A covert communication method based on block parameter uncertainty
By constructing a covert communication model for multi-user dynamic access scenarios and deriving eavesdropper judgment rules, and combining equivalent power variance and pulse shaping strategies, the problem of easy detection of eavesdroppers' communication behavior in multi-user dynamic environments is solved, and more efficient covert communication is achieved.
Patent Information
- Application Number
- CN202610396485.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-30
- Publication Date
- 2026-06-30
AI Technical Summary
Existing covert communication technologies have failed to effectively adapt to the uncertainty of block parameters in multi-user dynamic environments, making it easy for eavesdroppers to detect communication behavior, resulting in low communication capacity and a lack of adaptability, making it difficult to balance the relationship between covertness and communication capacity.
A covert communication model for multi-user dynamic access scenarios is constructed, the rules for judging covert communication by eavesdroppers are derived, an equivalent power variance is introduced, the optimal transmission power is obtained through a pulse shaping transmission strategy, and an equivalent power model of pulse shaping is constructed using a roll-off factor to ensure that eavesdroppers cannot reliably distinguish communication signals.
This significantly improves the model's applicability and practicality, ensures more rigorous and stable concealment, reduces the complexity of optimal power design, and enhances communication reliability and security.
Smart Images
Figure CN122317599A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of wireless communication technology, and in particular to a covert communication method based on block parameter uncertainty. Background Technology
[0002] In emerging wireless communication scenarios such as the Internet of Things (IoT) and the Internet of Vehicles (IoV), the open channel nature of communication makes communication security and concealment key issues restricting industry development. Covert communication, as a core technology for ensuring information transmission security, aims to prevent eavesdroppers from reliably detecting legitimate communication activities, thereby avoiding information interception or interference.
[0003] Current research on covert communication technology largely revolves around fixed-parameter scenarios, assuming that key parameters such as the power and symbol rate of the interference source remain constant. However, in real-world multi-user dynamic environments, the operating state of the interference source dynamically adjusts with changes in the communication scenario. While its key parameters remain stable within a single code block, they fluctuate randomly across different code blocks based on a priori distributions, forming a typical characteristic of "block parameter uncertainty." Existing technologies have failed to adequately adapt to this real-world scenario and have several limitations: Firstly, traditional solutions do not incorporate block parameter uncertainty into the construction of covert conditions, allowing eavesdroppers to easily distinguish between interference signals and covert communication signals through optimal hypothesis testing, resulting in a high risk of communication behavior being detected. Secondly, existing methods struggle to balance the relationship between covertness constraints and communication capacity, often excessively reducing transmission power to ensure covertness, leading to a sharp reduction in communication capacity and low spectrum resource utilization. Furthermore, they lack adaptability to dynamic scenarios, easily resulting in increased bit error rate and decreased decoding reliability when user access probability changes or channel noise fluctuates. Furthermore, some solutions neglect the spectral modulation effect of pulse shaping parameters, failing to further improve the stability of covert communication through waveform design, and thus failing to meet the requirements of reliable covert communication. Summary of the Invention
[0004] This invention addresses covert communication scenarios where interference sources exist. By combining the uncertainty of block parameters and utilizing the general covert conditions of intersecting popular spaces, it constructs an equivalent power model of pulse shaping using the roll-off coefficient to achieve the optimal power for the transmitter's covert communication.
[0005] To achieve the above objectives, the present invention provides the following solution: A covert communication method based on block parameter uncertainty includes: Construct a covert communication model for multi-user dynamic access scenarios and derive the covert communication judgment rules for eavesdroppers. Based on the aforementioned covert communication judgment rules, the general conditions for covert communication parties to evade hypothesis testing are analyzed. Based on the general conditions for covert communication to evade hypothesis testing, an equivalent power variance is introduced to obtain the optimal transmission power when the interference source uses a pulse shaping transmission strategy.
[0006] Optionally, a covert communication model for multi-user dynamic access scenarios is constructed, and the rules for judging the covert communication of eavesdroppers are derived, including: A multi-user covert communication system is constructed, and a unified discrete-time signal model is established based on the multi-user covert communication system. The multi-user covert communication system includes: Alice, a legitimate sender; Jammer, an interference source; Bob, a legitimate receiver; and Willie, an eavesdropper. The discrete-time signal model, based on the sampled baseband waveform, can flexibly describe different scenarios. Based on the discrete-time signal model, the rules for judging the covert communication of eavesdroppers are derived.
[0007] Optionally, based on the discrete-time signal model, the rules for determining the covert communication of an eavesdropper are derived as follows: In the discrete-time signal model, the signal within an observation code block is represented as a... vector Simultaneously, key parameters of the interference source are set, including power or symbol rate. In each observation code block of length N sampling points, the eavesdropper Willie needs to distinguish the null hypothesis. and alternative hypothesis Two assumptions; Signal vectors based on null and alternative hypotheses This completes the deduction of the eavesdropper's covert communications.
[0008] Optionally, the null hypothesis The signal observed by the eavesdropper Willie originated only from interference sources with blocky uncertainty and background noise; The alternative hypothesis The signal observed by the eavesdropper Willie originated from a covert user, a source of interference, and background noise.
[0009] Alternatively, in the alternative hypothesis Below, signal vector for: ; in: The signal vector of the sender, Alice. This is the interference signal vector of the interference source Jammer. Let be the additive white Gaussian noise vector at the location of the eavesdropper Willie; Under the null hypothesis Below, signal vector for: .
[0010] Optionally, based on the covert communication judgment rules, the general conditions for covert communication parties to evade hypothesis testing include: Let the received signal model at the legitimate receiver Bob be: ;in, Additive white Gaussian noise at the legitimate receiver Bob; Set the channel gain between the sender Alice, the legitimate receiver Bob, and the eavesdropper Willie to 1, and normalize all attenuation effects to the signal power; Willie's hypothesis testing task is based on signal vectors. The goal of covert communication is to determine whether the sender, Alice, exists; the objective of covert communication is to ensure that the eavesdropper, Willie, cannot reliably distinguish between these two assumptions, namely, when the code block length... At that time, two probability distributions and The total variation distance between them is less than 1; make Let the observed vectors be the vectors; assume there exists a sequence of feature vectors with a fixed dimension. , feature vector sequence Under both assumptions, it converges with probability to a limiting random vector; Suppose that the decision of the optimal detector can asymptotically depend only on the feature vector. Then the distribution between the original high-dimensional observation vectors The limit is equal to the limit of the random vector distributions. ,Right now: ; in, It is a limit random vector The probability density function, k=0 or 1; The eavesdropper Willie employs optimal hypothesis testing, and its detection performance is determined by the total variation distance. The decision is made that this distance characterizes the null hypothesis. Noise distribution and alternative hypotheses The difference in the distribution of mixed noise in the signal; among which, The probability density function with the null hypothesis. The probability density function for the alternative hypothesis; The concealment conditions after transformation are: ; For the existence of block uncertainty The IID symbol model, The necessary and sufficient condition is that, by Parameterized two limiting statistical manifolds and There exists a non-empty intersection in the moment space.
[0011] Optionally, the feature vector sequence Under both assumptions, the following convergent with probability to a limiting random vector include: Under the null hypothesis Down: ; In alternative hypothesis Down: ;in, This represents a probabilistic convergence of a limiting random vector. and The distribution is determined by the uncertainty parameters of the interference source. It is determined by the prior distribution.
[0012] Optionally, based on the general conditions for covert communication to evade hypothesis testing, under the interference source using a pulse-shaping transmission strategy, an equivalent power variance is introduced to obtain the optimal transmission power, including: Consider a structure-matching scenario: the sender Alice and the interference source Jammer have the same signal structure and symbol rate. Total power emitted by the jammer source With known parameters fixed, a block-based random strategy is used to select pulse shaping parameters. ; Suppose that the eavesdropper Willie uses a band-limited receiver to maximize the signal-to-noise ratio; when the parameter When the variable is a continuous random variable, the equivalent interference power observed by the eavesdropper Willie It is also a random variable; Using equivalent variance mapping, let the signal power spectral density of the interference source Jammer be... ;in, Let be the probability density function. The frequency response of the root-raised cosine filter; The eavesdropper Willie applied a receiver filter. The equivalent variance of the Jammer interference source is: ; in, It is a continuous function, and its support set is ; Under the Gaussian codebook assumption, the detection problem degenerates into a zero-mean Gaussian distribution that distinguishes different variances; alternative hypothesis The lower difference set is ; Next, determine the non-orthogonality condition. The necessary and sufficient condition is The spectral cutoff effect of Willie's matched filter will... The uncertainty is transformed into in-band energy uncertainty, as long as Sufficiently small to be covered by fluctuations, the two distributions are indistinguishable, ensuring ; Alice, the sender, selects the transmit power. Make In time, it can be achieved This means fulfilling the need for covert communication.
[0013] The beneficial effects of this invention are as follows: This invention constructs a unified discrete-time signal model. By flexibly setting the pulse shaping matrix, it can simultaneously cover both shaped waveform models and non-pulse-shaped IID models, eliminating the need for separate model design for different waveform scenarios. Furthermore, the model introduces a "block uncertainty" setting for interference sources (key parameters are constant within code blocks but randomly vary between code blocks), accurately matching the actual scenario of dynamic fluctuations in interference source parameters during multi-user dynamic access, significantly improving the model's applicability and practicality.
[0014] This invention does not rely on empirical concealment strategies, but rather derives the core criterion for the Willie binary hypothesis test—the Total Variation Distance (TVD)—and clarifies the necessary and sufficient condition for concealment: "two limiting statistical manifolds have a non-empty intersection in the moment space." This condition ensures that as the code block length increases, the difference in probability distributions between the two hypotheses (the presence or absence of Alice's signal) observed by Willie is always controlled within a range where TVD is strictly less than 1. Theoretically, this eliminates the possibility of Willie reliably distinguishing communication behavior. Compared to traditional concealment methods that rely solely on power reduction, this method provides a more rigorous and stable concealment guarantee.
[0015] This invention introduces the concept of "equivalent power variance" under the interference source pulse shaping strategy. By mapping the relationship between Jammer's signal power spectral density and Willie's receiving filter, the detection problem is transformed into a Gaussian variance discrimination problem. Based on this, the optimal transmit power can be quickly determined directly by the criterion that "the equivalent power variation range covers Alice's signal power." This satisfies the concealment requirement that Willie cannot distinguish, while avoiding situations where Alice's power is too low, preventing the legitimate receiver (Bob) from decoding. Furthermore, in structural matching scenarios, the selection of pulse shaping parameters such as the roll-off factor no longer constrains concealment, further reducing the complexity and constraints of optimal power design. Attached Figure Description
[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0017] Figure 1 This is a schematic diagram of a covert communication method based on block parameter uncertainty according to an embodiment of the present invention; Figure 2 This is an example diagram of a concealment failure mechanism that does not conform to general concealment conditions in an embodiment of the present invention; Figure 3 The figure shows the simulation results of the concealment effect of Alice under different structures in the embodiment of the present invention as a function of code block length. Detailed Implementation
[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0019] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0020] like Figure 1 As shown, this embodiment proposes a covert communication method based on block parameter uncertainty, including: Step S1: Construct a covert communication model for multi-user dynamic access scenarios and derive the covert communication judgment rules for eavesdroppers; Step S2: Based on the covert communication judgment rules, analyze the general conditions under which the covert communication party evades hypothesis testing; Step S3: Based on the general conditions for covert communication to evade hypothesis testing, under the transmission strategy of pulse shaping used by the interference source, an equivalent power variance is introduced to obtain the optimal transmission power.
[0021] Specifically, step S1 in this embodiment includes: A multi-user covert communication system is constructed, consisting of Alice (legitimate sender), Jammer (interference source), Bob (legitimate receiver), and Willie (eavesdropper). A unified discrete-time signal model is established. This model, based on sampled baseband waveforms, can flexibly describe different scenarios. The signal within an observation code block can be represented as a... vector .
[0022] The core of the covert communication process revolves around a binary hypothesis testing problem faced by an eavesdropper (Willie). In each observation code block of length N sampling points, Willie needs to distinguish between the following two hypotheses: H0 (Null Hypothesis): The signal observed by Willie originated only from the jammer, a source of blocky uncertainty, and background noise.
[0023] H1 (Alternative Hypothesis): The signal observed by Willie originated from a hidden user (Alice), a source of interference, and background noise.
[0024] At the same time, it is necessary to set key parameters of the interference source, such as power or symbol rate, which are constant within a code block, but will vary randomly between different code blocks according to a prior distribution, which constitutes "block uncertainty".
[0025] Under alternative hypothesis H1, the signal consists of three parts: ; in: This is Alice's signal vector. It was sent by Alice. A sequence of IID symbols, It is The matrix represents the sampling matrix corresponding to the pulse shaping and symbol rate used by Alice. This is Jammer's interference signal vector. Similarly, It was produced by Jammer A sequence of IID symbols, It is its corresponding Sampling matrix. Jammer's block uncertainty is reflected in the matrix. or symbol sequence The statistical properties (such as power) are determined by a random parameter. This parameter is determined from a prior distribution at the beginning of each communication code block of length N. Extract from. It is the additive white Gaussian noise (AWGN) vector at Willie, whose elements follow a distribution. ,Right now .
[0026] This model is universal, as reflected in its ability to... and Different settings can cover whether or not a shape is formed: 1. Shaped Waveform Model: When Alice and Jammer use a pulse shaping function... At that time, matrix The elements are ,in It is the sampling period. It is a symbol period.
[0027] 2. Impulse-Free IID Symbol Model: When considering the most basic symbol-level interactions, it can be viewed as a pulse shaping function based on the Dirac scheme. The function, and sampling is performed at sign time. At this point, the forming matrix Degenerates into identity matrix Its component form is .
[0028] Specifically, step S2 in this embodiment includes: Bob's goal is to correctly decode the information from Alice. The received signal model at Bob's location is: .in It is additive white Gaussian noise at Bob.
[0029] To simplify the analysis, the channel gain between Alice, Bob, and Willie is set to 1, and all attenuation effects are normalized to the signal power. Bob needs to analyze the signal power after adding interference and noise. Recovering symbols This requires Alice's signal power to be high enough, which leads to the famous "square root law" phenomenon in covert communication.
[0030] Willie's hypothesis testing task is based on observation vectors. (For brevity, subscripts are omitted hereafter) to determine whether Alice exists. This constitutes a classic binary hypothesis testing problem. The goal of covert communication is to ensure that Willie cannot reliably distinguish between these two hypotheses, i.e., when the code block length... At that time, two probability distributions and The total variation distance (TVD) between them is strictly less than 1.
[0031] make Let N be the observation vector. Assume there exists a sequence of feature vectors with a fixed dimension (not increasing with N). The sequence converges with probability to a limiting random vector under two different assumptions: Under H0: ; H1 below: in This indicates convergence in probability. Limiting random vector. and The distribution is determined by the uncertainty parameters of the interference source. The prior distribution determines this. If the decision of the optimal detector can be asymptotically (when...) (Time) depends only on the feature vector Then the distribution between the original high-dimensional observation vectors The limit is equal to the limit of the random vector distributions. ,Right now: ; in, It is a limit random vector The probability density function.
[0032] Willie employs optimal hypothesis testing, and its detection performance is determined by the total variation distance. The decision is made based on the distance representation. Noise distribution and Differences in the distribution of mixed noise in the signal.
[0033] Therefore, the hidden condition after transformation is that for the existence of block uncertainty... The IID symbol model, The necessary and sufficient condition is that, by Parameterized two limiting statistical manifolds and In a moment space, there exists a non-empty intersection. For example... Figure 2 As shown, problems such as spectrum orthogonality, higher-order moment mismatch, and insufficient range can all lead to manifold non-intersection, resulting in TVD taking the value 1 when the code block size N approaches infinity, which cannot meet the requirements of covert communication.
[0034] Specifically, step S3 in this embodiment includes: considering a structure-matching scenario, Alice and Jammer have the same signal structure and symbol rate. Jammer's total transmit power With known parameters fixed, a block-based random strategy is used to select pulse shaping parameters. .
[0035] Assume Willie uses a band-limited receiver (matched filter) to maximize the signal-to-noise ratio. Let Jammer's total transmit power be... Fixed. If If it is a continuous random variable, then the equivalent interference power observed by Willie... It is also a random variable.
[0036] Using the equivalent variance mapping, let Jammer's signal power spectral density be... .
[0037] Willie applies a receiver filter The equivalent variance of the Jammer interference is: ; It is a continuous function, and its support set is .
[0038] In this way, under the Gaussian codebook assumption, the detection problem degenerates into distinguishing zero-mean Gaussian distributions with different variances. The lower difference set is .
[0039] Next, determine the non-orthogonality condition. The necessary and sufficient condition is The spectral cutoff effect of the Willie matched filter will... The uncertainty is transformed into in-band energy uncertainty, as long as Sufficiently small to be covered by fluctuations, the two distributions are indistinguishable, ensuring .
[0040] This means that if the range of variation in the equivalent power is sufficient to cover Alice's signal power... In other words, Alice only needs to select a suitable transmission power. Make That will achieve In other words, it fulfills the need for covert communication.
[0041] Depend on Figure 3 It can be seen that when Jammer, the interference source, employs a pulse shaping strategy, Alice must use a structure-matched waveform design to ensure concealment; otherwise, TVD will tend towards 1 with increasing N at a non-convergent rate. In the structure-matched scenario, the choice of roll-off factor strategy is no longer a key factor restricting covert communication. It can be seen that as long as the power requirements are met, neither polarization nor uniform distribution of the roll-off factor will lead to a catastrophic increase in TVD.
[0042] This method can obtain the optimal covert transmission power based on the transmission mode of the interference source, which significantly improves the reliability and security of communication in the presence of the interference source.
[0043] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A covert communication method based on block parameter uncertainty, characterized in that, include: Construct a covert communication model for multi-user dynamic access scenarios and derive the covert communication judgment rules for eavesdroppers. Based on the aforementioned covert communication judgment rules, the general conditions for covert communication parties to evade hypothesis testing are analyzed. Based on the general conditions for covert communication to evade hypothesis testing, an equivalent power variance is introduced to obtain the optimal transmission power when the interference source uses a pulse shaping transmission strategy.
2. The covert communication method based on block parameter uncertainty according to claim 1, characterized in that, Constructing a covert communication model for multi-user dynamic access scenarios and deriving the covert communication judgment rules for eavesdroppers includes: A multi-user covert communication system is constructed, and a unified discrete-time signal model is established based on the multi-user covert communication system. The multi-user covert communication system includes: Alice, a legitimate sender; Jammer, an interference source; Bob, a legitimate receiver; and Willie, an eavesdropper. The discrete-time signal model, based on the sampled baseband waveform, can flexibly describe different scenarios. Based on the discrete-time signal model, the rules for judging the covert communication of eavesdroppers are derived.
3. The covert communication method based on block parameter uncertainty according to claim 2, characterized in that, Based on the aforementioned discrete-time signal model, the rules for determining the covert communication of eavesdroppers are derived as follows: In the discrete-time signal model, the signal within an observation code block is represented as a... vector Simultaneously, key parameters of the interference source are set, including power or symbol rate. In each observation code block of length N sampling points, the eavesdropper Willie needs to distinguish the null hypothesis. and alternative hypothesis Two assumptions; Signal vectors based on null and alternative hypotheses This completes the deduction of the eavesdropper's covert communications.
4. The covert communication method based on block parameter uncertainty according to claim 3, characterized in that, The null hypothesis The signal observed by the eavesdropper Willie originated only from interference sources with blocky uncertainty and background noise; The alternative hypothesis The signal observed by the eavesdropper Willie originated from a covert user, a source of interference, and background noise.
5. The covert communication method based on block parameter uncertainty according to claim 3, characterized in that, In alternative hypothesis Below, signal vector for: ； in: The signal vector of the sender, Alice. This is the interference signal vector of the interference source Jammer. Let be the additive white Gaussian noise vector at the location of the eavesdropper Willie; Under the null hypothesis Below, signal vector for: 。 6. The covert communication method based on block parameter uncertainty according to claim 3, characterized in that, Based on the aforementioned covert communication judgment rules, the general conditions for covert communication parties to evade hypothesis testing include: Let the received signal model at the legitimate receiver Bob be: ;in, Additive white Gaussian noise at the legitimate receiver Bob; Set the channel gain between the sender Alice, the legitimate receiver Bob, and the eavesdropper Willie to 1, and normalize all attenuation effects to the signal power; Willie's hypothesis testing task is based on signal vectors. The goal of covert communication is to determine whether the sender, Alice, exists; the objective of covert communication is to ensure that the eavesdropper, Willie, cannot reliably distinguish between these two assumptions, namely, when the code block length... At that time, two probability distributions and The total variation distance between them is less than 1; make Let the observed vectors be the vectors; assume there exists a sequence of feature vectors with a fixed dimension. , feature vector sequence Under both assumptions, it converges with probability to a limiting random vector; Suppose that the decision of the optimal detector can asymptotically depend only on the feature vector. Then the distribution between the original high-dimensional observation vectors The limit is equal to the limit of the random vector distributions. ,Right now: ； in, It is a limit random vector The probability density function, k=0 or 1; The eavesdropper Willie employs optimal hypothesis testing, and its detection performance is determined by the total variation distance. The decision is made that the total variation distance characterizes the null hypothesis. Noise distribution and alternative hypotheses The difference in the distribution of mixed noise in the signal; among which, The probability density function with the null hypothesis. The probability density function for the alternative hypothesis; The concealment conditions after transformation are: ； For the existence of block uncertainty The IID symbol model, The necessary and sufficient condition is that, by Parameterized two limiting statistical manifolds and There exists a non-empty intersection in the moment space.
7. The covert communication method based on block parameter uncertainty according to claim 6, characterized in that, Feature vector sequence Under both assumptions, the following convergent with probability to a limiting random vector include: Under the null hypothesis Down: ; In alternative hypothesis Down: ;in, This represents a probabilistic convergence of a limiting random vector. and The distribution is determined by the uncertainty parameters of the interference source. It is determined by the prior distribution.
8. The covert communication method based on block parameter uncertainty according to claim 1, characterized in that, Based on the general conditions for covert communication to evade hypothesis testing, and assuming the interference source uses a pulse-shaping transmission strategy, an equivalent power variance is introduced to obtain the optimal transmission power, including: Consider a structure-matching scenario: the sender Alice and the interference source Jammer have the same signal structure and symbol rate. Total power emitted by the jammer source With known parameters fixed, a block-based random strategy is used to select pulse shaping parameters. ; Suppose that the eavesdropper Willie uses a band-limited receiver to maximize the signal-to-noise ratio; when the parameter When the variable is a continuous random variable, the equivalent interference power observed by the eavesdropper Willie It is also a random variable; Using equivalent variance mapping, let the signal power spectral density of the interference source Jammer be... ;in, Let be the probability density function. The frequency response of the root-raised cosine filter; The eavesdropper Willie applied a receiver filter. The equivalent variance of the Jammer interference source is: ； in, It is a continuous function, and its support set is ; Under the Gaussian codebook assumption, the detection problem degenerates into a zero-mean Gaussian distribution that distinguishes different variances; alternative hypothesis The lower difference set is ; Next, determine the non-orthogonality condition. The necessary and sufficient condition is The spectral cutoff effect of Willie's matched filter will... The uncertainty is transformed into in-band energy uncertainty, as long as Sufficiently small to be covered by fluctuations, the two distributions are indistinguishable, ensuring ; Alice, the sender, selects the transmit power. Make In time, it can be achieved This means fulfilling the need for covert communication.