A Wireless Powered Covert Backscatter Communication Method Based on Information Segmentation

Abstract

This invention discloses a wireless power-powered covert backscatter communication method based on information segmentation, belonging to the field of secure communication technology. Specifically, the backscatter tag segments the original information sequence to obtain first information and second information. The first information is transmitted on the backscatter link, and the backscatter tag achieves covert communication by modulating a randomized continuous wave signal. The second information is transmitted through an active uplink, where the backscatter tag actively transmits signals using collected energy to achieve information transmission. This invention, within a wireless power-powered backscatter communication architecture, combines the covertness of the backscatter phase with the information segmentation mechanism. It introduces guessing entropy as a security metric at the information level and models the average number of attempts by an eavesdropper to reconstruct the original information, increasing the difficulty for unauthorized eavesdroppers to obtain the original transmitted data, thus achieving secure information transmission in the communication system.

Description

Technical Field

[0001] This invention belongs to the field of secure communication technology, specifically relating to a wireless power supply covert backscatter communication method based on information segmentation. Background Technology

[0002] The integration of wireless power supply technology and backscatter communication (BackCom) has led to a wireless power-powered BackCom system architecture that combines BackCom with active information transmission. This system utilizes wireless power to provide energy support for low-power tags, enabling active communication and offering advantages such as high energy efficiency and low power consumption. Current research on improving the security of wireless power-powered BackCom systems primarily focuses on optimizing physical layer security features. Typical methods include artificial noise injection and cooperative relaying, which reduce the signal-to-noise ratio of the received signal to improve the system's anti-eavesdropping capabilities. However, these methods generally neglect the security design of the information transmission layer, leaving the overall security protection capability of the system limited when facing eavesdroppers with strong computational or detection capabilities.

[0003] To further enhance the security of information transmission in the system, some research has begun to explore the introduction of information segmentation techniques at the information layer. This method divides the original bit sequence into two sub-information streams, which are then transmitted through different transmission links (backscatter link and active transmission link), thereby increasing the difficulty for an eavesdropper to recover the complete information. Since the eavesdropper cannot obtain the reconstruction rules between the sub-information streams, even if they successfully intercept part of the link information, they cannot deduce the complete content of the original information, thus effectively improving communication security at the information layer.

[0004] However, BackCom schemes based on information segmentation still have certain shortcomings. Existing research generally treats the BackCom phase as a public channel, lacking covert design mechanisms. This allows unauthorized eavesdroppers to still identify and obtain sensitive information (such as keys or partial sub-information) in the backscatter link during detection, thereby weakening the system's covertness and security. Summary of the Invention

[0005] In view of this, the purpose of this invention is to provide a wireless power supply covert backscatter communication method based on information segmentation. By introducing randomized continuous waves in the BackCom phase to enhance covertness, and by using information segmentation technology at the information level to improve system security, the invention achieves synergistic optimization between transmission performance and communication security in the wireless power supply BackCom system.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A wireless power supply covert backscatter communication method based on information segmentation, comprising:

[0008] The backscatter tag divides the original information sequence to obtain first information and second information. The first information is transmitted on the backscatter link. The backscatter tag achieves covert communication by modulating the reflection randomized continuous wave signal. The second information is transmitted through the active uplink. The backscatter tag uses the collected energy to actively transmit signals to achieve information transmission.

[0009] The information segmentation process includes: introducing guessing entropy as a security metric at the information level; constructing a joint optimization problem with the goal of maximizing the guessing entropy of the eavesdropper; and introducing optimization problems for Randomized Continuous Wave (RCW) signal parameters and the time allocation coefficient of the wireless power supply BackCom. After decomposing the joint optimization problem, the solution to the joint optimization problem is obtained, thus yielding the information segmentation scheme.

[0010] The beneficial effects of this invention are as follows:

[0011] This invention enhances stealth by introducing randomized continuous waves in the BackCom phase and improves system security by introducing guessing entropy at the information level and using information segmentation technology, thereby achieving synergistic optimization between transmission performance and communication security in the wireless power supply BackCom system.

[0012] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0013] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0014] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0015] Figure 1 This is a schematic diagram of a single-user wireless power supply concealed BackCom scenario in an embodiment of the present invention;

[0016] Figure 2 This is a schematic diagram of an information segmentation process in an embodiment of the present invention;

[0017] Figure 3This is a schematic diagram illustrating the relationship between the maximum transmit power and achievable speed of the signal under different transmission schemes during the backscattering stage in an embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram illustrating the relationship between maximum transmit power and guessed entropy under different minimum transmit bit numbers in this embodiment of the invention;

[0019] Figure 5 This is a schematic diagram illustrating the relationship between the bandwidth and the guessed entropy of the RCW signal under different maximum transmit powers in an embodiment of the present invention.

[0020] Figure 6 This is a schematic diagram illustrating the relationship between the maximum transmit power and the estimated entropy and the number of transmitted bits under different transmission schemes in embodiments of the present invention. Detailed Implementation

[0021] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0022] This invention proposes a wireless power-powered covert backscatter communication method based on information segmentation. Under the wireless power-powered BackCom architecture, this method combines the covertness of the backscatter phase with an information segmentation mechanism to achieve secure transmission of information in the communication system. Specifically, the backscatter tag first segments the original information sequence into two parts. One part is transmitted on the backscatter link, where the tag achieves covert communication by modulating reflected RCW signals, preventing unauthorized eavesdroppers from obtaining this part of the data. The other part is transmitted via the active uplink, where the tag actively transmits signals using collected energy. Due to the public nature of this part of the information transmission, eavesdroppers can fully know the transmitted data. However, because eavesdroppers do not know the specific bits of the backscattered information or their positions in the original data, they cannot completely reconstruct the original information frame. To address this, this invention introduces guessing entropy as a security metric at the information level. By modeling the average number of attempts by an eavesdropper to reconstruct the original information, the security level of the system is analyzed. To achieve a balance between system security and transmission performance, this invention constructs a joint optimization problem with the goal of maximizing guess entropy, jointly solving for the RCW signal parameters and the time allocation coefficients of the wireless power supply BackCom. Simulation results show that the method described in this invention significantly improves the eavesdropper's guess entropy compared to traditional information segmentation schemes, while achieving a reasonable trade-off between transmission performance and security.

[0023] To further explain the working principle of this application, a specific embodiment is provided for illustration, and the specific technical solution is as follows:

[0024] 1. Wireless Powered Covert BackCom System Model Construction:

[0025] like Figure 1 As shown, this invention considers a single-user wirelessly powered covert BackCom scenario. In this scenario, a full-duplex wireless transceiver (reader) communicates with a backscatter tag using a single-carrier RCW signal. Simultaneously, a listener (Willie) attempts to monitor the communication between the reader and the tag. Considering resource constraints, the reader, backscatter tag, and Willie are all equipped with a single antenna. Furthermore, the backscatter tag integrates energy harvesting and information transmission circuitry to achieve both energy acquisition and information transmission.

[0026] Specifically, consider the following communication process, assuming the total communication time is... T The time allocation coefficient for the first stage is That is, the duration of the first phase of communication is .exist Within the system, the backscatter tag operates in both the energy harvesting and backscattering phases, and can continuously switch between these two modes. In energy harvesting mode, the tag operates its energy harvesting circuit, absorbing the energy from the received RCW signal and using it to charge its battery. Alternatively, the tag enters backscattering mode, where it receives the RCW signal from the reader, modulates it using a limited character input, embeds the desired information into the RCW, and backscatters it back to the reader. In this mode, it is assumed that the tag no longer charges its battery, using all received energy for information modulation and signal reflection. During the first phase of communication, it is assumed that the reader knows the specific time slot for the tag's backscatter transmission, and also fully understands the complete randomization information of the RCW signal. Therefore, the reader is capable of demodulating the data embedded in the RCW, thus achieving information transmission during the BackCom process in the first phase. In the second phase of information transmission, the active communication phase... During the communication phase, the reader stops broadcasting radio frequency (RF) signals, and the tag actively transmits signals to the reader using the collected energy to achieve information transmission. To obtain a higher transmission rate, the tag uses a Gaussian-distributed random signal as input during the active communication phase to approximate the channel capacity. Furthermore, a listener equipped with a single antenna, Willie, monitors the entire communication activity. During the backscatter phase, Willie uses a radiometer-based detector to detect whether the tag is transmitting information.

[0027] To ensure that during communication, that is, in time... The security of each frame of information transmission process makes it impossible for Willie to completely recover any frame of information. This invention considers an information segmentation model. For example... Figure 2 As shown, this model divides a frame of original information (containing a string of data symbols of several bits) that the user needs to transmit into two parts. One part of the data symbols (such as the key, data symbols at random positions within the original data symbols, etc.) is transmitted to the reader via backscattering. Because the reader can effectively interfere with Willie's detection using the randomization characteristics of RCW, it becomes difficult for Willie to detect the tag's BackCom behavior, thus preventing Willie from obtaining this part of the information. The other part of the data symbols is transmitted to the reader via the uplink during the active transmission phase. Since the tag uses Continuous Wave (CW) as the RF signal during the active communication phase, Willie can fully know the specific data symbols being transmitted. In the information segmentation model, considering the stealth of the BackCom transmission in the first phase, Willie cannot accurately know the number of bits transmitted via backscattering, the specific data symbols being transmitted, or the positions of these symbols in the original information. These uncertainties significantly increase the difficulty for Willie to recover the complete original information, thereby improving the security of information transmission between the reader and the tag.

[0028] 2. Construction of RCW signal model and transmission channel model:

[0029] Phase 1 time Inside, the reader is in the first... k The model of a single-carrier RCW signal transmitted in one time slot can be expressed as:

[0030] (1)

[0031] in, Let be the angular frequency of the RCW signal, satisfying the following condition: , This represents the center frequency. j is the imaginary unit, satisfying the condition... , where e is the natural constant. Assume the bandwidth of the RCW signal is... B This allows us to obtain the symbol duration (the length of one time slot). , represented as .also, Represented as in the first k The amplitude coefficient of a single-carrier RCW signal within a time slot remains constant within one time slot and follows a cyclically symmetric complex Gaussian (CSCG) distribution across different time slots, i.e.:

[0032] (2)

[0033] in and These represent the mean and variance of the RCW signal, respectively. The amplitude coefficient of the RCW signal... The randomization property can effectively interfere with Willie's detection of BackCom's behavior in the first stage, thus ensuring BackCom's stealth.

[0034] In this invention, the transmission channel of the RF signal between the reader and the tag (in this paper, the tag refers to a backscatter tag) can be represented as follows: and Meanwhile, the channels between the reader and the tag and Willie can be represented as follows: and Without loss of generality, the transmission channel experienced by the RF signal is modeled as a block fading Ricean channel; other channel types are also applicable to this model. Specifically, the transmission channel of the RF signal between the reader and the tag (in this paper, the tag refers to the backscattered tag) can be modeled as follows:

[0035] (3)

[0036] in, For the Rice factor, the line-of-sight (LoS) component can be modeled as:

[0037] (4)

[0038] in, This represents the Loss Channel Fading Coefficient, and the distance between the reader and the tag is... ,definition For channel power gain, where , , v This indicates the wave speed. Additionally, the transmit and receive antenna gains are respectively... and For uncertain Rayleigh fading channels (NLoS), it can be modeled as follows:

[0039] (5)

[0040] in, This represents the NLoS channel fading coefficient. It is assumed that the channel gain is constant within each time block and that different time blocks are independent of each other. The reader can estimate this from the pilot signal. and Furthermore, channel reciprocity can be assumed. Furthermore, assuming Willie knows the specific location information of the reader and tag, and further knows the channel amplitude gain... and Considering the worst-case scenario, Willie knew perfectly well... and Information.

[0041] 3. Construction of the tag energy harvesting model:

[0042] In the first phase, the tag operates in two modes: backscattering and energy harvesting, which alternate randomly without a fixed order. Assume the first phase... The duration of the energy harvesting phase within is ,in This represents the energy harvesting time coefficient. For ease of analysis, this invention considers a linear energy harvesting model; however, the system model proposed in this invention is also applicable to nonlinear energy harvesting models. Considering the RF signal power emitted by the reader is... ,in , The maximum transmit power of the RF signal sent by the reader. During the energy harvesting phase, the tag is at the [missing information]. k The RF signal received in each time slot can be represented as:

[0043] (6)

[0044] Among them, the label is in the first k The RF signal energy collected in each time slot can be expressed as:

[0045] (7)

[0046] in, This indicates the energy conversion efficiency of the tag's energy harvesting circuit. This indicates that the reader and the tag are in the first position. k Channel power gain for each time slot, assuming k Large enough, the tag collects the following amount of energy during the energy harvesting phase:

[0047] (8)

[0048] The energy collected by the tag will be used for model transmission during the active communication phase.

[0049] 4. Reader signal reception model construction:

[0050] In backscatter mode, the tag absorbs a portion of the energy of the received RF signal for information modulation, and then backscatters the modulated RF signal. In the... k The backscattered signal received by the reader in each time slot is:

[0051] (9)

[0052] in, and These are represented by the tag's power reflection coefficient and the reader's self-interference coefficient, respectively. Indicates the label in the first position. k For ease of analysis, this invention assumes that the tag uses Binary Phase Shift Keying (BPSK) modulation, i.e., the data symbols transmitted in each time slot are of equal probability. ,in . This represents the amplitude coefficient of the self-interference channel. Furthermore, The additive white Gaussian noise at the reader receiver satisfies the following conditions: To simplify the problem, the thermal noise and residual self-interference at the reader receiver are combined and modeled as follows: satisfied ,in, , It is a scaling factor. Indicates to Take the average. Assuming the RF signal is transmitted by the reader and received by the reader via the backscatter link, the equivalent channel matrix it traverses can be expressed as:

[0053] (10)

[0054] therefore, It can be further simplified to:

[0055] (11)

[0056] The reader's received signal was then analyzed to maximize the transmission performance during the backscattering phase.

[0057] 5. Construction of the transmission model in the active communication phase

[0058] Phase Two Inside, the tag utilizes the energy harvested in energy harvesting mode to actively transmit information to the reader. During the active transmission phase, the tag employs single-carrier CW mode and uses a Gaussian signal for information transmission to improve performance. Compared to discrete symbol modulation, Gaussian signals can achieve a higher capacity limit. During the active transmission phase, the reader... k The signals received in each time slot by the tag actively transmitted are:

[0059] (12)

[0060] in, The transmitted Gaussian signal satisfies the following conditions: , Let V be the variance of the Gaussian signal. This represents the noise received by the reader during the active communication phase. It is assumed that the noise distribution in this part is the same as the noise distribution received by the reader during the backscattering phase, satisfying the CSCG distribution, i.e. Therefore, the transmission rate between the tag and the reader during the active communication phase can be obtained as follows:

[0061] (13)

[0062] in, B Let be the bandwidth of the RF signal transmitted by the tag in the active phase. Here, we assume this bandwidth is the same as the bandwidth of the RF signal transmitted by the reader in the first phase. Furthermore, the number of bits transmitted in the active transmission phase can be obtained as follows:

[0063] (14)

[0064] In addition, the tag's active transmission of RF signals to the reader consumes its own battery power. Therefore, the tag's energy consumption during the active communication phase is:

[0065] (15)

[0066] in, Let be the constant circuit power consumption of the tag. Assuming the tag completely consumes the energy in its battery after completing active communication, the tag's transmitted RF signal power can be obtained as:

[0067] (16)

[0068] Therefore, the energy absorbed by the tag during the energy harvesting phase must be greater than the constant circuit loss during the active communication phase in order to achieve active transmission.

[0069] 6. Willie's detection model construction:

[0070] Willie passively monitors the backscatter transmission of tags and can infer the probability distribution of RCW signal energy. However, the inherent randomization of RCW signal amplitude hinders Willie's accurate detection of the specific time slot of backscatter transmission. Based on this, Willie's received signal model can be modeled as a binary assumption problem, assuming... and These represent the two cases: the tag did not transmit backscatter and it did communicate via backscatter, respectively. Therefore, Willie in the... k The signal received in each time slot can be represented as:

[0071] (17)

[0072] in, For the thermal noise at the Willie receiver, satisfying Furthermore, the equivalent matrix experienced by the RF signal after being backscattered by the tag and received by Willie can be expressed as follows: .

[0073] Willie Within a given timeframe, attempt to determine in which time slots the tag engaged in backscatter communication. Assume... and These represent Willie's determination that the tag is in energy harvesting mode and backscattering mode, respectively. False alarm probability. This refers to Willie's erroneous detection of backscatter propagation, resulting in a false negative probability. This corresponds to Willie's failure to detect backscatter transmission. Considering and Scenarios where prior probabilities are equal, i.e. This indicates that Willie cannot utilize past detection results to improve its judgment of tag backscattering behavior. In this case, Willie's detection performance can be represented by the detection error probability, which can be expressed as:

[0074] (18)

[0075] Willie aims to minimize [the impact of radiation] by adjusting the threshold of its equipped radiometer. To ensure the secrecy of communication, it is usually necessary to meet the worst-case scenario requirements. To ensure Willie has a high probability of false detection, among which This indicates a hidden requirement, which is usually kept at a low level.

[0076] 7. Willie's detection performance analysis:

[0077] Based on the reader's received signal model, the achievable rate between the reader and the tag under finite character input is analyzed to measure the transmission performance of BackCom. Simultaneously, based on relative entropy and Willie's received signal model, the concealment constraints of the BackCom phase are given. For simplified notation, time slot indices are omitted in subsequent analyses. k .

[0078] Willie's detection error probability can be given by relative entropy, obtained through Pinsker's inequality. The lower bound of can be represented as:

[0079] (19)

[0080] in, and This indicates that Willie observed the signal at and The probability density distribution under the assumption, yes and The relative entropy between them. To satisfy the required concealment constraints. ,use The lower bound is used as a substitute, that is Therefore, the concealment constraint can be further expressed as:

[0081] (20)

[0082] In this regard, considering that the RCW signal and noise are independent of each other, Willie's received signal Satisfying the CSCG distribution, it can be expressed as:

[0083] (twenty one)

[0084] in,

[0085] (twenty two)

[0086] In a given In this case, It can be represented as:

[0087] (twenty three)

[0088] Therefore, Willie received the signal in and The relative entropy between the probability density functions under the given conditions can be expressed as:

[0089] (twenty four)

[0090] 8. System reachability analysis and its approximate expression:

[0091] To measure the transmission performance during the backscatter phase, this invention uses the achievable rate as a metric. Since the tag uses a limited number of character inputs to transmit information, the achievable rate is expressed as Bits Per Channel Use (BPCU). Therefore, the reader's received signal... and sending signals s Mutual information between them can be represented as:

[0092] (25)

[0093] in, Indicates that in a given s In the case of entropy, Represented as given and s Under the conditions The conditional differential entropy, since the reader fully knows the randomization information of RCW, the achievable rate can be expressed as:

[0094] (26)

[0095] In addition, due to the noise signal received by the reader The CSCG distribution satisfies zero mean; therefore, the differential entropy... It can be represented as:

[0096] (27)

[0097] In order to derive the conditional differential entropy ,because It is known that the received signal The conditional probability distribution is:

[0098] (28)

[0099] In order to be in and known Receiving signals under the condition The conditional probability distribution, Representing absolute value, therefore, conditional differential entropy It can be represented as:

[0100] (29)

[0101] definition You can get Furthermore, we can obtain:

[0102] (30)

[0103] definition Therefore, the achievable rate of the backscattering stage can be expressed as:

[0104] (31)

[0105] Therefore, the number of bits unloaded during the backscattering phase can be expressed as:

[0106] (32)

[0107] because The expression contains an expected expression, which cannot be solved by a finite number of elementary operations, posing a challenge to subsequent optimization. Therefore, an approximate expression is given here, which can be represented as:

[0108] (33)

[0109] in, ,and , for The conjugate of . An approximate expression for the number of bits unloaded during the backscattering stage can be obtained as:

[0110] (34)

[0111] The data symbols transmitted in the first stage backscattering phase and the data transmitted in the second stage can both form the data symbol string of the original frame signal, making it impossible for Willie to recover the original information.

[0112] 9. Security performance analysis based on guessing entropy:

[0113] Based on the information segmentation model, a frame of original data (a string of binary data symbols) is divided into two parts, used for the first stage of backscatter transmission and the second stage of active transmission, respectively. This invention analyzes the security performance of the communication process between the reader and the tag, using guessing entropy as the evaluation index for security performance. Specifically, due to the inherent characteristic that the first stage of covert backscatter communication has a low probability of being detected, Willie has difficulty detecting the correct data symbol string transmitted by backscatter. Since Willie cannot know the achievable rate between the reader and the tag during the backscattering phase, he assumes that the achievable rate during the backscattering phase is at its maximum value, i.e. ,definition The maximum number of bits in the backscattered transmission data symbol string is guessed by Willie. Furthermore, due to the openness of the wireless channel during active transmission, it is assumed that Willie fully knows the active transmission data symbols and transmission rate. Considering a more stringent case, that is, Willie fully knows the tag's transmit power during active communication and the total time occupied by the energy harvesting phase in the first phase, Willie needs to solve two challenges simultaneously to recover a complete frame of the original signal. (a) Sequence content guessing: Willie first needs to accurately guess the complete backscattered transmission data symbol string. (b) Symbol location: Based on the known content of the actively transmitted symbol string, Willie also needs to further determine the location of the backscattered transmitted symbols in the original sequence. The specific location within the text. Only by solving both problems simultaneously can Willie successfully recover the original data information transmitted from the tag to the reader.

[0114] Building on this, the core idea of ​​guess entropy is to measure, on average, how many guesses an attacker like Willie would need to make to obtain the correct information. Assume Willie knows the original sequence. Prior probability distribution of different data symbols In the given In this case, the number of guesses Willie needs to try is denoted as . Therefore, we hypothesize that entropy is defined as:

[0115] (35)

[0116] in, Let be a guessing function, whose value is the guess of a specific sequence. The minimum number of attempts required. Under the optimal guessing strategy (i.e., trying in descending order of sequence probability). Corresponding to sequence To guess the ranking position in the order.

[0117] In the BackCom scenario with wireless power supply, due to the openness of the transmission during the active communication phase, Willie knows the specific number of bits transmitted during the active transmission phase. However, Willie was unaware of the sequence transmitted during the backscatter phase. length q Suppose Willie believes q In the set The probability of a uniform distribution of length is:

[0118] (36)

[0119] For sequences Possible length q Willie guessed there would be One possible sequence (i.e., Willie's assumption about the data string transmitted in communication) have Each backscattered data symbol can be set to -1 or 1 in BPSK, and each backscattered data symbol is in the data string. (random positions within). It is worth noting that, due to and You can get .

[0120] From Willie's perspective, the entire sequence space consists of sequences of varying lengths. The probability of each sequence is:

[0121] (37)

[0122] It is worth noting that this probability depends on the length. q ,when q When smaller, The smaller the number of sequences, the higher their probability. Therefore, sequences formed by data strings of the same length have the same probability, but sequences formed by data strings of different lengths have different probabilities. Thus, to minimize the expected number of guesses, Willie should first guess sequences with higher probabilities, then sequences with lower probabilities. Since the probability of a short sequence (such as an empty sequence) is greater than that of a long sequence, Willie's optimal strategy can be: (a) first guess all sequences of length 0 (there is only one, i.e., an empty sequence); (b) if he doesn't guess correctly (i.e., the actual sequence is not empty), then guess all sequences of length 1; (c) if he doesn't guess correctly, then guess sequences of length 2; (d) and so on, until the sequence of length is... Within the same length, all sequences have the same probability, so Willie can guess these sequences in any order. Therefore, the optimal guessing order is to guess all sequences within each length in ascending order of length. Definition To begin guessing the length is q The total number of sequences that have been guessed before the given sequence, i.e., all sequences with lengths less than [a certain value]. q The total number of sequences can be obtained as follows:

[0123] (38)

[0124] Consider a specific length of q The sequence, in Willie's guessed order, is located at the [number]th [order]. There are 10 locations, among which It is in length qThe order in the sequence ( From 1 to However, since sequences of the same length are equally probable, Willie can guess the sequence in any order when guessing within this length, because each sequence is of length 1. q The number of guesses for the sequence is in the interval The sequence is uniformly distributed within the range. For the expected number of guesses, a specific order is not required because sequences of the same length have the same probability, so the order in which the sequence is guessed will not affect the expected value (as long as Willie guesses consecutively). Specifically, for a sequence of length... q For the sequence, the conditional expected number of guesses is:

[0125] (39)

[0126] Given the uncertainty in the length of the joint sequence, the total guess entropy, which is a weighted average of the conditional expectations, can be expressed as:

[0127] (40)

[0128] This guessing entropy model quantifies the ability of covert communication to resist guessing attacks, providing theoretical security guarantees for system design.

[0129] 10. Optimize problem description

[0130] In the information segmentation model, the reader and label aim to maximize Willie's guess entropy by rationally allocating the time for backscatter propagation and active propagation. To simplify the representation analysis, we define... Let be the average power of the RCW signal. The optimization problem can be expressed as:

[0131]

[0132]

[0133]

[0134] (41)

[0135]

[0136]

[0137]

[0138]

[0139] Among the optimization conditions This indicates the stealth of the first-stage backscatter transmission, making it impossible for Willie to detect it and difficult to ascertain the specific data of the backscatter transmission. Furthermore, The minimum number of bits representing a frame of signal, i.e., the number of bits for backscatter transmission and active transmission, should be greater than [a certain value]. To solve this optimization problem, it can be decomposed into two sub-problems: RCW signal parameter optimization and time allocation optimization. Specifically, according to the guessing entropy formula MERGEFORMAT (40), it can be seen that, under the condition that the number of transmitted bits in the active communication stage is constant, increasing the number of transmitted bits in the backscattering stage can effectively increase Willie's guessing entropy. Since the RCW signal parameters in this stage are independent of the subsequent time allocation, the optimization of RCW signal parameters can be regarded as a separate sub-problem. Furthermore, maximizing the number of transmitted bits in the backscattering stage is equivalent to maximizing its achievable rate, so the parameters of the multi-carrier RCW signal can be optimized first to achieve the maximization of the BackCom achievable rate. Given that the analytical expression of the achievable rate is not closed, this invention uses its approximate expression as a substitute, and thus the RCW parameter optimization problem in the backscattering stage can be expressed as:

[0140]

[0141]

[0142] (42)

[0143]

[0144]

[0145] To solve this optimization problem, this chapter employs the Lagrange dual ascent method to find the optimal solution. and By transforming the primal optimization problem into a dual problem, distributed solution is achieved. Therefore, the Lagrange function can be expressed as:

[0146]

[0147] (43)

[0148] in, These are Lagrange multipliers. Therefore, the optimization problem... It can be transformed into its dual problem form, which can be expressed as:

[0149] (44)

[0150] Given the initial values ​​of the Lagrange multipliers, the optimization problem is... The solution process first targets the variables. and Calculate its local optimum and update the corresponding Lagrange multipliers accordingly. By repeatedly performing these two steps, the algorithm gradually converges to the optimum. and .

[0151] Due to the Lagrange function pair and Find the partial derivatives and set them to zero to solve. and Due to the complexity of local optima, this section uses the gradient ascent method to find them. and The local optimal solution, the iterative update expression is:

[0152] (45)

[0153] in, and These represent the corresponding update step size. and They represent and The p +1 iteration result. Lagrange function pair The partial derivatives are:

[0154] (46)

[0155] Lagrange function pairs The partial derivatives are:

[0156] (47)

[0157] in, It can be represented as:

[0158] (48)

[0159] akin, and It can be represented as:

[0160] (49)

[0161] also, It can be represented as:

[0162] (50)

[0163] It can be represented as:

[0164] (51)

[0165] The expression is as follows:

[0166] (52)

[0167] After obtaining the Lagrange function with respect to and After obtaining the partial derivatives, the Lagrange multipliers are iterated using the gradient descent method. This causes the Lagrange function to converge to its minimum. The specific iterative process is as follows:

[0168] (53)

[0169] in, , , and They represent The update step size. According to (43), the gradient of the Lagrange function with respect to the Lagrange multipliers can be easily obtained, which can be expressed as:

[0170] (54)

[0171] Through continuous iteration and optimization Finally, the constraints are satisfied. and The maximum value. At the same time, in maximizing... Under these conditions, the optimal settings for RCW are obtained. and Then, use (31) to calculate .

[0172] After obtaining the maximum number of bits in the backscattering stage, consider maximizing Willie's guess entropy by optimizing the time allocation coefficients. This sub-optimization problem can be expressed as:

[0173] (55)

[0174] Due to the discreteness of the entropy function and the complexity of its expression, a particle swarm optimization algorithm is used here for optimization.

[0175] This invention aims to maximize Willie's guess entropy and effectively improves the concealment of multi-user BackCom by utilizing the randomization characteristics of multi-carrier RCW. The simulation uses a uniform carrier frequency and node location coordinates, with BPSK modulation. . Figure 3 The maximum transmit power of the signal under different transmission schemes during the backscattering phase is shown. With achievable rate The relationship between the two is as follows. To evaluate the covert transmission performance of RCW signals, two comparative scenarios were constructed using CW signals as a benchmark: covert transmission and uncovert transmission. Compared to CW signals, which are almost impossible to transmit efficiently in covert conditions, the randomization characteristics of RCW can effectively interfere with Willie's detection, thus significantly improving the achievable rate of the communication system. Furthermore, since the reader fully understands the randomization information of RCW, it can effectively demodulate the modulation information embedded in the RCW signal. Simultaneously, RCW requires only a small randomization component to ensure the covertness of communication between the reader and the tag, allowing the achievable rate of RCW to approach the optimal performance of CW signals in uncovert transmission. Moreover, as the transmission power continues to increase, the achievable rate gradually converges to... ,in M This is the modulation order of the tag, which is consistent with the theoretical analysis.

[0176] Figure 4 Showing different minimum transmission bit numbers Under these conditions, maximum transmit power With guessing entropy The relationship between them. It can be seen that with maximum transmission power... As the transmit power increases, the energy the tag can absorb during the energy harvesting phase also increases, allowing it to send more bits during the active transmission phase. With the minimum number of bits transmitted remaining constant, the tag can allocate more time to the backscatter phase, leading Willie's estimate of the number of bits transmitted during backscatter, thus increasing Willie's guessing entropy for the entire data symbol sequence and improving the security of communication between the reader and the tag. Furthermore, at lower transmit power, a higher minimum number of bits allows the tag to allocate more time to the energy harvesting and active transmission phases, improving the communication system's transmission performance; however, this directly compresses the available time in the backscatter phase. Simultaneously, due to the public nature of the active communication phase, this reduces Willie's guessing entropy for the transmitted data symbol sequence, correspondingly weakening the secure transmission capability of the communication system. As the transmit power continues to increase, the tag's transmission capability in the active transmission phase strengthens, and the constraint of the minimum number of bits on tag transmission gradually weakens, allowing the tag to allocate transmission time more flexibly to improve guessing entropy. Furthermore, to assess the security of the wirelessly powered covert backscatter communication system, the comparative scheme of this invention assumes that Willie knows the exact backscatter rate and can successfully decode the information transmitted by BackCom. However, since Willie is unaware of the information encoding technology, he does not know how to construct the original information based on the information transmitted by active communication and BackCom. Compared to the comparative scheme, the randomization characteristic of RCW enables covert transmission during the backscatter phase, preventing Willie from knowing the rate and specific information of BackCom transmission, greatly increasing the difficulty for Willie to guess the original transmitted information.

[0177] Figure 5 Different maximum transmit powers are given Bandwidth and guessed entropy of the RCW signal The relationship between the two methods is as follows: It can be seen that as the RCW signal bandwidth increases, the tag information transmission rate increases, and the number of bits transmitted via backscatter and active communication within the same transmission time increases, leading to an increase in Willie's guessing entropy for the original information sequence. Simultaneously, increasing the transmission power also increases the number of transmitted bits, further increasing Willie's guessing entropy. Compared to the comparative scheme, this invention significantly improves the guessing entropy by considering the concealment of the backscattering phase. Even at lower power, the guessing entropy of the proposed scheme is still higher than that of the comparative scheme at higher power, making it more difficult for Willie to reconstruct the original transmitted information, thus significantly enhancing the security performance of the communication system.

[0178] Figure 6 The maximum transmit power under different transmission schemes was demonstrated. With guessing entropy The relationship between the number of bits transmitted and the specific advantages of wirelessly powered covert BackCom. To explore the specific advantages of BackCom, this invention considers the following benchmark schemes:

[0179] a. Comparative approach: This approach takes into account that Willie knows the transmission rate of the backscatter phase and can decode the specific bit information transmitted in the backscatter phase, but does not know the specific encoding method between the bits transmitted in the backscatter phase and the active communication phase.

[0180] b. BackCom transmission only: Assuming there is no energy harvesting phase and no active transmission phase, the tag only performs backscattering to transmit information after receiving the RF signal.

[0181] c. Active transmission only: The tag does not have a backscattering stage. In the first stage, it is only used for energy harvesting. In the second stage, it transmits information through active transmission.

[0182] from Figure 6 (a) It can be seen that, when transmitting the same number of bits, the guessing entropy of the proposed scheme using the wirelessly powered covert BackCom method is significantly higher than that of the comparative scheme using a combination of backscatter communication and active communication. Furthermore, the guessing entropy of the BackCom-only transmission scheme is higher than that of the proposed scheme at low transmit power. This is because, at lower transmit power, the proposed scheme transmits fewer bits via backscatter, with most of the time allocated to the energy harvesting and active transmission phases to meet the minimum number of bits transmitted, resulting in lower guessing entropy. At higher transmit power, the proposed scheme achieves significantly improved transmission rates in both the backscatter and active transmission phases, and its guessing entropy is also significantly higher than that of the BackCom-only scheme. In contrast, the guessing entropy of the active transmission-only scheme is extremely low because the transmission behavior in the active transmission scheme is completely exposed to Willie's detection.

[0183] To measure the transmission performance of different transmission schemes, Figure 6 (b) Shows the transmit power under different transmission schemes. The relationship between the number of transmitted bits and the transmission bit count. It can be seen that in the BackCom transmission scheme only, the number of transmitted bits increases with increasing transmit power, because increasing transmit power improves the signal-to-noise ratio of the communication link. In the active transmission scheme only, because the tag uses Gaussian input modulation, the number of transmitted bits reaches its maximum value, and the communication system achieves optimal transmission performance. However, due to... Figure 6 (a) It can be seen that under the active transmission scheme alone, the transmission behavior of the communication system is completely exposed to Willie's eavesdropping, resulting in a high security risk. In contrast, to ensure the security of the communication system's transmission, we consider a certain guessing entropy, i.e. The transmission performance of the proposed scheme and the comparative scheme are compared. It can be seen that the proposed scheme achieves near-optimal transmission performance under different transmit power conditions (active transmission only), while the comparative scheme fails to meet security constraints at lower transmit power. Only when the transmission power is high does its transmission performance gradually approach that of the scheme presented in this paper.

[0184] Simulation results show that the method described in this invention significantly improves the eavesdropper's guessing entropy compared to traditional information segmentation schemes, while achieving a reasonable trade-off between transmission performance and security.

[0185] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A wireless power supply covert backscatter communication method based on information segmentation, characterized in that, include: Backscattering labels obtain first information and second information by performing information segmentation on the original information sequence; Set the total communication time to T The communication process is divided into a first stage and a second stage, with the time allocation coefficient for the first stage being... ; Phase 1 At that time, the first information is transmitted on the backscatter link, and the backscatter tag achieves covert communication by modulating the reflected randomized continuous wave signal; Phase Two At that time, the second information is transmitted through the active uplink, and the backscatter tag actively transmits signals using the collected energy to achieve information transmission; The information segmentation process includes: introducing guessing entropy as a security metric at the information level, using the guessing entropy of the eavesdropper as a measure. To maximize the objective, construct a joint optimization problem. Furthermore, the optimization problems of randomized continuous wave signal parameters and time allocation coefficients for wireless power supply backscatter communication are introduced. After decomposing the joint optimization problem, the solution to the joint optimization problem is obtained, and the information segmentation scheme is obtained. Among them, the constructed joint optimization problem Represented as: in, The entropy represents the eavesdropper's guessing ability, which quantifies the resistance to guessing attacks in wirelessly powered, covert backscatter communication; optimization conditions This indicates the stealth of the first stage of backscatter transmission, making it impossible for eavesdroppers to detect the backscatter transmission and difficult to know the specific data of the backscatter transmission. express and The relative entropy between them and Indicates that the listener observed the signal at and The probability density distribution under the assumption, and These represent two scenarios: the tag did not transmit backscatter and it did communicate via backscatter, respectively. This indicates a hidden requirement; This represents the mean power of a randomized continuous wave signal. and These represent the mean and variance of the randomized continuous wave signal, respectively. This represents the time allocation coefficient for the first phase. Indicates the energy harvesting time coefficient; This indicates the maximum transmit power of the radio frequency signal sent by the wireless transceiver. This indicates the number of bits actively transmitted in the second phase. This indicates the number of bits unloaded in the first phase. This represents the minimum number of bits in a single frame of signal. The listener's guessing entropy Represented as: in, It represents the guessing entropy of the eavesdropper, which quantifies the ability of covert communication to resist guessing attacks; Represents the sequence of the first stage of transmission The total length; Represents the sequence of the first stage of transmission Length, q In the set Evenly distributed in the middle; This represents the probability of each length. ; This indicates that for a length of q The number of conditional expectation guesses for the sequence; This represents the possible sequence that the eavesdropper guesses to exist; This indicates that the length was initially guessed to be... q The total number of sequences that have been guessed before the given sequence, i.e., all sequences with lengths less than [a certain value]. q The total number of sequences.

2. The wireless power supply covert backscatter communication method based on information segmentation according to claim 1, characterized in that, Parameter optimization problem of decomposed randomized continuous wave signal Represented as: in, This represents an approximate value of the achievable rate during the backscattering phase, and the optimization conditions. This indicates the stealth of the first-stage backscatter transmission. This indicates a hidden requirement; This represents the mean power of a randomized continuous wave signal. and These represent the mean and variance of the randomized continuous wave signal, respectively. This indicates the maximum transmit power of the radio frequency signal sent by the wireless transceiver; Using the Lagrange dual ascent method to solve the parameter optimization problem of randomized continuous wave signals and It includes the following steps: Step 1: Solve the original optimization problem This is transformed into a dual problem to achieve distributed solution, and can be expressed using the Lagrange function as follows: in, They represent the Lagrange multipliers respectively; Original optimization problem It can be transformed into its dual problem form. , is represented as: Step 2: After giving the initial values ​​of the Lagrange multipliers, The solution process includes the following steps: Step 2.1, for variables and Calculate its local optimum; Step 2.2: Update the corresponding Lagrange multipliers based on the calculation results of Step 2.1; Step 2.3: By repeatedly performing steps 2.1 and 2.2, the algorithm gradually converges to the optimal value. and .

3. The wireless power supply covert backscatter communication method based on information segmentation according to claim 2, characterized in that, Step 2 specifically includes: Using gradient ascent to find variables and The local optimal solution, whose iterative update expression is: in, and These represent the corresponding update step size. and They represent and The p +1 iteration result, and They represent and The p The result of the second iteration Represent the Lagrange function pair The partial derivatives, Represent the Lagrange function pair The partial derivatives; Lagrange function pairs The standard expression for the partial derivative is: in, m and l Indicates the first m and l Each time slot, i.e. and Indicates the first m and l Equal probability data symbols transmitted by each time slot label Indicates the cardinality of the user's backscatter transmission data symbol set; in, This is represented as an equivalent substitution expression; This indicates the channel between the wireless transceiver and the backscatter tag; This represents the equivalent channel experienced by a radio frequency signal transmitted by a wireless transceiver, received by a tag, backscattered and transmitted, and received by an eavesdropper. in, This represents an equivalent substitution expression; ,and ,in , The equivalent channel through which radio frequency signals are transmitted by the wireless transceiver, received by the tag, backscattered, and then received by the wireless transceiver. for conjugate, This represents the noise variance at the receiver end of the wireless transceiver; Lagrange function pairs The standard expression for the partial derivative is: in, The expression is as follows: The calculation yields the Lagrange function with respect to... and After obtaining the partial derivatives, the Lagrange multipliers are iterated using the gradient descent method. This causes the Lagrange function to converge to its minimum value; the specific iterative process is as follows: in, , , and They represent The update step size; combined with the Lagrange function to calculate the gradient of the Lagrange multiplier, can be expressed as: Through continuous iteration and optimization Finally, the constraints are satisfied. The maximum value; At the same time, in maximizing Under these conditions, the optimal settings for randomized continuous waves are obtained. The achievable rate is obtained by using the achievable rate formula of the backscattering stage. The calculation.

4. A wireless power supply covert backscatter communication method based on information segmentation according to claim 1 or 2, characterized in that, Based on solving the optimization problem The first stage was obtained To calculate the maximum number of bits transmitted in the first phase, and after obtaining this maximum number of bits, the time allocation coefficients for wireless backscatter communication are optimized to maximize the eavesdropper's guess entropy. The optimization problem is... Represented as: Among them, optimization problems Optimization is performed using the particle swarm optimization algorithm. This represents the guessing entropy of the eavesdropper, which quantifies the ability of covert communication to resist guessing attacks. This represents the time allocation coefficient for the first phase. Indicates the energy harvesting time coefficient; This indicates the number of bits actively transmitted in the second phase. This indicates the number of bits unloaded in the first phase. This represents the minimum number of bits in a single frame of signal.

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