the following steps:

[0055] Step 3.1, simplify the optimization problem of minimizing the average SL into two sub-problems, and calculate the first-order derivative of SL with respect to P ESP :

[0056]

[0057] Since λ ∈ (0, 1), the value of is negative, indicating that a larger P ESP will result in lower latency. The optimal signal-to-noise ratio and block length of P ESP are also the optimal solutions of the average SL. When P d = 1, the equal sign of holds, where

[0058] P ESPAffected by both the block length and the signal-to-noise ratio, the optimization problem is divided into two sub-problems, namely, the optimal block length optimization when determining the signal-to-noise ratio and the optimal signal-to-noise ratio optimization when determining the block length;

[0059] Step 3.2. Optimize the optimal block length L:

[0060] Sub-problem 1: For the determined γ and D, the optimization problem is expressed as

[0061]

[0062] For a relatively small L, the implicit solution of the optimal L is shown in (20):

[0063]

[0064] For a relatively large L, the optimal L is derived as Threshold γ t Satisfies the equation

[0065] Step 3.3. Optimize the optimal signal-to-noise ratio γ:

[0066] Sub-problem 2: For the determined L and D, the optimization problem is expressed as:

[0067]

[0068] For a relatively small L, the implicit solution of the optimal γ is shown in (22):

[0069]

[0070] For a relatively large L, the optimal γ can be derived as Threshold L t Is the value that satisfies the equation Value.

[0071] As a further improvement of the present invention, step 4 specifically includes the following steps:

[0072] Step 4.1. When the communication scenario is a given signal-to-noise ratio γ and transmission information amount D, the problem is a convex optimization problem. Compare the given signal-to-noise ratio γ with the signal-to-noise ratio threshold γ t If it is greater than the threshold γ t , then adopt the algorithm of formula (20) to determine the optimal block length through a search strategy; if it is less than the threshold γ t , then adopt the optimal block length Design;

[0073] Step 4.2. When the communication scenario is a given block length L and transmission information amount D, the problem is a convex optimization problem. Compare the given block length L with the block length threshold L tCompare, if it is greater than the threshold L t , then the algorithm (28) is used to determine the optimal signal-to-noise ratio through the search strategy; if it is less than the threshold L t , then the optimal signal-to-noise ratio is used design;

[0074] Step 4.3: When the block length L and the signal-to-noise ratio γ are not given in the communication scenario, the problem is a convex optimization problem. When P ESP The peak value of increases with the increase of signal-to-noise ratio and block length; by iterating the optimal L in (20) and the optimal SNR in (28) until convergence, the optimal block length L and the optimal signal-to-noise ratio γ that achieve the optimal safety delay are obtained.

[0075] The beneficial effects of the present invention are:

[0076] 1. The present invention provides an effective secure probability (ESP) and an average secure latency (Average SL) that comprehensively describe the reliability, low latency, and secure transmission of the physical layer of short packets. In view of the disadvantage that the shorter the data packet is, the worsening transmission reliability, the complex problem is simplified by differentiation; the problem is divided into two sub-problems by using a cyclic iterative algorithm; the optimal resource allocation formula is determined by using a first-order Taylor expansion, and the optimal resource allocation strategy for transmission under a given signal-to-noise ratio and a given block length scenario is determined, solving the problem of lack of theoretical guidance in the design of short packet transmission resource optimization allocation. The present invention proposes two key indicators, ESP and average secure latency, and provides new tools and methods for short packet communication performance evaluation. Not only can it achieve precise design of resources, but it is also committed to reducing the energy consumption and cost of communication systems, improving resource utilization efficiency, and enhancing the stability and reliability of wireless communication networks in complex environments, thereby promoting communication technology to develop in a more efficient and energy-saving direction.

[0077] 2. The present invention provides a comprehensive evaluation index for short packet physical layer transmission that integrates reliability, low latency and security - average safety delay; a resource optimization strategy for short packet physical layer transmission to achieve optimal performance in reliability, low latency and security. When the amount of information is given, an analytical expression for allocating data block length and signal-to-noise ratio is given to allocate physical layer resources to achieve the lowest average safety delay. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 is a flow chart of an embodiment of the present invention;

[0079] Figure 2 Schematic diagram of average safety delay SL in an embodiment of the present invention;

[0080] Figure 3 (a) in the embodiments of the present invention shows the relationship between the probability of Bob decoding and Eve detecting and decoding P d (1 - P E ) and the block length; Figure 3 (b) in the embodiments of the present invention shows the relationship between P ESP and the block length;

[0081] Figure 4 (a) in the embodiments of the present invention shows the schematic diagram of the theoretical analysis of the average SL and L under different SNRs and λ; Figure 4 (b) in the embodiments of the present invention shows the schematic diagram of the theoretical analysis of the average SL and SNR under different Ls and λ;

[0082] Figure 5 shows the relationship between P ESP and the signal - to - noise ratio and the block length in the embodiments of the present invention. Detailed implementation manners

[0083] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0084] Embodiment

[0085] As Figure 1 shown, a transmission optimization method for physical - layer joint covert security delay is as follows: The overall idea is to first determine the current resource usage situation and obtain the current allocable resource information. Then, based on the short - packet transmission physical - layer wiretap channel model, a resource allocation strategy for finite block length and signal - to - noise ratio is proposed for the requirements of high reliability, low latency, and high security. For the problem of minimizing the security delay target, the corresponding optimal resource design algorithm is selected according to the communication scenario, and finally the optimal resource allocation scheme for the block length L and the signal - to - noise ratio γ is obtained. The specific steps are as follows:

[0086] Step 1: Establish a physical - layer wiretap channel model based on short - packet transmission;

[0087] Considering legitimate users, such as Alice and Bob, who attempt to transmit D bits of information that should not be detected by eavesdroppers, such as Eve. Note that in short - packet - based low - altitude communication, although Eve is close to Bob, they are still distinguishable. Assume that the legitimate channel adopts a quasi - static Rayleigh fading channel model. The channel coefficient in the legitimate channel is denoted as h b , and the channel coefficient between Alice and Eve is defined as h e . Therefore, the signal - to - noise ratios of the received signals at Bob and Eve are respectively and When Alice sends information with block length L to Bob in the dedicated time slot T, the signal received by Bob can be written as

[0088]

[0089] where i is equal to the index of the block length, p represents the transmit power, x represents the transmitted signal, represents the channel noise between Alice and Bob. Eve performs a statistical hypothesis test based on two cases during the time slot to determine whether Alice has transmitted a data packet. Eve's observed signal is given by

[0090]

[0091] where H 0 is the null hypothesis, H 1 represents the alternative hypothesis, represents the channel noise between Alice and Eve.

[0092] For a determined information rate R = D / L, the decoding error probability is

[0093]

[0094] where is the Gaussian Q function, γ represents the signal-to-noise ratio, C(γ)=log(1 + γ) represents the channel capacity, is the channel dispersion. When Eve attempts to detect the transmission, two types of detection errors will inevitably be encountered, namely missed detection and false alarm. Combining the missed detection probability and the false alarm probability, the detection error probability can be expressed as

[0095] P de = 1 - V T (H 0 , H 1 ), (4)

[0096] where is the total variation probability of judging H 0 and H 1 . It can be seen that is the correct probability that Eve is detected. Obviously, when the detection error exceeds Eve will make a misjudgment and the transmission becomes covert. According to Pinsker's inequality, is expressed as

[0097]

[0098] where represents H 0 and H 1The relative entropy between them. Therefore, the probability that Eve detects the propagation can be expressed as

[0099]

[0100] To ensure reliable transmission, this embodiment adopts a retransmission mechanism. Since Eve is very close to Bob, the signal-to-noise ratio of Eve is also close to the correlation of Bob. Therefore, Bob can simulate Eve's detection through a likelihood ratio test based on two assumptions and Eve's decoding situation, and then provide a timely feedback signal.

[0101] Step 2: Propose new metrics for short-packet communication that integrate reliability, low latency, and security, namely the effective secure probability (ESP) and the average secure latency (Average SL)

[0102] Define ESP as the probability that the communication is reliable and covert. In a covert communication system, one goal is to achieve reliable transmission between Alice and Bob while ensuring that Eve incorrectly detects the transmission or fails to decode the data packet. These situations are shown in Table 1.

[0103] Table 1 Summary of Situations

[0104]

[0105]

[0106] In the table, the decoding of "—" for Eve means that it is not necessary to consider whether the decoding is successful because Eve does not detect the transmission. As shown in the table, for cases 4 and 5, the communication is reliable and covert, and ESP can be calculated as

[0107] P ESP =(1 - P B )(1 - P d (1 - P E ))), (7)

[0108] where P B defines the probability that Bob incorrectly decodes the data packet, P E gives the probability that Eve incorrectly decodes the included data packet, (1 - P d (1 - P E )) represents that Eve incorrectly detects the transmission or fails to decode the data packet.

[0109] Since retransmission is triggered when communication fails, another factor affecting latency is the transmission time. Due to the short block length, the coding latency is much smaller compared to the transmission duration. Thus, each transmission time equals the duration and can be given by T = 1 / W, where W represents the subcarrier spacing.

[0110] When Bob's decoding is unsuccessful or Eve successfully detects and decodes the communication, the successful and secure transmission from Alice to Bob fails. If the transmission fails, Alice will retransmit the information in the next time slot until successful. After that, Alice will wait for the transmission of the next data packet. To characterize the impact of block length and signal-to-noise ratio on latency in covert communication, a new metric called SL is introduced, which means the time elapsed since the transmission of a valid data packet from Alice, where the valid data packet is secretly transmitted and successfully decoded by Bob.

[0111] Figure 2 An example is shown where t i represents the time when the i-th short data packet starts transmission, (i = 1…n), and t' i represents the time when the data packet is successfully transmitted to Bob, and T Wi = t i - t' i-1 represents the time the transmitter waits for the i-th packet after transmitting the (i - 1)-th data packet, and λ is the probability of generating a short data packet in each time slot A i = t' i - t i defines the SL of the i-th data packet, which means the time elapsed for the successful transmission of the data packet. If the transmission is successful, SL will immediately return 0 and wait for the transmission of the next data packet. Thus, at any time t, SL will be

[0112]

[0113] where SL i,k represents the latency of the k-th transmission of the i-th data packet. The average SL is obtained by averaging SL over all time slots and represents the average time for Bob to receive the information securely and reliably. For an interval (0, τ)), the average SL can be calculated as

[0114]

[0115] where S i is the area of the i-th triangle, N represents the number of valid data packets, and Λ represents the average arrival rate of data packets over all time slots. Additionally, E(S i ) represents the average value of S i and can be expressed as

[0116]

[0117] Λ can be expressed as

[0118]

[0119] A i The average value of can be calculated as

[0120]

[0121] In addition, for T W The average value of can be calculated as

[0122]

[0123] By combining (12) and (13), the average arrival rate of the data packet can be obtained as

[0124]

[0125] Similarly, E(S i ) can be derived as

[0126]

[0127] By substituting (14) and (15) into (9), the average SL will be

[0128]

[0129] Based on (16), the following insights are obtained. First, the SNR γ, block length L, time slot T, and generation rate λ jointly affect the average SL. Second, compared with the SL in (12), the average SL includes the weighted proportion of the transmission time, i.e., It provides a measure of the system workload for the transmitter.

[0130] The optimization problem of minimizing the average SL can be expressed as

[0131]

[0132] where (17a) indicates that the positive integer L is restricted by the minimum value D and the maximum value L max constraint.

[0133] Step 3: Optimal design of block length and signal-to-noise ratio

[0134] Step 3.1: Simplify the problem into two sub-problems

[0135] To simplify the problem, calculate the first derivative of SL with respect to P ESP as

[0136]

[0137] Since λ ∈ (0, 1), the value of is negative, which means that a larger P ESP will result in lower latency. In addition, it is found that the optimal signal-to-noise ratio and block length of P ESP are also the optimal solutions for the average SL. When P d = 1, the equality sign of holds, where

[0138] In addition, it is found that P ESP is jointly affected by the block length and the signal-to-noise ratio. Therefore, the optimization problem is divided into two sub-problems, namely, the optimal block length optimization when determining the signal-to-noise ratio and the optimal signal-to-noise ratio optimization when determining the block length. Finally, an algorithm for solving problem (17) is given.

[0139] Step 3.2 Optimize the optimal block length L

[0140] Sub-problem 1: For the determined γ and D, the optimization problem can be expressed as

[0141]

[0142] For a smaller L, the implicit solution of the optimal L is shown in (20).

[0143]

[0144] For a larger L, the optimal L can be derived as The threshold γ t should satisfy the equation

[0145] Proof:

[0146] P ESP The first derivative of with respect to L can be calculated as

[0147]

[0148] According to (3) and (6), can be expressed as

[0149]

[0150] where Then can be derived as

[0151]

[0152] Applying the Taylor series to the Q function in P e can be calculated as

[0153]

[0154] By substituting (6), (22), (23), and (24) into (21), we get and applying the search algorithm to the implicit solution in (20) to obtain the optimal L.

[0155] For higher signal-to-noise ratios, as the block length increases, P d approaches 1, meaning that Eve always detects the transmission. Thus, P ESP approaches Therefore, P ESP The first derivative of P with respect to L will be

[0156]

[0157] Since in (27) is negative, P e should be equal to to make Then we have

[0158]

[0159] Therefore, for higher signal-to-noise ratios, the optimal L is The threshold γ that distinguishes between two cases t is whether the optimal L makes P d equal to 1, which means Finally, γ t satisfies

[0160] Theorem 1 provides the optimal transmission design with respect to the block length when determining the SNR and D, which can be used for power-constrained communication. A smaller signal-to-noise ratio or a larger D results in a longer optimal block length. Additionally, a higher signal-to-noise ratio guarantees lower packet error probabilities for both the receiver and the eavesdropper, but also leads to a higher detection probability.

[0161] Step 3.3 Optimize the optimal signal-to-noise ratio γ

[0162] Sub-problem 2: Similar to (19), for the determined L and D, the optimization problem can be expressed as

[0163]

[0164] Theorem 2: For a smaller L, the implicit solution of the optimal γ is as shown in (22).

[0165]

[0166] For a larger L, the optimal γ can be derived as The threshold L t is the one that satisfies the equation value

[0167] Proof: Similar to (21), P ESP The first derivative of P with respect to γ can be derived as

[0168]

[0169] According to (3), can be calculated as

[0170]

[0171] In addition, can be calculated as

[0172]

[0173] By substituting (6), (26), (30), and (31) into (29), making and applying the search algorithm to the implicit solution in (28), the optimal γ is obtained. For a longer block length, as the signal-to-noise ratio increases, P d approaches 1. In this case, when are equal. Similar to the proof in (28), the optimal γ can be derived as The threshold L that distinguishes between the two cases t satisfies

[0174] Theorem 2 provides the optimal transmission design with respect to SNR for determining the block length L and D, which is applicable to fixed-block-length transmission to determine the optimal SNR based on the determined L and D.

[0175] Step 4: Determine the jointly optimal parameters according to the optimal block length L in Step 3.2 and the optimal signal-to-noise ratio γ scheme in Step 3.3.

[0176] Note that, the larger P ESP is, the lower the average SL is, so the optimal L and the optimal signal-to-noise ratio are from (20) and (28).

[0177] Step 4.1: When the communication scenario is a given signal-to-noise ratio γ and the amount of transmitted information D, this problem is a convex optimization problem. Compare the given signal-to-noise ratio γ with the signal-to-noise ratio threshold γ t If it is greater than the threshold γ t , then use the algorithm in (20) to determine the optimal block length through a search strategy. If it is less than the threshold γ t , then use the optimal block length design.

[0178] Step 4.2: When the communication scenario is given a block length L and the amount of transmitted information D, this problem is also a convex optimization problem. Compare the given block length L with the block length threshold L t . If it is greater than the threshold L t , then use the algorithm in Equation (28) to determine the optimal signal-to-noise ratio through a search strategy. If it is less than the threshold L t , then use the optimal signal-to-noise ratio design.

[0179] Step 4.3: When neither the block length L nor the signal-to-noise ratio γ is given in the communication scenario, this problem is also a convex optimization problem.

[0180] It can be found that when , that is P ESP 's peak value increases with the increase of the signal-to-noise ratio and the block length. Therefore, by iterating the optimal L in (20) and the best SNR in (28) until convergence, the optimal block length L and the optimal signal-to-noise ratio γ that achieve the optimal secure delay can be obtained.

[0181] In addition, the numerical results verify the effectiveness of the analysis. The effects of the signal-to-noise ratio, block length, and packet generation rate on ESP and the average SL are also analyzed. In the simulation, the parameters are set as D = 64 bits and the noise power W = 120 kHz.

[0182] In Figure 3 , it can be seen that when the block length is short, ESP is small. This is because when the packet is shorter than the threshold, the reliability performance of communication is poor, which means that Bob's decoding is more likely to fail. Although there is a large degree of concealment, it is also difficult for Eve to decode the information. As the block length increases, this trend weakens. On the other hand, when the block length exceeds the threshold at which Eve's performance equals Bob's reliability, ESP will decrease. This is because as long as Bob can easily decode the information, Eve can also easily decode it. In addition, as the block length increases, Eve's detection probability P d approaches 1, so the coverage constraint P d (1 - P E ) becomes (1 - P E ), as shown in (a) of Figure 3 . In addition, it can be seen from (b) of Figure 3 that as the signal-to-noise ratio increases, P ESP gradually approaches , which is consistent with the analysis. It is particularly worth noting that when the signal-to-noise ratio is greater than the threshold, that is, -6.743 dB, the two curves almost overlap, which means that for signal-to-noise ratios greater than the threshold, a simple optimal block length form can be adopted However, if the signal-to-noise ratio is less than the threshold, the optimal block length L must be taken in (20). It can be verified that both γ = -7 dB and γ = -10 dB are lower than the threshold. Therefore, the optimal block lengths calculated by the search algorithm in (20) are 243 bits and 489 bits. When the signal-to-noise ratio is -5 dB, which is higher than the threshold, the optimal block length is 161 bits. The results of Theorem 1 are consistent with the simulation results, which proves the effectiveness of the derivation in this embodiment.

[0183] In Figure 4 (a), it is noted that there is a minimum average SL. This is because when the data packet is shorter than the threshold, a larger L will result in a larger ESP, thus reducing retransmission and delay. The average SL then increases with the increase of the block length. This is because a longer data packet length makes it easier for Eve to detect and decode the information. In addition, this embodiment finds that a higher λ will result in a higher average SL because with a higher λ, the transmission frequency is higher.

[0184] Figure 4 (b) shows the theoretical analysis of the average SL versus SNR for different L and D. There is a minimum average SL in terms of the signal-to-noise ratio. In addition, the optimal signal-to-noise ratio varies with the block length. Similar to the verification of Theorem 1, when the data packet lengths are 64 bits, 100 bits, 150 bits, and 200 bits, according to Theorem 2, the optimal signal-to-noise ratios are 0 dB, 2.531 dB, 4.633 dB, and 6.050 dB respectively, which are consistent with the simulation results.

[0185] Figure 5 shows P ESP versus the signal-to-noise ratio and the block length. The markers represent the results of the iterative algorithm, which are consistent with the maximum P ESP . Because the value of is negative, the optimal solution to problem (17) is solved by iterating the optimal solutions in Theorem 1 and Theorem 2. In addition, this embodiment finds that the optimal block length is the longest, and the optimal signal-to-noise ratio can be obtained by applying the search algorithm in (22).

[0186] The embodiments described above only represent the specific implementation manners of the present invention. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A transmission optimization method for physical layer joint concealed security delay, characterized in that: The following steps are involved: Step 1: Establish a physical layer eavesdropping channel model based on short packet transmission; Step 2: Establish new indicators that integrate reliability, low latency, and security for short packet communications, including effective security probability ESP and average security delay SL; Step 3: Optimize the design of block length and signal-to-noise ratio; Step 4: Determine the joint optimal parameters according to the optimal block length and the optimal signal-to-noise ratio.

2. The transmission optimization method for physical layer joint concealed security delay according to claim 1 is characterized in that: The step 1 is specifically as follows: Assume that legitimate user A transmits D bits of information to legitimate user B, and the channel coefficient in the legitimate channel is represented as h b , the channel coefficient between the legitimate user A and the illegal user E is defined as h e ; Then the signal-to-noise ratios of the signals received by the legal user B and the illegal user E are and When legitimate user A sends information with a block length of L to legitimate user B in a dedicated time slot T, the signal received by legitimate user B is: Where i is equal to the index of the block length, p represents the transmit power, and x represents the transmit signal. represents the channel noise between the legitimate user A and the legitimate user B; the illegal user E performs a statistical hypothesis test based on two cases during the time slot to determine whether the legitimate user A transmits a data packet; the observation signal of the illegal user E is as follows: Where H0 is the null hypothesis and H1 is the alternative hypothesis. represents the channel noise between the legitimate user A and the illegal user E; For a certain information rate R = D / L, the decoding error probability is: in is the Gaussian Q function, γ represents the signal-to-noise ratio, C(γ)=log(1+γ) represents the channel capacity, is the channel dispersion; considering the missed detection probability and false alarm probability, the detection error probability when the illegal user E attempts to detect the transmission is expressed as: P de =1-V T (H0,H1), (4) in is the total probability of change between H0 and H1. is the correct probability of illegal user E being detected; when the detection error exceeds Illegal user E will make a misjudgment; according to Pinsker inequality, It is expressed as: in Denotes the relative entropy between H0 and H1, and the probability that an illegal user E detects the propagation is expressed as: Using the repetitive transmission mechanism, the legitimate user B simulates the detection of the illegal user E through a likelihood ratio test based on two hypotheses and the decoding situation of the illegal user E, and then provides a feedback signal.

3. The transmission optimization method for physical layer joint concealed security delay according to claim 2 is characterized in that: The step 2 is specifically as follows: The effective safety probability ESP is calculated as: P ESP =(1-P B )(1-P d (1-P E )), (7) Where P B Defines the probability that legitimate user B decodes a data packet incorrectly, P E The probability that an illegal user E decodes a data packet incorrectly is given, (1-P d (1-P E )) indicates that an illegal user E erroneously detected a transmission or failed to decode a data packet; When communication fails, retransmission is triggered, and each transmission time is equal to the duration, given by T = 1 / W, where W represents the subcarrier spacing; Assume t i represents the time when the i-th short data packet starts to be transmitted, (i=1…n), t′ i Indicates the time when the data packet is successfully transmitted to the legitimate user B, T Wi =t i -t′ i-1 represents the time the transmitter waits for the i-th packet after transmitting the (i-1)-th packet, and λ is the probability A of generating a short packet in each time slot i =t′ i -t i The SL of the i-th data packet is defined, which represents the time taken to effectively transmit the data packet; If the transmission is successful, SL returns to 0 immediately and waits for the next packet to be transmitted. At any time t, SL will be: Among them SL i,k represents the delay of the kth transmission of the i-th data packet; the average SL is obtained by averaging the SL over all time slots, which represents the average time for the legitimate user B to receive the information safely and reliably; for an interval (0, τ), the average SL is calculated as: Where S i is the area of ​​the ith triangle, N is the number of valid data packets, Λ is the average arrival rate of data packets in all time slots; E(S i ) indicates S i The average value is expressed as: Λ is expressed as: A i The average value of is calculated as: T W The average value of is calculated as: Combining (12) and (13), we get the average arrival rate of data packets: E(S i ) is exported as: Substituting (14) and (15) into (9), the average SL is: SNRγ, block length L, time slot T, and generation rate λ jointly affect the average SL. Compared with the SL in (12), the average SL contains a weighted proportion of the transmission time, i.e. Provides a measure of system workload for the transmitter; The optimization problem of minimizing the average SL is expressed as: Where (17a) indicates that the positive integer L is subject to the minimum value D and the maximum value L max limit.

4. The transmission optimization method for physical layer joint concealed security delay according to claim 3 is characterized in that: The step 3 specifically comprises the following steps: Step 3.1: Simplify the optimization problem of minimizing the average SL into two subproblems and calculate SL relative to P. ESP The first derivative of : Since λ∈(0,1), A negative value indicates a larger P ESP This will result in lower latency, P ESP The optimal signal-to-noise ratio and block length of is also the optimal solution for average SL when P d =1, The equality of P ESP Affected by the block length and signal-to-noise ratio, the optimization problem is divided into two sub-problems, namely, the optimization of the optimal block length when the signal-to-noise ratio is determined and the optimization of the optimal signal-to-noise ratio when the block length is determined; Step 3.2: Optimize the optimal block length L: Sub-problem 1: For the determined γ and D, the optimization problem can be expressed as For smaller L, the implicit solution of the optimal L is shown in (20): For larger L, the optimal L is derived as Threshold γ t Satisfy the equation Step 3.3, optimize the optimal signal-to-noise ratio γ: Sub-problem 2: For a given L and D, the optimization problem is expressed as: For smaller L, the implicit solution of the optimal γ is shown in (22): For larger L, the optimal γ can be derived as Threshold L t is to satisfy the equation The value of .

5. The transmission optimization method for physical layer joint concealed security delay according to claim 4 is characterized in that: The step 4 specifically comprises the following steps: Step 4.1: When the communication scenario is a given signal-to-noise ratio γ and the amount of transmitted information D, the problem is a convex optimization problem. The given signal-to-noise ratio γ is equal to the signal-to-noise ratio threshold γ. t Compare, if it is greater than the threshold γ t , then the algorithm (20) is used to determine the optimal block length through the search strategy; if it is less than the threshold γ t , then the optimal block length is used design; Step 4.2: When the communication scenario is a given block length L and the amount of information transmitted D, the problem is a convex optimization problem. The given block length L is compared with the block length threshold L. t Compare, if it is greater than the threshold L t , then the algorithm (28) is used to determine the optimal signal-to-noise ratio through the search strategy; if it is less than the threshold L t , then the optimal signal-to-noise ratio is used design; Step 4.3: When the block length L and the signal-to-noise ratio γ are not given in the communication scenario, the problem is a convex optimization problem. When P ESP The peak value of increases with the increase of signal-to-noise ratio and block length; by iterating the optimal L in (20) and the optimal SNR in (28) until convergence, the optimal block length L and the optimal signal-to-noise ratio γ that achieve the optimal safety delay are obtained.

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