Multi-user hidden networking method based on dual-time scale constraint

Abstract

The invention discloses a multi-user hidden networking method based on double time scale constraints. The method comprises the following steps: 1, slicing time-frequency network resources to obtain an available time-frequency slot set; 2, obtaining a basic random sequence M < k > under the action of a system clock and a user authentication key; 3, performing cyclic shift transformation on the basic random sequence M < k > to obtain an extended sequence family NL * K; step 4, carrying out orthogonalization processing on the extended sequence family NL * K to obtain a decision sequence family HL * K, and guiding multiple users to access the network; 5, authorized user access protocol performance analysis is carried out, and dual-time-scale constraint is carried out to achieve the optimal networking throughput; step 6, reliability and security analysis is carried out on the covert communication system; and 7, analyzing the tolerance of the covert communication system, and solving by using an improved SA-PSO algorithm. According to the method, multiple users are guided to asynchronously access the covert communication network through dynamic management and allocation of spectrum resources, and the method has the characteristics of high efficiency, flexibility, stability and accuracy.

Description

Technical Field

[0001] This invention belongs to the field of covert communication technology, specifically relating to a multi-user covert networking method based on dual time scale constraints. Background Technology

[0002] The openness of wireless networks provides a crucial foundation for the Internet of Things (IoT), but this openness also makes networks more vulnerable to malicious attacks and unauthorized access, posing significant security risks. Unauthorized third parties may use such open media to conduct malicious eavesdropping, leading to frequent incidents of privacy data breaches and posing a serious threat to communication security. Covert communication technology utilizes the uncertainty in signal transmission to conceal the communication itself, thereby ensuring the security and privacy of communication. By ensuring low-detection and low-interception transmission of information, covert communication not only improves the security of the communication process but also fundamentally resists eavesdropping and interception attacks, thus attracting widespread attention from academia and industry. However, in complex electromagnetic environments, with the increasing number of authorized users and the continuous upgrading of interference methods, existing covert communication systems still lack sufficient theoretical support for multi-user access and network transmission, making it difficult to effectively evaluate and optimize network performance, thereby limiting overall transmission efficiency.

[0003] Existing technologies still have significant limitations in two typical real-world scenarios.

[0004] In dense access scenarios, where multiple devices share limited channels (such as mobile cellular networks and wireless LANs), existing throughput optimization strategies still face significant challenges from resource contention conflicts. These conflicts can easily lead to performance degradation, and due to the lack of efficient coordination mechanisms and global information sharing, it is difficult to achieve optimal system-level resource allocation and global throughput.

[0005] Covert communication scenarios: Although traffic offloading techniques in heterogeneous networks can effectively improve spectral efficiency and reduce system power consumption, the resulting inter-layer interference not only reduces transmission reliability but also introduces additional security threats. Interference signals can be exploited by attackers to detect communication behavior, thereby increasing the risk of communication exposure and privacy breaches. Inter-layer interference remains one of the main bottlenecks restricting the performance of heterogeneous networks.

[0006] Therefore, given the continued scarcity of spectrum resources and the complex and ever-changing electromagnetic environment, in order to solve the problem of limited network performance of covert communication systems, it is urgent to develop a dynamic spectrum access mechanism with environmental awareness capabilities. This mechanism can adapt to channel conditions and service requirements in real time, overcome the constraints of interference and limited spectrum resources on network performance, and improve the spectrum efficiency and network capacity of multi-user covert communication networks, thereby providing basic support for covert communication with high security requirements. Summary of the Invention

[0007] To overcome the shortcomings of the existing technology, the present invention aims to provide a multi-user covert networking method based on dual time scale constraints. This method guides multiple users to asynchronously access the covert communication network through dynamic management and allocation of spectrum resources, and has the characteristics of high efficiency, flexibility, robustness and accuracy.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for multi-user covert networking based on dual time-scale constraints includes the following steps; Step 1: Perform time-frequency network resource slicing to obtain a set of available time-frequency slots; Step 2: Based on the available time slot set, and under the influence of the system clock and the user authentication key, obtain the basic random sequence. M k ; Step 3: Transform the basic random sequence M k Cyclic shift transformation yields an extended sequence family N L×K ; Step 4: Extend the sequence family N L×K Orthogonalization process yields a family of decision sequences H L×K To guide multiple users to access the network; Step 5: Authorize user access protocol performance analysis and apply dual time scale constraints to achieve optimal network throughput; Step Six: Reliability and security analysis of the covert communication system; Step 7: Analyze the tolerance of the covert communication system and use the improved SA-PSO algorithm to solve for the upper and lower limits of the number of users the system can accommodate.

[0009] Step one specifically involves: The communication units of the entire covert communication system are configured to exist. K A legitimate user, firstly, sets the transmission bandwidth to... W The shared channels are all divided into q Zero non-overlapping parts yield a set of idle frequency slots. F 0={ f 1, f 2,…, f q0 Set the reuse factor of each frequency slot to 1; use spectrum sensing technology with high-order cumulants to obtain the contents of the idle frequency slots. q The set of available frequency slots for each element F ={ f 1, f 2,…, f q}; A transmission cycle is defined as the average data packet length transmitted by authorized users, and the period occupied within the cycle is... L ∈{1, 2, ..., p} time slots, resulting in a set of available time slots. T = { t 1, t 2,…, t p}

[0010] Step two specifically involves: Based on the already obtained set of available time slots, through the user authentication key key Controlled by random functions randi Generate includes L A basic random sequence of elements M 0 ={ m 0 i | i =1,2,…, L},in m 0 i ∈ F ={ f 1, f 2,…, f q} indicates that the authorized user is in the first... i Each time slot accesses the shared channel using its own frequency slot; to meet the requirements of multi-user access within a period of the covert communication system, iterative transformation processing of the individual sequence is employed using block cryptography. K Rounds of iterative transformations yield the basic random sequence. M k ={ mk 1, mk 2, …, mk L},in (1) In the formula mk i ∈ F ={ f 1, f 2,…, f q} indicates authorized user U k In the i The frequency slots used by each time slot to access the shared channel key i The authentication key used to authorize users to access the network units controlled by the current base station. box g This is the substitution box in the block cipher generation algorithm, and ⊕ is the XOR operator.

[0011] Step three specifically involves: Using round functions to transform the basic random sequence M k A cyclic shift transformation is performed to meet the system's requirement of allowing multiple legitimate users to access the system simultaneously. (2) In the formula, ε ∈{1, 2, 3, ...} represents the number of iterations of the round function, which yields a set of extended sequences, i.e., the family of basic sequences. ,in nk i Indicates that the authorized user is in the i Each time slot accesses the frequency slot used by the shared channel.

[0012] Step four specifically involves: For iterative sequence families N L×K middle K Each sequence is orthogonalized. (3) in, The shift factor is an orthogonal transformation factor, which is then orthogonalized to make... It is necessary to access the decision sequence family. ; in accessing the decision sequence family H L×K Under the guidance of the system, legitimate users access the corresponding frequency slots of the shared channel in an orderly manner, and sequentially select the corresponding frequency slots in each time slot.

[0013] Step five specifically involves: The performance of the access protocol is analyzed, and the optimal network throughput is achieved by utilizing dual time scale constraints. A. Short time scale: Construct a probabilistic model based on multi-user conflict-free networking to guide the server to access dynamic access protocol and calculate resource allocation on demand, so as to improve system throughput and business efficiency; B. Long-term scale: Based on the probabilistic model of the collision-free network, calculate the unit throughput, service efficiency and system throughput, and conduct mathematical analysis to study the function graph characteristics, so as to achieve the optimal throughput performance under different user volume conditions.

[0014] Step six specifically involves: i) Reliable transmission performance analysis; ii) Security transmission performance analysis.

[0015] Step seven specifically involves: i) Macrocell network capacity analysis Let the minimum allowable reliable transmission probability of the system be denoted as . P r,minCombining the system reliable transmission expression (23), we obtain the inequality. (28) Number of users u Incorporating polynomial and logarithmic functions, the above equation is transformed into a nonlinear constrained problem. (P1): (29) To simplify the problem, a penalty factor is used. and penalty function This nonlinear constrained problem is transformed into an unconstrained nonlinear programming problem. (30) Solving equation (30) above will yield the upper limit of the macrocell network capacity; Similarly, the minimum probability of the system being able to resist interception is denoted as... P s,min Combining the system's secure transmission probability expression (26), we get (31) Number of users u Containing both polynomial and logarithmic functions, the lower bound of macrocell network capacity is expressed as the following nonlinear constraint problem. (P2): (32) Using penalty factors and penalty function This nonlinear constrained problem is transformed into an unconstrained nonlinear programming problem. (33) Solving equation (33) yields the lower limit of the macrocell network capacity. Solving equations (30) and (33) provides the upper and lower limits of the macro base station network capacity of the covert communication system based on the spectrum dynamic control access protocol, which satisfies reliability and security requirements. The capacity analysis of microcells is similar to that of macrocells. Adjusting the minimum reliable transmission probability and minimum secure transmission probability parameters according to different security and reliability requirements in different scenarios yields the upper and lower limits of the number of authorized users that can be accessed.

[0016] ii) Solving network capacity based on the Simulated Annealing-Particle Swarm Optimization (SA-PSO) algorithm.

[0017] A multi-user covert networking system based on dual time scale constraints includes a spectrum dynamic control access protocol generation module and a networking performance evaluation module; The spectrum dynamic control access protocol generation module is used to realize intelligent mapping from physical resources to access decisions; The spectrum dynamic control access protocol generation module first slices the time-frequency resources to form discrete available resource units. Then, using the system clock and user authentication key as random sources, it generates a unique basic sequence for each user. Through cyclic shifting and orthogonalization, the sequence is expanded into a family of orthogonal, pseudo-random decision sequences. Based on the real-time channel status and user service requirements, the spectrum dynamic control access protocol generation module allocates conflict-free, dynamically changing access time-frequency slots for each user at specific times, dynamically generating conflict-free access time slots and frequency band allocation strategies. This enables covert and conflict-free access for multiple users at the underlying level, guiding multiple users to access the network covertly and efficiently as needed. The network performance evaluation module performs macroscopic performance analysis and evaluation on the network running based on the above-mentioned spectrum dynamic control access protocol generation module. The network performance evaluation module analyzes the throughput performance of multi-user access protocols under dual time-scale constraints. Simultaneously, it quantitatively assesses the system's anti-interference and anti-eavesdropping capabilities by calculating the system's reliable and secure transmission probabilities. Based on this, and assuming reliable and secure system operation, the module establishes a network tolerance analysis model and utilizes an improved SA-PSO algorithm to solve for the upper and lower limits of the number of users the network can accommodate, providing accurate and quantitative decision-making basis for long-term planning and adaptive adjustment of network resources.

[0018] The beneficial effects of this invention are: To address the lack of effective theoretical support for multi-user access and network transmission in existing covert communication systems, which makes it difficult to evaluate and optimize network performance, this invention proposes a covert communication networking protocol for multiple users. By dynamically managing and allocating spectrum resources, it guides multiple users to asynchronously access the covert communication network, providing theoretical support for overcoming the performance defects of multi-user covert networking.

[0019] To address the challenge of effectively optimizing throughput and service efficiency in covert communication networks operating in complex electromagnetic environments, this invention introduces a dual-time-scale constraint optimization mechanism based on a multi-user covert networking protocol, proposing a multi-user covert networking method based on dual-time-scale constraints. Under short-time-scale constraints, a probabilistic model based on conflict-free multi-user networking is constructed to guide the server in allocating on-demand real-time computing resources according to the dynamic access protocol, thereby improving system throughput and service efficiency. Under long-time-scale constraints, continuous system-level optimization is performed based on a short-time optimal strategy, ultimately achieving global optimization of system throughput and service efficiency. This mechanism provides a hierarchical, adaptive optimization framework that effectively addresses network dynamics.

[0020] To address the challenge of determining the capacity boundaries of covert networks under reliability and security constraints, this invention proposes an analytical method. This method, while strictly guaranteeing reliable and secure transmission probabilities, determines the upper and lower limits of the number of users a network can accommodate, thereby defining network capacity and providing a crucial theoretical basis for evaluating and optimizing the upper limit of covert network size.

[0021] To address the highly complex and difficult-to-solve problem of network capacity and performance optimization considering multiple constraints (spectrum access, resource allocation, reliability, security, and number of users), this invention proposes a transformation and solution strategy. First, a penalty factor mechanism is used to transform the complex constraint optimization problem into an unconstrained nonlinear programming problem. Then, an improved SA-PSO algorithm is employed to efficiently solve the transformed problem, thereby determining the capacity of the covert communication network. This strategy provides a method for simplifying complex constraint problems and achieving efficient computation.

[0022] This invention constructs a probabilistic model for multi-user conflict-free networking under short-term constraints, guiding servers to allocate computational resources on demand based on dynamic access protocols to improve system throughput and service efficiency. Under long-term constraints, it optimizes system throughput and service efficiency based on optimal computational resource allocation strategies. Simultaneously, by conducting reliability and security analysis on the covert communication system, it calculates reliable and secure transmission probabilities to evaluate its anti-interference and anti-eavesdropping performance, providing a theoretical basis for system optimization design. Under the premise of ensuring the reliability and security of the communication system, it analyzes the upper and lower limits of the number of users the network can accommodate, simplifies the problem to an unconstrained nonlinear programming problem using a penalty factor, and solves it using an improved SA-PSO algorithm, thereby determining the capacity of the covert communication network. Attached Figure Description

[0023] Figure 1 This is a framework diagram of the technical solution of the present invention.

[0024] Figure 2 This is a schematic diagram of the spectrum dynamic control access protocol.

[0025] Figure 3 This is a flowchart of the sequence family orthogonalization process.

[0026] Figure 4 This is a diagram illustrating legitimate user access to the network.

[0027] Figure 5 This is a schematic diagram of the particle swarm optimization algorithm.

[0028] Figure 6 This is a schematic diagram of the SA-PSO algorithm.

[0029] Figure 7To determine the probability of conflict-free networking between the developed protocol and the protocol-free network. Comparison of simulation results.

[0030] Figure 8 For the throughput parameter of covert communication system as a function of service arrival rate Simulation diagram of the changes.

[0031] Figure 9 System throughput versus service arrival rate under different parameters Simulation diagram of the changes.

[0032] Figure 10 The capacity limit of a macrocell network follows the system's minimum reliable transmission probability. Simulation diagram.

[0033] Figure 11 The lower limit of macro cell network capacity depends on the system's minimum anti-interception probability. Simulation diagram. Detailed Implementation

[0034] The present invention will now be described in further detail with reference to the accompanying drawings.

[0035] like Figures 1-6 As shown, a multi-user covert networking method based on dual time scale constraints includes the following steps; Step 1: Time-Frequency Network Resource Slicing Assume that the communication units of the entire covert communication system exist K A legitimate user, firstly, sets the transmission bandwidth to... W The shared channels are all divided into q Zero non-overlapping parts yield a set of idle frequency slots. F 0={ f 1, f 2,…, f q0 Set the reuse factor of each frequency slot to 1. Use high-order cumulant spectrum sensing technology to obtain the contents of the idle frequency slots. q The set of available frequency slots for each element F ={ f 1, f 2,…, f q The average data packet length transmitted by authorized users is set as one transmission cycle. T Occupied during the period L ∈{1, 2, ..., p} time slots, resulting in a set of time slots. T = { t 1, t 2,…, t p}

[0036] Step 2: Generate the basic random sequence M k Based on this, through user authentication keys key Controlled by random functions randi Generate includes L A basic random sequence of elements M 0 ={ m 0 i∣ i =1,2,…, L},in m 0 i∈ F ={ f 1, f 2,…, f q} represents the user U k exist i Each time slot accesses the frequency slot used by the shared channel. To meet the requirements of multi-user access within a period of the covert communication system, iterative transformation processing of the individual sequence is used. K Through iterative transformations, the basic random sequence can be obtained. M k ={ mk 1, mk 2,…, mk L} box g This refers to the substitution box in the block cipher generation algorithm.

[0037] in (1) Step 3: Obtain the extended sequence family through cyclic shift transformation. N L×K To meet the system's requirement of allowing multiple legitimate users to connect simultaneously, a round function is used to process the basic random sequence. Perform cyclic shift transformation (2) in, ε ∈{1, 2, 3, ...} represents the iteration number of the round function. This yields a set of extended sequences, i.e., a family of basic sequences. .

[0038] Step 4: Orthogonalize to obtain the family of decision sequences H L×K To ensure that the frequency bands selected by all licensed users do not interfere with each other within each time slot, this means that the sequences in the iterative sequence family are uncorrelated with each other. Therefore, the iterative sequence family must be... N L×K middle K The sequences are orthogonalized.

[0039] (3) in, This is the shift factor of the orthogonal transformation. Orthogonalization is then performed to... It is necessary to access the decision sequence family. .

[0040] Access to decision sequence family H L×K Under the guidance of the system, legitimate users can access the corresponding frequency slots of the shared channel in an orderly manner, sequentially selecting the corresponding frequency slots within each time slot to access the shared channel.

[0041] Step 5: Implement dual time-scale constraints to achieve optimal throughput. The performance of the access protocol is analyzed, and the optimal network throughput is achieved by utilizing dual time scale constraints. A. Short time scale: Construct a probabilistic model based on multi-user conflict-free networking to guide the server to access dynamic access protocols and calculate resource allocation on demand, thereby improving system throughput and business efficiency.

[0042] The authorized devices in the system are abstracted as network nodes and divided into three types of communication units based on different arrival rates. a unit, b Unit and c Unit. k∈{ 1, 2, 3, ..., K} Two with the same arrival rate G ∈{ G a , G b , G c Taking legitimate users as an example for analysis, we assume that the probability density of legitimate users accessing the channel follows a Poisson distribution.

[0043] In the covert communication system under development, the dynamic spectrum control access protocol proposed in this invention ensures the access decision sequence families generated by different communication cells. H L×K They are independent of each other. Although the sequences within a sequence family are orthogonal, the independent clocks of each communication unit in the covert transmission network cause licensed devices to access the shared channel asynchronously. Therefore, multiple licensed devices from different communication units may access the network through the same frequency slot in the same time slot.

[0044] like Figure 4 As shown, a Unit users U k and c Unit users U 1 in the t One time slot arrives simultaneously on the shared channel, which will... t One frequency slot is further divided into multiple sub-time slots. Analysis from a short time scale... U 1 is in t Access is via the first sub-time slot of 1, while the user U k Is t Network connection begins in the third sub-time slot of segment 1. In this case, the user... U 1 Access f 1 band, user U k The decision should be made to yield, and in accordance with the access decision sequence... t 2. Select the corresponding frequency slot for time slot and reconnect.

[0045] In the protocol under development, the independence of the access decision sequence for different communication units is the cause of network conflicts. t 1 time slot, a Authorized users of the unit U k Not with c Authorized users of the unit U The probability of a co-channel collision is 1. (4) In the formula, ∈ F ={ f 1, f 2,…, f q},express c Authorized users of the unit U 1 in the i Each time slot selects the frequency slot for access; ∈ F ={ f 1, f 2,…, f q},express a Authorized users of the unit U k In the i Each time slot selects the frequency slot for access; express c Authorized users of the unit U 1 and a Authorized users of the unit Uk In the i The probability of accessing different frequency slots in a given time slot.

[0046] Because the access protocol selects frequency slots independently for each time slot, ,but (5) because ,but (6) Therefore, the objective function simplifies to (7) Since L is a positive integer and the base is non-negative, maximizing Y is equivalent to maximizing the base. This is equivalent to minimizing Under constraints and Below, the optimal solution for minimizing the sum of squares is a uniform distribution, i.e. The proof is as follows.

[0047] It is obtained from the Cauchy-Schwarz inequality. (8) Substitution ,have to (9) Easily obtainable if and only if Equal access time. That is, when a user equally accesses any available frequency slot, It has a maximum value of (10) also, q This refers to the number of idle frequency slots. Because authorized devices within the system need to occupy [a certain number of] slots during signal transmission cycles. L Each time slot satisfies the following conditions within one transmission cycle: The maximum probability of conflict-free networking is traversed in the time domain. L Using Taylor series expansion for each time slot, and ignoring higher-order terms (second order and above), we can obtain: (11) The existence of covert communication systems k When there are multiple authorized devices, the probability of no co-channel conflict during network connection is: (12) In the formula, q L represents the number of idle frequency slots, and L represents the number of time slots. k Number of authorized users; B. Long-term scale: Based on the probabilistic model of the collision-free network, calculate the unit throughput, service efficiency and system throughput, etc., and conduct mathematical analysis to study the function graph characteristics to optimize throughput performance under different user volume conditions.

[0048] Throughput is a core metric for measuring the performance of a communication system, referring to the total number of data packets successfully transmitted by a network node per unit of time, directly reflecting the performance of covert communication access protocols. In a communication unit, the time and number of users accessing the shared channel are both random; therefore, the number of data packets transmitted by users can be considered a random variable. The number of these data packets arriving at the base station follows a Poisson distribution. G This indicates its arrival rate over a time interval. Inside, k The probability density function of a data packet arriving at the base station can be expressed as: (13) Then 2 L The throughput of a certain unit within a time slot can be expressed as (14) but L Unit throughput of a communication unit within a time slot (15) From the above equation (13), it can be analyzed that, G and q When determined, TP yes L The negative exponential function, when L When >0, TP Follow L Increases and then slowly decreases; G and L When determined, TP yes q The inverse proportional negative exponential function, q When >0, TP Follow q Increase, but increase slowly. When q , L When determined, in G The throughput function of a unit within the interval [0, +∞) varies with the independent variable. The value increases first and then decreases, and the maximum value is the one that appears.

[0049] To achieve the goals of maximizing resource utilization and optimizing network performance, a mathematical analysis of the cell throughput function is conducted. The optimal time, number of slots, and arrival rate for maximizing cell throughput are investigated. G Find the partial derivative and set it to zero to obtain the maximum unit throughput. (16) but G Pick G = q / (1+ L The maximum throughput of the unit can be obtained as follows: (17) To measure the service transmission efficiency of legitimate users accessing the network within the unit, the unit throughput is normalized to obtain the service efficiency of the researched communication unit. (18) Based on the above, the communication system is divided into different units according to the arrival rate. Three categories, assuming the existence of a business arrival rate parameter. δ Therefore, considering the differences in the volume of services per unit within the entire communication system, the arrival rates of the three types of communication units are substituted to obtain the throughput of the covert communication system. (19) To fully reflect the changes in system throughput with data arrival rate, it is assumed that the number of authorized users in each unit is basically within a fixed range, assuming that a service arrival rate parameter exists. δ The change in traffic volume in different units at a certain moment depends on the service arrival rate parameter. δ ,make (20) Substituting the values, we can obtain the system throughput. (twenty one) According to formula (21), the throughput of a covert communication system is affected by the number of time slots. L , number of frequency slots q and data arrival rate G Therefore, similar to the mathematical analysis of unit throughput, the optimal time slot and frequency slot allocation should be determined based on the number of legitimate users in the system and different data arrival rates to maximize system throughput performance.

[0050] Step Six: System Reliability and Security Analysis The preceding text has analyzed the system throughput and service efficiency of covert communication systems. However, reliability and security issues cannot be ignored. By conducting reliability and security analysis on covert communication systems and calculating reliable and secure transmission probabilities, we can assess their anti-interference and anti-eavesdropping performance, providing a theoretical basis for system optimization design. This also provides insights into the network tolerance problem of covert communication systems. Based on ensuring the reliability and security of covert communication, analyzing the upper and lower limits of users for macro base stations and micro base stations can determine network capacity.

[0051] i) Reliable transmission performance analysis The signal-to-interference-plus-noise ratio (SIR) of the signal received by the authorized user is (twenty two) in, P u This indicates the power of the signal received by the user from the base station. I un,u This indicates the interference power of the malicious interference source on the transmitted signal. I c,u This indicates the power of inter-unit co-frequency interference. N 0 represents the ambient noise power. According to the principle of the researched access protocol, malicious interference has already been removed during the generation of the available frequency slot set in step one. I un,u = 0, N 0 defaults to the power of complex Gaussian white noise with zero mean.

[0052] Assume the decoding threshold of the shared channel is δ u The reliable transmission probability is the probability that all information transmitted by the sender is successfully received and decoded by the receiver. P BS For macro base station power, P bs The power of the micro base station is [value], and the number of micro base stations is [value]. n Users associated with macro base stations will access frequency slots under the guidance of the developed protocol. f j The probability of transmission is expressed as . u This refers to the number of users associated with a macro base station. BS With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ε 2 The exponential distribution; v This refers to the number of users associated with a micro base station. With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ω 2 The exponential distribution. Then authorized users from macro base stations. BS The probability of reliable transmission of received data packets is (twenty three) Similarly, authorized users from micro base stations The probability of reliable transmission of received data packets is (twenty four) In the formula, P BS For macro base station power, P bs For micro base station power, n For the number of micro base stations, q For the number of frequency slots, L The number of time slots, v It is the number of users associated with the micro base station. δ u The decoding threshold for the shared channel. N 0 represents the power of complex Gaussian white noise with zero mean, and is used in micro base stations. With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ω 2 Exponential distribution, macro base station BS With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ε 2 The exponential distribution; ii) Security transmission performance analysis The signal-to-interference-plus-noise ratio (SIR) of the signal intercepted by the eavesdropper can be (25) in, P e This indicates the signal power sent to the eavesdropper. I un,e This indicates the interference power of the malicious interference source on the transmitted signal from the eavesdropper. I c,e This indicates the power of inter-unit interference to the eavesdropper on the same frequency. N 0 represents the ambient noise power. N 0 defaults to zero-mean complex Gaussian white noise power. According to the developed access protocol, the system can actively avoid interference signals from malicious sources. I un,e = 0.

[0053] Assume the decoding threshold of the transmission channel is δ e The probability of secure transmission is defined as the success rate at which information cannot be intercepted and decoded by eavesdroppers. Macro base station BS The channel gain to the eavesdropper is This value follows the parameter. λ 2 Exponential distribution; micro base stations The channel gain to the eavesdropping channel is This value follows the parameter. μ 2 The exponential distribution follows. Therefore, the secure transmission probability of a macro base station is... (26) Similarly, authorized users can obtain information from micro base stations. The probability of secure transmission of received data packets is (27) In the formula, P BS For macro base station power, P bs For micro base station power, n For the number of micro base stations, q For the number of frequency slots, L The number of time slots, v It is the number of users associated with the micro base station. δ e The decoding threshold for the shared channel. N 0 represents the power of complex Gaussian white noise with zero mean, for macro base stations. BS The channel gain to the eavesdropper is This value follows the parameter. λ 2 Exponential distribution; micro base stations The channel gain to the eavesdropping channel is This value follows the parameter. μ 2 The exponential distribution; Based on this, the user number variable in the derived formulas (23) and (26) is separated. u This allows us to obtain the upper and lower limits of the number of users associated with the macro base station under reliability and security constraints; the user number variables in the separated formulas (24) and (27) can be obtained. v This allows us to obtain the upper and lower limits of the number of users associated with the micro base station based on reliability and security constraints.

[0054] Step 7: Network Tolerance Analysis and Solution Based on the analysis of the system's reliable and secure transmission performance above, this paper studies the network tolerance problem of covert communication systems using the developed spectrum dynamic control access theory. Network capacity is a key indicator for evaluating network performance, indicating the maximum number of users the network can support under specific conditions. By analyzing the upper and lower limits of users for macro base stations and micro base stations while ensuring the reliability and security of covert communication, the network capacity can be determined. This analysis not only verifies the accuracy of the network capacity but also provides guidance for designing covert communication networks adapted to different scenarios.

[0055] i) Macrocell network capacity analysis Let the minimum allowable reliable transmission probability of the system be denoted as . P r,min Combining the system reliable transmission expression (23), we can obtain the inequality. (28) Number of users u Incorporating polynomial and logarithmic functions, the above equation can be transformed into a nonlinear constraint problem. (P1): (29) To simplify the problem, a penalty factor is used. and penalty function This nonlinear constrained problem is transformed into an unconstrained nonlinear programming problem. (30) Solving equation (30) above will yield the upper limit of the macrocell network capacity.

[0056] Similarly, the minimum probability of the system being able to resist interception is denoted as... P s,min Combining the system's secure transmission probability expression (26), we can obtain (31) Number of users u Containing both polynomial and logarithmic functions, the lower bound of macrocell network capacity is expressed as the following nonlinear constraint problem. (P2): (32) Using penalty factors and penalty function This nonlinear constrained problem is transformed into an unconstrained nonlinear programming problem. (33) Solving equation (33) yields the lower limit of the macrocell network capacity. Solving equations (30) and (33) provides the upper and lower limits of the macro base station network capacity of a covert communication system based on a spectrum dynamic control access protocol, satisfying reliability and security requirements. The capacity analysis for microcells is similar to that for macrocells. Adjusting the minimum reliable transmission probability and minimum secure transmission probability parameters for different security and reliability requirements in different scenarios yields the upper and lower limits of the number of authorized users that can access the network.

[0057] ii) Network capacity solution based on SA-PSO algorithm Given the numerous parameters and complex, variable solution space in the tolerance expressions for macrocell and microcell networks, a single heuristic algorithm is insufficient to meet the requirements of computational accuracy and reliability. Therefore, this paper proposes the SA-PSO algorithm, which combines simulated annealing with particle swarm optimization (PSO) and improves upon the traditional PSO algorithm. This algorithm achieves a balance between global optimization and local exploitation, providing a new solution for solving the tolerance problems of macrocell and microcell networks.

[0058] The particle swarm optimization algorithm treats particles as massless points and places them in a multidimensional solution space (with the same dimension as the independent variables). Each particle has a position, velocity (which determines the direction and distance of flight), and a corresponding fitness value. Let the particle swarm size be m and the solution space dimension be N; the particle swarm parameters are shown in Table 1.

[0059] Table 1 Particle Swarm Parameter Table A particle searches the solution space based on its historical best position (pbest) and the group's global best position (gbest). Its motion state is determined by its current state, individual experience, and group experience. Its expression is as follows: (34) in, rand (1) represents a random number within the interval (0,1). Inertia weight. ω It reflects trust in the current state of motion of the particle; acceleration factor a 1 and a 2. Control the degree of reference to individual optimal and group optimal experiences respectively. The particle position update formula is: The particle swarm optimization algorithm flowchart is shown in the figure below.

[0060] Particle swarm optimization (PSO) is a swarm intelligence-based optimization algorithm that searches for the optimal solution by simulating the movement of individuals in the solution space. However, traditional algorithms have limitations: they are sensitive to the initial population and easily deviate from the optimal path early on; they are also prone to premature convergence, getting trapped in local optima, which reduces their reliability and effectiveness. To improve these issues, this paper introduces an inertia weight model and a convergence factor model to optimize key parameters.

[0061] Inertia Weight Model: In the traditional particle swarm optimization algorithm, inertia weight... It is a constant in the interval (0,1). Studies have shown that larger... It is conducive to escaping local optima and is relatively small. To promote convergence. To balance the global exploration and local exploitation capabilities of the SA-PSO algorithm, It needs to be adaptively adjusted during the iteration process, that is, it decreases linearly with each iteration. The update strategy is as follows: (35) in , They are respectively The maximum and minimum values, , These represent the number of iterations and their maximum value, respectively.

[0062] Convergence Factor Model: To improve the convergence of the algorithm, the SA-PSO algorithm introduces a convergence factor model, the specific expression of which is as follows: (36) in Studies have shown that At this time, the algorithm has good convergence. In summary, the improved particle swarm optimization algorithm model is as follows: (37) The SA-PSO algorithm for solving network tolerance is as follows: Figure 6 As shown. Solving the tolerance of multi-user covert communication networks requires balancing trend capture and precise numerical calculation, demanding that the algorithm possess both global optimization and local exploitation capabilities. Therefore, an improved SA-PSO algorithm is adopted, using network tolerance as the independent variable. At the global level, simulated annealing is used to capture its dynamic trend and determine the solution set intervals under different conditions. Within each interval, an improved particle swarm optimization algorithm is used for local fine-grained search to obtain the final solution.

[0063] To demonstrate the practicality and effectiveness of the proposed solution, simulation results of the collision-free networking probability under no access protocol guidance are compared with theoretical curves of the collision-free probability under the guidance of the developed protocol. Time and frequency slot parameter settings. L =8、 q =1024, number of connected users k Within the range [0, 1024].

[0064] Depend on Figure 7As can be seen, the simulation results of the system lacking access protocol guidance exhibit significant dispersion and are consistently lower than the theoretical curve for collision-free probability. This indicates that without protocol guidance, authorized users' frequency band usage in the wireless network is highly chaotic, increasing the likelihood of co-channel collisions. In the absence of a protocol, each user independently accesses the shared channel, and their frequency band selection behavior is random and independent. Therefore, as the number of users in the system increases, the probability of collisions also increases, and the occurrence of collisions is highly random, which explains the large fluctuations in the simulation results.

[0065] Based on this, the case without protocol guidance is defined as the standard solution, and it will be compared with the protocol developed in this invention in the system performance analysis below.

[0066] (1) Simulation results and analysis of network throughput Figure 8 The arrival rate parameter is shown. δ The impact on system throughput includes the theoretical throughput curve of the studied protocol, simulation results, and simulation results of the standard scheme. System parameters are set as follows: L =8、 q =128, to simplify the analysis, assume the arrival rate of the three types of units is 128. g a = g b = g c = g =0.3, and the parameter settings in the simulation model are the same. As can be seen from the figure, the simulation results of the system throughput based on the studied protocol are in good agreement with the theoretical curve, thus verifying the theoretical derivation of system throughput in this paper. Furthermore, the system throughput curve of the studied protocol is higher than the simulation results of the standard scheme, showing better throughput performance. Due to the guidance of the dynamic control access protocol, users can access the network more orderly for data transmission, significantly improving spectrum utilization. In contrast, the scheme without protocol guidance suffers from increased retransmission probability due to frequent network collisions, resulting in lower system throughput than the studied protocol. This further confirms the necessity of network optimization for covert communication systems.

[0067] Figure 8 The display shows that system throughput increases with... δ The increase first reaches a peak, and then gradually declines. In the initial stage, δ The increase in arrival rate leads to a rise in traffic volume, with more authorized users accessing the shared channel, causing the number of data packets arriving at the base station to increase to its maximum value. According to the mathematical analysis in Section 4, when the arrival rate... G At approximately 14.2, the throughput reaches its extreme point, from which it can be calculated that... δ It is approximately 47.4, which matches the data in the graph. However, if δFurther increases will lead to a decrease in system throughput due to limited bandwidth resources and an increased risk of co-channel conflicts.

[0068] Figure 9 This demonstrates the variation in system throughput under different selections of time slot and frequency slot parameters. Analyzing the impact of a single variable, we find that with a fixed number of time slots, the throughput increases with the number of frequency slots. q With the increase of frequency slots, the system throughput increases; however, with a fixed number of frequency slots, as the number of time slots increases... L The increase in frequency slots leads to a decrease in system throughput. This is because allocating more frequency slots or shortening the transmission signal length can effectively reduce the probability of co-slot collisions during data access in covert communication systems. Therefore, the time and frequency slot parameters of the researched access protocol should be set according to different actual communication scenarios, based on the urgency of communication needs and the reasonable allocation of relevant resources, to balance the contradiction between system reliability, effectiveness, and economy. Guided by the throughput expression and mathematical analysis in Section 4, and taking into account the influence of the average number of authorized users per unit time and the arrival rate parameter of each unit, corresponding parameters are allocated in the time and frequency domains to achieve a suitable system throughput while approaching the maximum throughput, thereby obtaining optimized network performance.

[0069] (2) Network tolerance The simulation parameters for the covert communication system are set as follows: Table 2 Simulation parameters of covert communication system Figure 10 Demonstrates the lowest reliable transmission probability P r,min The impact on the upper limit of macro cell network capacity was analyzed, and the effect on the number of time slots was also examined. L Under the condition of 8, different frequency slot numbers q The role of macro base station network tolerance in the studied covert communication system is illustrated in the figure. It is clearly shown that as the minimum reliable transmission probability increases, the upper limit of users who can access the macro base station network decreases while ensuring reliability. This is because higher transmission reliability requirements limit the number of authorized users within a unit to reduce network collisions. Due to noise and fading in the shared channel, it is impossible to guarantee error-free transmission for every user; therefore, when the reliable transmission probability approaches 1, the upper limit of the number of users connected to the macro base station approaches zero. Furthermore, Figure 10 It also shows that, with the number of frequency slots q With the increase in the number of frequency slots, the network capacity limit also increases. This is because the increased number of frequency slots provides more options, reduces networking conflicts between units, and allows more authorized users to access the network while ensuring reliability.

[0070] Figure 11 Demonstrates the lowest probability of resistance to interception Pr,min The impact on the lower limit of macro cell network capacity was analyzed, and the effect on the number of time slots was also examined. L With a frequency of 8, different numbers of frequency slots q Impact on macro base station network tolerance. Observation. Figure 11 It can be observed that as the minimum probability of interception increases, the lower limit of macro base station network capacity also increases accordingly. This is because when there are few users accessing the shared channel, even with measures such as transformation encryption, the communication channel may still be intercepted by passive eavesdroppers, leading to information leakage. Therefore, increasing the number of licensed users to fully utilize the spectrum can effectively reduce the risk of channel interception, thereby enhancing system security. Simultaneously, the number of frequency slots... q The more frequency slots a system has, the fewer authorized users are required, meaning a lower minimum network capacity. This is because increasing the number of frequency slots provides users with more options for accessing the system at different times, making it more difficult for unauthorized eavesdroppers to intercept valid information. Therefore, under the same security requirements, a system with more frequency slots can allow fewer authorized users to access the system to achieve the required anti-interception performance.

[0071] This invention covers all methods involving multi-user covert networking protocols based on dual time-scale constraints to guide multi-user access to communication networks. This includes, but is not limited to: using a family of decision sequences based on dynamic spectrum control to guide legitimate users to access shared channels during the transmission and reception of communication signals, and applying access protocols based on dynamic spectrum control for communication. The invention optimizes network performance using a multi-user covert networking method based on dual time-scale constraints. Under short-term constraints, a probabilistic model based on collision-free multi-user networking is constructed, and on-demand real-time computing resource allocation is performed based on this model and the aforementioned protocol to improve system throughput and service efficiency. Under long-term constraints, system-level optimization is performed based on the optimal strategy for computing resource allocation to achieve optimal system throughput and service efficiency. The invention also analyzes the reliability and security of covert communication systems by applying methods for calculating reliable and secure transmission probabilities to evaluate their anti-interference and anti-eavesdropping performance, providing a theoretical basis for system optimization design. Finally, while ensuring the reliability and security of the communication system, the analysis method of this invention is used to determine the upper and lower limits of the number of users that can be accommodated. To address the highly complex and difficult-to-solve problem of network capacity and performance optimization, this invention employs a transformation and solution strategy. First, a penalty factor mechanism is used to transform the complex constrained optimization problem into an unconstrained nonlinear programming problem. Then, an improved SA-PSO algorithm is used to efficiently solve the transformed problem, thereby determining the capacity of the covert communication network.

[0072] This invention constructs a probabilistic model for multi-user conflict-free networking under short-term constraints, guiding servers to allocate computational resources on demand based on dynamic access protocols to improve system throughput and service efficiency. Under long-term constraints, it optimizes system throughput and service efficiency based on optimal computational resource allocation strategies. Simultaneously, by conducting reliability and security analysis on the covert communication system, it calculates reliable and secure transmission probabilities to evaluate its anti-interference and anti-eavesdropping performance, providing a theoretical basis for system optimization design. While ensuring the reliability and security of the communication system, it analyzes the upper and lower limits of the number of users the network can accommodate, simplifies the problem into an unconstrained nonlinear programming problem using a penalty factor, and solves it using an improved Simulated Annealing-Particle Swarm Optimization (SA-PSO) algorithm to determine the capacity of the covert communication network. This invention is expected to improve the limited networking performance of covert communication systems in practical applications, increase the throughput and network capacity of communication systems, and provide effective theoretical support and technical guarantees for protecting personal privacy and corporate secrets, and safeguarding national security.

[0073] This method is applicable to the networking of covert communication systems in complex electromagnetic environments, including but not limited to wireless communication and satellite communication applications involving personal privacy, corporate secrets, or national security.

[0074] This invention also protects various covert communication systems and related equipment developed based on the method. This includes, but is not limited to: systems integrating a spectrum dynamic control access protocol module in the design and implementation of communication systems for dynamically coordinating multi-user access and spectrum resource management; and servers or network control devices equipped with a dual-timescale optimization engine, which includes functional units for short-term probability modeling and resource allocation, as well as functional units for long-term system optimization. A communication node or device including a reliability and security transmission probability calculation and analysis module for real-time monitoring and ensuring the reliability and security of data transmission; a device with a network capacity boundary analysis module for dynamically evaluating and controlling the number of accessible users under reliability and security constraints; and a dedicated processor, computing card, or embedded system running an improved SA-PSO algorithm for efficiently solving the unconstrained nonlinear programming problem as described in claim 1.

[0075] The aforementioned systems and equipment can be deployed independently or integrated into existing communication infrastructure as add-on modules, and are suitable for various communication network environments that require high concealment and security.

[0076] Through the two protection points mentioned above, this invention strives to comprehensively cover multi-user covert communication networking technology based on dual time scale constraints, ensuring broad protection in technology implementation and application, thereby obtaining strong protection in terms of intellectual property rights.

Claims

1. A multi-user covert networking method based on dual time-scale constraints, characterized in that, Includes the following steps; Step 1: Perform time-frequency network resource slicing to obtain a set of available time-frequency slots; Step 2: Based on the available time slot set, and under the influence of the system clock and the user authentication key, obtain the basic random sequence. M k ; Step 3: Transform the basic random sequence M k Cyclic shift transformation yields an extended sequence family N L×K ; Step 4: Extend the sequence family N L×K Orthogonalization process yields a family of decision sequences H L×K To guide multiple users to access the network; Step 5: Authorize user access protocol performance analysis and apply dual time scale constraints to achieve optimal network throughput; Step Six: Reliability and security analysis of the covert communication system; Step 7: Analyze the tolerance of the covert communication system and use the improved SA-PSO algorithm to solve for the upper and lower limits of the number of users the system can accommodate.

2. The multi-user covert networking method based on dual time scale constraints according to claim 1, characterized in that, Step one specifically involves: The communication units of the entire covert communication system are configured to exist. K A legitimate user, firstly, sets the transmission bandwidth to... W The shared channels are all divided into q Zero non-overlapping parts yield a set of idle frequency slots. F 0={ f 1, f 2,…, f q0 Set the reuse factor of each frequency slot to 1; use spectrum sensing technology with high-order cumulants to obtain the contents of the idle frequency slots. q The set of available frequency slots for each element F ={ f 1, f 2,…, f q }; A transmission cycle is defined as the average data packet length transmitted by authorized users, and the period occupied within the cycle is... L ∈{1, 2, ..., p } time slots, resulting in a set of available time slots. T = { t 1, t 2,…, t p } 3. The multi-user covert networking method based on dual time scale constraints according to claim 2, characterized in that, Step two specifically involves: Based on the already obtained set of available time slots, through the user authentication key key Controlled by random functions randi Generate includes L A basic random sequence of elements M 0 ={ m 0 i | i =1,2,…, L },in m 0 i ∈ F ={ f 1, f 2,…, f q } indicates that the authorized user is in the first... i Each time slot accesses the shared channel using its frequency slots; this individual sequence is then... K Rounds of iterative transformations yield the basic random sequence. M k ={ mk 1, mk 2, …, mk L },in (1) In the formula mk i ∈ F ={ f 1, f 2,…, f q } indicates authorized user U k In the i The frequency slots used by each time slot to access the shared channel key i The authentication key used to authorize users to access the network units controlled by the current base station. box g This is the substitution box in the block cipher generation algorithm, and ⊕ is the XOR operator.

4. The multi-user covert networking method based on dual time scale constraints according to claim 3, characterized in that, Step three specifically involves: Using round functions to transform the basic random sequence M k A cyclic shift transformation is performed to meet the system's requirement of allowing multiple legitimate users to access the system simultaneously. (2) In the formula, ε ∈{1, 2, 3, ...} represents the number of iterations of the round function, which yields a set of extended sequences, i.e., the family of basic sequences. ,in nk i Indicates that the authorized user is in the i Each time slot accesses the frequency slot used by the shared channel.

5. A multi-user covert networking method based on dual time scale constraints according to claim 4, characterized in that, Step four specifically involves: For iterative sequence families N L×K middle K Each sequence is orthogonalized. (3) in, The shift factor is an orthogonal transformation factor, which is then orthogonalized to make... It is necessary to access the decision sequence family. ; in accessing the decision sequence family H L×K Under the guidance of the system, legitimate users access the corresponding frequency slots of the shared channel in an orderly manner, and sequentially select the corresponding frequency slots in each time slot.

6. The multi-user covert networking method based on dual time scale constraints according to claim 5, characterized in that, Step five specifically involves: The performance of the access protocol is analyzed, and the optimal network throughput is achieved by utilizing dual time scale constraints. A. Short time scale: Construct a probabilistic model based on multi-user conflict-free networking to guide the server to access dynamic access protocol and calculate resource allocation on demand, so as to improve system throughput and business efficiency; The authorized devices in the system are abstracted as network nodes and divided into three types of communication units based on different arrival rates. a unit, b Unit and c Unit; with k∈{ 1, 2, 3, ..., K} Two with the same arrival rate G ∈{ G a , G b , G c The analysis of legitimate users is performed, and the probability density of legitimate users accessing the channel is set to follow a Poisson distribution; The dynamic spectrum control access protocol ensures the access decision sequence families generated by different communication cells. H L×K They are independent of each other; a Unit users U k and c Unit users U 1 in the t One time slot arrives simultaneously on the shared channel, which will... t One frequency slot is further divided into multiple sub-time slots; analysis is performed on a short time scale. U 1 is in t Access is via the first sub-time slot of 1, while the user U k Is t The network connection begins in the third sub-time slot of 1; in this case, the user U 1 Access f 1 band, user U k The decision should be made to yield, and in accordance with the access decision sequence... t 2. Select the corresponding frequency slot for time slot reconnection; The independence of access decision sequences for different communication units is the cause of network collisions. t 1 time slot, a Authorized users of the unit U k Not with c Authorized users of the unit U The probability of a co-channel collision is 1. (4) In the formula, ∈ F ={ f 1, f 2,…, f q },express c Authorized users of the unit U 1 in the i Each time slot selects the frequency slot for access; ∈ F ={ f 1, f 2,…, f q },express a Authorized users of the unit U k In the i Each time slot selects the frequency slot for access; express c Authorized users of the unit U 1 and a Authorized users of the unit U k In the i The probability of each time slot accessing a different frequency slot is given by ,but (5) In the formula P j Indicates authorized user access to frequency slots f j The probability, j ∈{1,2,…, q },because ,but (6) The objective function simplifies to (7) Since L is a positive integer and the base is non-negative, maximizing Y is equivalent to maximizing the base. This is equivalent to minimizing Under constraints and Below, the optimal solution for minimizing the sum of squares is a uniform distribution, i.e. ; The proof is as follows: Obtained from the Cauchy-Schwarz inequality (8) Substitution ,have to (9) Easily obtainable if and only if Time to take, etc. P j Indicates authorized user access to frequency slots f j The probability, j ∈{1,2,…, q That is, when a user equally accesses any available frequency slot, a Authorized users of the unit U k and c Authorized users of the unit U 1. Probability of no co-slot collision It has a maximum value of (10) In the formula, q This refers to the number of idle frequency slots; the signal transmission cycle of authorized devices within the system requires the use of [a specific frequency slot]. L Each time slot satisfies the following conditions within one transmission cycle: The maximum probability of conflict-free networking is traversed in the time domain. L In each time slot, using Taylor series expansion and ignoring higher-order terms above second order, we obtain: (11) The existence of covert communication systems k When there are multiple authorized devices, the probability of no co-channel conflict during network connection is: (12) In the formula, q L represents the number of idle frequency slots, and L represents the number of time slots. k Number of authorized users; B. Long-term scale: Based on the probabilistic model of the collision-free network, calculate the unit throughput, service efficiency and system throughput, and conduct mathematical analysis to study the function graph characteristics so as to achieve the optimal throughput performance under different user volume conditions; If we take G This indicates its arrival rate over a time interval. Inside, k The probability density function of the data packets arriving at the base station is expressed as follows: (13) Then 2 L The throughput of a certain unit within a time slot is expressed as (14) In the formula, L The number of time slots, q The number of idle frequency slots. express k The probability density function of each data packet arriving at the base station. G This indicates its arrival rate. If the probability of conflict-free networking is given, then... L Unit throughput of a communication unit within a time slot (15) From the above equation (13), we can deduce that G and q When determined, TP yes L The negative exponential function, when L When >0, TP Follow L Increases and then slowly decreases; G and L When determined, TP yes q The inverse proportional negative exponential function, q When >0, TP Follow q Increase, but increase slowly; when q , L When determined, in G The throughput function of a unit within the interval [0, +∞) varies with the independent variable. The value is the maximum if it first increases and then decreases. right G Find the partial derivative and set it to zero to obtain the maximum value of the unit throughput, i.e. (16) but G Pick G = q / (1+ L The maximum throughput of the unit is obtained as follows: (17) Normalizing the unit throughput yields the service efficiency of the researched communication unit. (18) Based on arrival rate, different units of the communication system are divided into Three categories, each with a defined service arrival rate parameter. δ Substitute the arrival rates of the three types of communication units to obtain the throughput of the covert communication system. (19) Set the service arrival rate parameter. δ The change in traffic volume in different units at a certain moment depends on the service arrival rate parameter. δ ,make (20) Substitute to obtain system throughput (21) According to formula (21), the throughput of a covert communication system is affected by the number of time slots. L , number of frequency slots q and data arrival rate G The optimal time slot and frequency slot allocation is determined based on the number of legitimate users in the system and different data arrival rates, thereby maximizing the system throughput performance.

7. A multi-user covert networking method based on dual time-scale constraints according to claim 6, characterized in that, Step six specifically involves: i) Reliable transmission performance analysis The signal-to-interference-plus-noise ratio (SIR) of the signal received by the authorized user is (22) in, P u This indicates the power of the signal received by the user from the base station. I un,u This indicates the interference power of the malicious interference source on the transmitted signal. I c,u This indicates the power of inter-unit co-frequency interference. N 0 represents the ambient noise power; according to the principle of the researched access protocol, malicious interference has been removed when the available frequency slot set is generated in step one, therefore... I un,u = 0, N 0 represents the power of complex Gaussian white noise with zero mean; Set the decoding threshold for the shared channel to δ u The reliable transmission probability is the probability that all information transmitted by the sender is successfully received and decoded by the receiver. P BS For macro base station power, P bs The power of the micro base station is [value], and the number of micro base stations is [value]. n Users associated with macro base stations will be guided by the developed protocol to access frequency slots. f j The probability of transmission is expressed as ; u This refers to the number of users associated with a macro base station. BS With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ε 2 The exponential distribution; v This refers to the number of users associated with a micro base station. With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ω 2 The exponential distribution then authorizes users from macro base stations. BS The probability of reliable transmission of received data packets is (23) Similarly, authorized users from micro base stations The probability of reliable transmission of received data packets is (24) In the formula, P BS For macro base station power, P bs For micro base station power, n For the number of micro base stations, q For the number of frequency slots, L The number of time slots, v It is the number of users associated with the micro base station. δ u The decoding threshold for the shared channel. N 0 represents the power of complex Gaussian white noise with zero mean, and is used in micro base stations. With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ω 2 Exponential distribution, macro base station BS With authorized users in the L Access frequency slots in time slots f j The channel gain for transmission is This value follows the parameter. ε 2 The exponential distribution; ii) Security transmission performance analysis The signal-to-interference-plus-noise ratio of the signal intercepted by the eavesdropper is expressed as: (25) in, P e This indicates the signal power sent to the eavesdropper. I un,e This indicates the interference power of the malicious interference source on the transmitted signal from the eavesdropper. I c,e This indicates the power of inter-unit interference to the eavesdropper on the same frequency. N 0 represents the ambient noise power. N 0 represents the power of complex Gaussian white noise with zero mean; I un,e = 0; Set the decoding threshold of the transmission channel to δ e The probability of secure transmission is defined as the success rate at which information cannot be intercepted and decoded by eavesdroppers; macro base stations BS The channel gain to the eavesdropper is This value follows the parameter. λ 2 Exponential distribution; micro base stations The channel gain to the eavesdropping channel is This value follows the parameter. μ 2 If the distribution follows an exponential pattern, then the secure transmission probability of the macro base station is: (26) Similarly, authorized users can access micro base stations. The probability of secure transmission of received data packets is (27) In the formula, P BS For macro base station power, P bs For micro base station power, n For the number of micro base stations, q For the number of frequency slots, L The number of time slots, v It is the number of users associated with the micro base station. δ e The decoding threshold for the shared channel. N 0 represents the power of complex Gaussian white noise with zero mean, for macro base stations. BS The channel gain to the eavesdropper is This value follows the parameter. λ 2 Exponential distribution; micro base stations The channel gain to the eavesdropping channel is This value follows the parameter. μ 2 The exponential distribution; The number of users in the separated formulas (23) and (26) u That is, to obtain the upper and lower limits of the number of users associated with the macro base station under the constraints of reliability and security; and to separate the user number variables in the resulting formulas (24) and (27). v This means obtaining the upper and lower limits of the number of users associated with the micro base station based on reliability and security constraints.

8. A multi-user covert networking method based on dual time-scale constraints according to claim 7, characterized in that, Step seven specifically involves: i) Macrocell network capacity analysis Let the minimum allowable reliable transmission probability of the system be denoted as . P r,min Combining the system reliable transmission expression (23), we obtain the inequality. (28) Number of users u Incorporating polynomial and logarithmic functions, the above equation is transformed into a nonlinear constrained problem. (P1): (29) Using penalty factors and penalty function This nonlinear constrained problem is transformed into an unconstrained nonlinear programming problem. (30) Solving equation (30) above will yield the upper limit of the macrocell network capacity; Similarly, the minimum probability of the system being able to resist interception is denoted as... P s,min Combining the system's secure transmission probability expression (26), we get (31) Number of users u Containing both polynomial and logarithmic functions, the lower bound of macrocell network capacity is expressed as the following nonlinear constraint problem. (P2): (32) Using penalty factors and penalty function This nonlinear constrained problem is transformed into an unconstrained nonlinear programming problem. (33) Solving equation (33) above will yield the lower limit of the macro cell network capacity. Solving equations (30) and (33) will yield the upper and lower limits of the macro base station network capacity of the covert communication system based on the spectrum dynamic control access protocol, which meets the requirements of reliability and security. The capacity analysis of microcells is similar to that of macrocells. By adjusting the minimum reliable transmission probability and minimum secure transmission probability parameters for different security and reliability requirements in different scenarios, the upper and lower limits of the number of authorized users that can be accessed can be obtained. ii) Solving network capacity based on the simulated annealing-particle swarm optimization (SA-PSO) algorithm Particle swarm optimization treats particles as massless points placed in a multidimensional solution space, where each particle has a position, velocity, and corresponding fitness value; let the particle swarm size be... m The solution space dimension is N ,in , indicating the first The position vector of each particle; , indicating the first The speed of flight of each particle; , indicating the first The optimal position found by each particle; , representing the optimal position found by the entire particle swarm; The particle searches the solution space based on its historical best position and the population's global best position, as expressed below. (34) in, rand (1) represents a random number within the interval (0,1), with inertial weight. ω It reflects trust in the current state of motion of the particle; acceleration factor a 1 and a 2. Control the degree of reference to individual optimal and group optimal experiences respectively; the particle position update formula is: ; The inertia weight decreases linearly with iteration. The update strategy is as follows: (35) in , They are respectively The maximum and minimum values, , These represent the number of iterations and their maximum value, respectively. Convergence Factor Model: The SA-PSO algorithm introduces a convergence factor model, the specific expression of which is as follows: （36） In summary, the improved particle swarm optimization algorithm model is as follows: (37) In the formula, a 1 and a 2 is the acceleration factor, which controls the degree of reference to individual optimal and group optimal experiences respectively. rand(1) represents a random number in the interval (0,1). For inertial weights, , They are respectively The maximum and minimum values, , These represent the number of iterations and their maximum value, respectively. , indicating the first The position vector of each particle; , indicating the first The speed of flight of each particle; , indicating the first The optimal position found by each particle; , which represents the optimal position found by the entire particle swarm.

9. A multi-user covert networking system based on dual time-scale constraints for implementing the method of any one of claims 1-8, characterized in that, This includes a spectrum dynamic control access protocol generation module and a network performance evaluation module; The spectrum dynamic control access protocol generation module is used to realize intelligent mapping from physical resources to access decisions; The spectrum dynamic control access protocol generation module first slices the time and frequency resources to form discrete available resource units; Using the system clock and user authentication key as random sources, a unique basic sequence is generated for each user; and through cyclic shifting and orthogonalization processing, this sequence is expanded into a family of orthogonal, pseudo-random decision sequences; the spectrum dynamic control access protocol generation module allocates conflict-free, dynamically changing access time slots for each user at specific times according to the real-time channel status and user service requirements, dynamically generates conflict-free access time slots and frequency band allocation strategies, realizes covert and conflict-free access for multiple users at the underlying level, and guides multiple users to access the network covertly and efficiently as needed; The network performance evaluation module performs macroscopic performance analysis and evaluation on the network running based on the above-mentioned spectrum dynamic control access protocol generation module. The network performance evaluation module analyzes the throughput performance of multi-user access protocols under dual time-scale constraints. Simultaneously, it quantitatively assesses the system's anti-interference and anti-eavesdropping capabilities by calculating the system's reliable and secure transmission probabilities. Based on this, and assuming reliable and secure system operation, the module establishes a network tolerance analysis model and utilizes an improved SA-PSO algorithm to solve for the upper and lower limits of the number of users the network can accommodate, providing accurate and quantitative decision-making basis for long-term planning and adaptive adjustment of network resources.

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