A method for evaluating the security performance of a bistatic backscatter communication system under outdated channel state information

Abstract

The application relates to a method for evaluating the security performance of a two-station backscattering communication system under outdated channel state information, comprising the following steps: constructing a two-station backscattering communication system model; presetting a label access strategy based on order statistics; constructing a two-station backscattering communication system model; determining the actual backscattering link channel coefficient corresponding to the selected label in the data transmission stage; determining the received signal-to-noise ratio of a destination node and the received signal-to-noise ratio of an eavesdropping node; determining the cumulative distribution function of the actual backscattering link gain of the selected label in the data transmission stage; obtaining the closed-form expression of the system strict secrecy outage probability, the high signal-to-noise ratio asymptotic expression and the ergodic secrecy capacity expression; and evaluating the security performance of the two-station backscattering communication system model under outdated channel state information according to the closed-form expressions of the system strict secrecy outage probability and the ergodic secrecy capacity.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and physical layer security technology, and in particular to a method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information. Background Technology

[0002] Thanks to its ultra-low power consumption, backscatter communication (BackCom) is considered a potential key technology to support the large-scale deployment of Internet of Things (IoT) devices [1]. However, the inherent broadcast characteristics of wireless channels make backscatter transmission more vulnerable to passive eavesdropping attacks, thus highlighting the necessity of achieving secure transmission and carrying out physical layer security design.

[0003] [1] Liu Y, Ye Y, Yan G, et al. Outage performance analysis for anopportunistic source selection based on two-way cooperative ambient backscattercommunication system[J]. IEEE Communications Letters, 2020, 25(2): 437-441.

[0004] Physical layer security, as a lightweight security paradigm, utilizes the inherent randomness of wireless channels to enhance confidentiality and has been extensively studied. Existing research has proposed various solutions to improve security in backscatter communication scenarios. For example, reference [2] proposes a joint design method for dynamic reflection coefficient and optimal tag (backscattering device) selection in backscatter communication scenarios to reduce the system security outage probability (SOP). Reference [3] analyzes the impact of channel correlation between the forward link and the backscatter link on confidentiality performance in a single-site BackCom system with eavesdroppers. It can be noted that the above studies are usually based on an ideal assumption: that perfect, timely and accurate CSI can be obtained when tag scheduling is performed.

[0005] [2] Liu Y, Ye Y, Hu R Q. Secrecy outage probability in backscattercommunication systems with tag selection[J]. IEEE Wireless Communications Letters, 2021, 10(10): 2190-2194.

[0006] [3] Zhang Y, Gao F, Fan L, et al. Secure communications for multi-tagbackscatter systems[J]. IEEE Wireless Communications Letters, 2019, 8(4):1146-1149.

[0007] However, in actual systems, due to factors such as terminal mobility, channel time-varying and feedback delay, there is a deviation between the CSI used for tag scheduling and the CSI used for actual data transmission, which results in the problem of outdated CSI. Some existing studies have focused on the impact of outdated CSI on backscattering systems. For example, reference [4] conducted tag selection research under outdated CSI conditions for a single-site BackCom scenario and derived the corresponding interruption probability expression. Reference [5] analyzed and evaluated the interruption performance of the backscattering system in a multi-tag environment, taking into account non-ideal factors such as radio frequency (RF) hardware damage and outdated CSI. However, the above studies mainly focus on the performance characterization at the reliability index level, and there is still a lack of systematic research and a unified analysis framework for the impact of outdated CSI on the system's security performance. It is worth noting that when the quality of the eavesdropping link is better than that of the backscattering link, the traditional security criteria still allow the system to continue transmitting information, which may face a serious risk of information leakage. Under outdated CSI conditions, this security risk will be significantly amplified because the mismatch of tag scheduling will increase the probability that the quality of the eavesdropping channel is better than that of the selected backscattering link. In addition, existing analyses [4], [6], and [7] are based on the assumption of independent and identically distributed Rayleigh fading channels. This assumption may not be able to fully characterize the differences in links under actual backscatter propagation conditions such as multiple labels and heterogeneous distances, thus limiting the applicability of the analysis results to engineering scenarios.

[0008] [4] Deng D, Li X, Dang S, et al. Outage analysis for tag selection in reciprocal backscatter communication systems[J]. IEEE Wireless Communications Letters, 2021, 11(2): 210-214。

[0009] [5] Ali M, Sharma P K. Outage Analysis of Multi-Tag Ambient Backscatter Systems Under RFHIs and Outdated CSI[J]. IEEE Wireless Communications Letters, 2025。

[0010] [6] Hwang K S, Ju M C, Alouini M S. Outage performance of opportunistic two-way amplify-and-forward relaying with outdated channel state information[J]. IEEE transactions on communications, 2013, 61(9): 3635-3643。

[0011] [7] Michalopoulos D S, Suraweera H A, Karagiannidis G K, et al. Amplify-and-forward relay selection with outdated channel estimates[J]. IEEE Transactions on Communications, 2012, 60(5): 1278-1290。 Summary of the Invention

[0012] The purpose of this invention is to provide a method for evaluating the security performance of a bi-station backscatter communication system using outdated Channel State Information (CSI). Traditional security performance evaluation frameworks often fail to clearly distinguish the channel states where the eavesdropping link is superior to the backscattering link. In practical scenarios where tag scheduling relies on outdated CSI, this limitation leads to a sharp increase in the probability of eavesdropping advantage, resulting in a significant degradation of the system's security performance. To address this problem, this invention introduces a strict security criterion as the core evaluation indicator, explicitly incorporating the quality of the eavesdropping link into the security performance evaluation system. Based on this criterion, under an independent but not necessarily identically distributed (iID) Rayleigh fading channel model, for a partial tag selection strategy based on order statistics, this invention derives closed-form expressions for the system's Strict Secrecy Outage Probability (S-SOP) and Ergodic Secrecy Capacity (ESC), and further provides an asymptotic expression for S-SOP under high signal-to-noise ratio conditions. Numerical results show that CSI obsolescence not only leads to an increase in S-SOP, but also a decrease in ESC. Furthermore, as the degree of CSI obsolescence worsens, the gap between ESC under strict and traditional confidentiality guidelines widens further, fully validating the necessity and effectiveness of introducing strict confidentiality guidelines under obsolete CSI conditions.

[0013] To achieve the above objectives, the present invention provides the following solution: A method for evaluating the security performance of a bistatic backscatter communication system under outdated channel state information, comprising: Construct a model of a bi-station backscatter communication system; A preset tag access strategy based on sequence statistics is used to select the tag with the highest backscatter link gain for backscatter transmission; Construct an outdated channel state information model to describe the temporal correlation between the channel state information obtained during the label selection phase and the actual channel state during the data transmission phase; Based on the bi-station backscatter communication system model, the tag access strategy, and the outdated channel state information model, the selected tag for the data transmission phase is determined. Corresponding actual backscatter link channel coefficient The signal-to-noise ratio (SNR) received by the target node and the SNR received by the eavesdropping node are determined according to the first and second preset formulas, respectively; and the selected tag is determined according to the third preset formula. Actual backscatter link gain during data transmission phase The cumulative distribution function; Based on the selected label Corresponding actual backscatter link channel coefficient The destination node's received signal-to-noise ratio, the eavesdropping node's received signal-to-noise ratio, and the selected tag. The cumulative distribution of backscatter link gain is used to obtain the closed-form expression, the high signal-to-noise ratio asymptotic expression, and the traversal security capacity expression for the system's strictly confidential interruption probability. Based on the closed-form expression of the system's strict confidentiality interruption probability and ergonomic confidentiality capacity, the confidentiality performance of the bi-station backscatter communication system model under outdated channel state information is evaluated.

[0014] Optionally, the bistation backscatter communication system model includes: a single radio frequency source. Single destination node Single eavesdropping node as well as One tag; In the bistation backscatter communication system model, the radio frequency source By transmitting only an unmodulated carrier wave or a common excitation signal, the selected tag modulates the incident radio frequency signal by adjusting its own reflection coefficient, thereby transmitting its confidential information to the destination node. All wireless channels are modeled as quasi-static Rayleigh fading.

[0015] Optionally, the tag access strategy for the sequential statistics includes: The destination node sorts the tags according to their backscatter link channel gain.

[0016] Optionally, the outdated channel state information model is: ; in, This represents the actual channel coefficients during data transmission. This represents the channel coefficient at the tag selection time. express Circularly symmetric complex Gaussian random variables with the same variance express and The correlation coefficient between them.

[0017] Optionally, performing the backscatter transmission includes: The destination further compares the backscatter link channel gain of the selected tag with its corresponding eavesdropping link channel gain; if Then the tag is allowed. Perform backscatter transmission; otherwise, the tag remains silent; where, This represents the channel coefficient at the tag selection time. This indicates the corresponding eavesdropping link channel gain.

[0018] Optionally, the first preset formula is: ; in, Represents a node via link The received signal-to-noise ratio, This represents the average transmitted signal-to-noise ratio of the links to D and E. This represents the variance of the complex Gaussian noise at points D and E. This indicates the forward link channel gain from the RF source to the selected tag. Represents the reflection coefficient at a fixed power. This indicates the transmit power of the RF source, and D and E represent the destination node and the eavesdropping node, respectively. The channel coefficients at the tag selection time; The second preset formula is: ; in, This indicates the signal-to-noise ratio received by the eavesdropping node. This indicates the corresponding eavesdropping link channel gain.

[0019] Optionally, the third preset formula is: ; in, Indicates the selected label Actual backscatter link gain during data transmission phase The cumulative distribution function, This represents the sorted label index. This indicates removing an index from the tag index set. The resulting set Indicates the total number of tags; Indicates the process of inclusion-exclusion expansion from set Any subset of the tag indexes selected from the list. This represents the third auxiliary parameter determined by the outdated correlation coefficient. This represents the first auxiliary parameter determined by the outdated correlation coefficient, the power gain of the backscatter link of the selected tag, and the average power gain of the backscatter link of other tags. This represents a second auxiliary parameter determined by the outdated correlation coefficient, the power gain of the backscatter link of the selected tag, and the average power gain of the backscatter link of other tags.

[0020] Optionally, the closed-form expression for the system's strictly confidentiality interruption probability is: ; in, This indicates the probability of a system interruption requiring strict confidentiality. This represents the sorted label index; This indicates removing an index from the tag index set. The resulting set; Indicates the total number of tags; Indicates the process of inclusion-exclusion expansion from set Any subset of the tag indexes selected from; Represents a set T Tag index in; Indicates the correlation coefficient due to obsolescence. Selected tag backscatter link power gain The first auxiliary parameter is determined together with the average power gain of the backscattering link of other tags; Indicates the correlation coefficient due to obsolescence. Selected tag backscatter link power gain The second auxiliary parameter is determined together with the average power gain of the backscattering link of other tags; This represents the secrecy interruption decision threshold determined by the target secrecy rate; Indicates the target secrecy rate; This represents the third auxiliary parameter determined by the outdated correlation coefficient; This represents the correlation coefficient between the channel coefficients during the label selection phase and the actual channel coefficients during the data transmission phase. This represents the variance of the forward link channel coefficients from the radio frequency source to the selected tag; This represents the variance of the backscatter link channel coefficients from the selected tag to the destination node; This represents the variance of the channel coefficients of the eavesdropping link from the selected tag to the eavesdropping node; Represents the reflection coefficient at a fixed power. Represents a first-order modified Bessel function; The asymptotic expression for the high signal-to-noise ratio of the system's strict security interruption probability is: ; in, The high signal-to-noise ratio asymptotic value representing the probability of a system's strict security interruption.

[0021] Alternatively, the closed-form expression for traversing the secrecy capacity is: ; in, This indicates traversing the confidential capacity. This represents the instantaneous signal-to-noise ratio under strict confidentiality standards. express The probability density function, Represents the integral variable. Represents the differential with respect to the variable u. express The cumulative distribution function, Represents the secant function. Denotes the order of the Gauss-Chebyshev product. This represents the index of a Gauss-Chebyshev quadrature node. Indicates the first Gauss-Chebyshev integration nodes Indicates the product of the quadrature nodes The variables obtained from the mapping.

[0022] The beneficial effects of this invention are as follows: This invention introduces strict confidentiality criteria under outdated channel state information conditions, and incorporates the high-risk state of the eavesdropping link having an instantaneous quality better than the legitimate backscatter link into the confidentiality performance evaluation process, which can more accurately characterize the information leakage risk of the system compared with the traditional confidentiality interruption criteria.

[0023] This invention considers the time mismatch between channel state information during the tag selection phase and the actual channel state during the data transmission phase, and can effectively reflect the impact of factors such as feedback delay, node mobility, and channel time-varying on the security performance of a bi-station backscatter communication system.

[0024] This invention performs system modeling and performance derivation under independent, non-co-distributed Rayleigh fading channel conditions, and is applicable to bi-station backscatter communication scenarios with significant differences in multi-label location, link distance, and channel quality, thereby improving the applicability of the security performance evaluation method.

[0025] This invention provides a closed-form expression for the probability of strict system security interruption, a high signal-to-noise ratio asymptotic expression, and an ergonomic security capacity expression, which can reduce the computational complexity of system security performance evaluation and provide a theoretical basis for tag number configuration, reflection coefficient setting, and system security parameter design. Attached Figure Description

[0026] 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.

[0027] Figure 1 This is a schematic diagram of the dual-station backscatter communication system model structure according to an embodiment of the present invention; Figure 2Different correlation coefficients in embodiments of the present invention A schematic diagram showing the relationship between S-SOP and transmit power; Figure 3 Different number of labels in embodiments of the present invention A schematic diagram showing the relationship between S-SOP and transmit power; Figure 4 This is a schematic diagram illustrating the relationship between ESC and transmit power under strict and traditional confidentiality guidelines in an embodiment of the present invention. Figure 5 This is a schematic flowchart of a method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information, according to an embodiment of the present invention. Detailed Implementation

[0028] 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.

[0029] 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.

[0030] like Figure 5 This embodiment proposes a method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information, including: A method for evaluating the security performance of a bistatic backscatter communication system under outdated channel state information, comprising: Construct a model of a bi-station backscatter communication system; A preset tag access strategy based on sequence statistics is used to select the tag with the highest backscatter link gain for backscatter transmission; Construct an outdated channel state information model to describe the temporal correlation between the channel state information obtained during the label selection phase and the actual channel state during the data transmission phase; Based on the bi-station backscatter communication system model, the tag access strategy, and the outdated channel state information model, the selected tag for the data transmission phase is determined. Corresponding actual backscatter link channel coefficient The signal-to-noise ratio (SNR) received by the target node and the SNR received by the eavesdropping node are determined according to the first and second preset formulas, respectively; and the selected tag is determined according to the third preset formula. Actual backscatter link gain during data transmission phase The cumulative distribution function; Based on the selected label Corresponding actual backscatter link channel coefficient The destination node's received signal-to-noise ratio, the eavesdropping node's received signal-to-noise ratio, and the selected tag. The cumulative distribution of backscatter link gain is used to obtain the closed-form expression, the high signal-to-noise ratio asymptotic expression, and the traversal security capacity expression for the system's strictly confidential interruption probability. Based on the closed-form expression of the system's strict confidentiality interruption probability and ergonomic confidentiality capacity, the confidentiality performance of the bi-station backscatter communication system model under outdated channel state information is evaluated.

[0031] like Figure 1 As shown, this embodiment, in a multi-tag bi-station backscatter communication system with outdated channel state information (CSI), incorporates the quality of the eavesdropping link into the confidentiality criterion for IoT communication scenarios with a single eavesdropper, and adopts a partial tag selection strategy based on order statistics to achieve system security performance evaluation under non-ideal CSI. Regarding the above tag selection strategy, under independent but not necessarily identically distributed (INID) Rayleigh fading channels, closed-form expressions and high signal-to-noise ratio asymptotic expressions for the system's strict secrecy outage probability (S-SOP) and ergodic secrecy capacity (ESC) are derived and verified through simulation.

[0032] Specifically, the bistationary backscatter communication system model in this embodiment, namely the backscatter communication (BackCom) network, consists of a single RF source. Single destination node Single eavesdropping node as well as It consists of several tags. In the system under consideration, a dedicated RF source... It transmits only an unmodulated carrier wave or a common excitation signal, without carrying any confidential information. The selected tag modulates the incident RF signal by adjusting its own reflection coefficient, thereby transmitting its confidential information to the destination node. Therefore, this invention focuses on the confidentiality of tag confidential information transmitted in a backscatter link. Furthermore, and There is no direct link between them, which may be due to and This is caused by significant shielding between them. All wireless channels are modeled as quasi-static Rayleigh fading. Specifically, the link... , and The channel coefficients are modeled as follows: , and ,in Assume the destination node can obtain information through channel estimation. and and possess CSI.

[0033] Furthermore, the tag access strategy for the sequential statistics includes: The destination node sorts the tags according to their backscatter link channel gain.

[0034] Specifically, in this embodiment, some label selection strategies are as follows: To analyze the impact of outdated CSI on multi-tag backscatter communication systems, this invention considers a tag access strategy based on order statistics. Specifically, during the tag selection phase, the destination node sorts the candidate tags according to their backscatter link channel gain, as follows: (1) It should be pointed out that, The index representing the optimal sorting label (this invention defines the index of the optimal label as...) ,but (representing maximum channel gain), and This corresponds to the index of the lower-ranked label. To verify the applicability of the scheduling mechanism in the obsolete CSI scenario, this invention compares the system performance when different ranking labels are selected through simulation. The underlying logic is that if the CSI becomes obsolete, causing the scheduling mechanism to completely fail, the system performance obtained by selecting different ranking labels will tend to be consistent, and the performance gap between the optimal label and the lower-ranked label will also disappear.

[0035] Specifically, in this embodiment, the outdated CSI model is: Due to destination mobility and feedback delay, the channel coefficients during data transmission differ from the estimates obtained at the label selection time, but remain temporally correlated with them. Let... This represents the channel coefficient at the tag selection time. This represents the actual channel coefficients during data transmission. Using a time-correlated outdated CSI model, the imperfect CSI of the selected tag during data transmission can be modeled as follows: That is, the outdated channel state information model is: (2) In the above formula This represents the actual channel coefficients during data transmission. This represents the channel coefficient at the tag selection time. express Circularly symmetric complex Gaussian random variables with the same variance, while express and The correlation coefficient between them. According to Jakes' autocorrelation model, Can be written as ,in Represents relative velocity. For symbols For symbol period, Indicates the carrier frequency. At the speed of light, This represents the zeroth-order Bessel function of the first kind.

[0036] To clarify the strict transmission mechanism employed in this embodiment, the tag scheduling process can be summarized as follows. First, the destination end sorts the tags according to their backscatter link channel gain and selects the tag with the highest backscatter link gain for transmission, denoted as . Subsequently, before actual data transmission, the destination further compares the backscatter link channel gain of the selected tag with its corresponding eavesdropping link channel gain. If Then the tag is allowed. Perform backscatter transmission. Otherwise, the tag remains silent. It is important to emphasize that, under the condition of outdated CSI, the CSI acquired during the tag selection phase may be outdated during the actual data transmission phase. This causes scheduling decisions based on this CSI to deviate from the actual channel state at the time of information transmission, thus leading to tag scheduling mismatch. Nevertheless, due to the time correlation of the wireless channel, the CSI acquired during the tag selection phase is not completely independent of the actual channel state during data transmission. Therefore, it can still provide a valid basis for the aforementioned order-based tag scheduling. Furthermore, once a tag is selected, subsequent data transmission will only involve the selected tag, without requiring continuous global reordering across all tags.

[0037] Specifically, in this embodiment, the received signal and signal-to-noise ratio are: Target node and eavesdropping nodes The received signal is represented as and .in, Indicates the destination node Received signal, Indicates eavesdropping node Received signal, Indicates label The fixed reflection coefficient, express The transmission power, express The transmitted unit power signal, This represents the complex Gaussian noise at points D and E. This represents the actual channel coefficients during data transmission. Indicates the forward link channel gain from the RF source to the selected tag; Based on the above analysis, the target node via link The received signal-to-noise ratio (SNR) can be expressed as: (3) Similarly, through The link is The received SNR is given by the following formula: (4) In equations (3) and (4) This represents the average transmit SNR of the links to D and E.

[0038] Specifically, in this embodiment, the S-SOP is derived as follows: Based on equations (3) and (4), the link Instantaneous confidentiality can be expressed as: (5) Therefore, S-SOP can be represented as: (6) in To achieve a confidentiality rate for the target.

[0039] Combining equation (5) and equation (6) The item can be further expanded as follows: (7) Substituting equation (7) into equation (6), It can be reformulated as: (8) It should be noted that, as can be seen from equation (8), both strict and traditional confidentiality criteria define an event where the confidentiality capacity falls below the target threshold as a confidentiality interruption, provided that transmission is allowed. However, the fundamental difference between these two criteria lies not in the interruption threshold itself, but in the post-scheduling processing mechanism. Specifically, traditional confidentiality criteria allow tags to transmit information even under unfavorable channel conditions. In contrast, the strict confidentiality mechanism adopted in this invention actively abandons transmission opportunities with a high risk of information leakage. Therefore, the strict confidentiality mechanism adopted in this invention can still achieve a higher ESC, which will be further verified in subsequent simulation results.

[0040] Next derivation The cumulative distribution function (CDF).

[0041] definition for Let there be 1 independent random variables, arranged in ascending order as follows: .but For the first A sequence statistic. Event This indicates that a unique index exists. Make ( The probability density function (PDF) is And in the remaining samples, there are exactly... The number of samples is less than .

[0042] To characterize the probability of this event, a value of is introduced. subset of Based on the independence assumption, for all subsets that satisfy the conditions... With index By iterating and summing, we can obtain ,in Using the inclusion-exclusion principle, we can apply this to consecutive products. Expand the product term. Specifically, expand the product term and work over all possible subsets. By summing, this embodiment obtains Similarly, for complementary index sets, we can obtain... At this point, the maximum backscatter link gain (i.e. The PDF (at that time) can be derived as follows: (9) The PDF can be obtained by integrating the conditional probability function: (10) in It can be equivalent to .also, and These are related variables, and their joint PDF is .

[0043] In summary, equation (10) can be... The integral expression simplifies to: (11) Finally, using the standard integral identity Solve the inner integral You can get The exact closed-form solution. Further integration of equation (11) yields... The actual backscatter link channel coefficient (CDF).

[0044] therefore, The CDF can be represented as: (12) In the above formula , , .

[0045] For ease of derivation, variables are defined. as well as . and The PDFs are represented as follows: and .

[0046] Using equation (12), equation (8) can be rewritten as equation (13). In equation (13), step (c) represents the substitution of... CDF and variables and The PDF was then further simplified algebraically. Furthermore, in equation (13)... It can be calculated directly, and This can be achieved by using integral identities. What was obtained was thus acquired. A closed expression. Here .

[0047] (13) In summary, under the context of obsolete CSI, It can be calculated using the following expression: (14) Under high signal-to-noise ratio conditions Interruption probability It can be approximated as: (15) From equation (15), it can be observed that increasing the correlation coefficient... Or increase the number of tags It will increase the value in equation (15) This reduces the S-SOP of the system under consideration. Furthermore, under high signal-to-noise ratio conditions, the S-SOP approaches a constant. Therefore, the diversity order is zero, i.e. This is due to the inherent constraints imposed by the eavesdropper; even with an increase in the signal-to-noise ratio, these constraints limit further improvements in security.

[0048] Specifically, in this embodiment, the ESC derivation is as follows: ESC characterizes the average randomness across all fading states. Its expression is: (16) In the above formula The corresponding CDF can be represented as .

[0049] In ESC analysis, the strict confidentiality criterion is primarily reflected in the instantaneous confidentiality rate. Specifically, when the eavesdropping link is stronger than the backscatter link, In this channel state, continued transmission not only fails to achieve a positive security rate but may also lead to information leakage risks. Therefore, under strict security guidelines, these states are considered insecure transmission states, and their contribution to ESC is set to zero.

[0050] Therefore, under the condition of obsolete CSI, the ESC based on strict confidentiality principles can be derived as follows: (17) In equation (17), step (d) represents integration by parts, and step (e) represents substitution of variables. Step (f) indicates the use of Gauss-Chebyshev integration. Refer to equation (7). It can be rewritten as And following the derivation steps in equation (13), we can obtain The closed expression is obtained, thus yielding A closed expression.

[0051] Simulation results: The simulation parameters are set as follows: The average channel power gain is given by the following formula: , ,as well as ,in At the speed of light, , , , They are respectively , , and Antenna gain at [location]. All antenna gains are set to [value]. . , and Representing nodes respectively and tags exist The distance on the link, of which The path loss exponent is... The carrier frequency is In a two-dimensional Cartesian coordinate system, , and Fixed at respectively m、 m and At point m. The labels are evenly distributed in areas with... With m as the center and radius as Inside the circle of m, at position m ,in exist Uniformly distributed within. Other parameters are: , , ,as well as bit / s / Hz.

[0052] like Figure 2 As shown, the analytical results in equation (14) and the high signal-to-noise ratio asymptotic approximation in equation (15) agree well with the Monte Carlo simulation results, thus verifying the correctness of the derived expressions. According to the Jakes model, the speed of the destination end node decreasing from 120 mph to 40 mph will... The value increased from 0.963 to 0.995, thus reducing S-SOP. This is because the stronger time correlation makes the CSI acquired at the tag selection time closer to the actual channel state during data transmission, thereby improving the reliability of identifying the optimal tag. Furthermore, compared to the perfect CSI case (i.e.,...) Compared to older versions, outdated CSI will significantly degrade the security performance of the system.

[0053] like Figure 3 As shown, S-SOP with The decrease due to the increase in the total number of tags (i.e., the total number of tags) indicates that increasing the number of tags can improve the confidentiality performance of the system. Figure 3middle," "and" "Corresponds to selecting the suboptimal label, that is, respectively in and Choose the label with the second highest backscatter link gain from the available labels. Similarly, in... Figure 2 middle," "Indicates selecting the suboptimal label, that is, in The label with the second-highest backscatter link gain was selected from the available labels. Therefore, Figure 2 and Figure 3 This indicates that, under different parameter configurations, there is a significant performance gap between the highest-ranked tag and the lowest-ranked tag, thus verifying the feasibility of adopting this tag access strategy under obsolete CSI conditions.

[0054] Figure 4 The impact of the number of tags and the correlation coefficient on ESC was compared under strict and traditional confidentiality guidelines. Several significant observations were drawn. First, increasing the number of tags or increasing the correlation coefficient... First, it improves ESC. Second, the strict confidentiality principle achieves an even higher ESC. Finally, given a certain number of tags, the ESC difference between the two principles becomes more significant as obsolescence increases. This is because the strict confidentiality principle eliminates transmission events that could lead to serious information leakage risks, thus ensuring more robust and secure transmission for the entire system.

[0055] 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 to the technical solutions of the present invention by those skilled in the art 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 method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information, characterized in that, include: Construct a model of a bi-station backscatter communication system; A preset tag access strategy based on sequence statistics is used to select the tag with the highest backscatter link gain for backscatter transmission; Construct an outdated channel state information model to describe the temporal correlation between the channel state information obtained during the label selection phase and the actual channel state during the data transmission phase; Based on the bi-station backscatter communication system model, the tag access strategy, and the outdated channel state information model, the selected tag for the data transmission phase is determined. Corresponding actual backscatter link channel coefficient ; The signal-to-noise ratio (SNR) received by the target node and the SNR received by the eavesdropping node are determined according to the first preset formula and the second preset formula, respectively. The selected label is determined according to the third preset formula. Actual backscatter link gain during data transmission phase The cumulative distribution function; Based on the selected label Corresponding actual backscatter link channel coefficient The destination node's received signal-to-noise ratio, the eavesdropping node's received signal-to-noise ratio, and the selected tag. The cumulative distribution of backscatter link gain is used to obtain the closed-form expression, the high signal-to-noise ratio asymptotic expression, and the traversal security capacity expression for the system's strictly confidential interruption probability. Based on the closed-form expression of the system's strict confidentiality interruption probability and ergonomic confidentiality capacity, the confidentiality performance of the bi-station backscatter communication system model under outdated channel state information is evaluated.

2. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, characterized in that, The bistation backscatter communication system model includes: a single radio frequency source. Single destination node Single eavesdropping node as well as One tag; In the bistation backscatter communication system model, the radio frequency source By transmitting only an unmodulated carrier wave or a common excitation signal, the selected tag modulates the incident radio frequency signal by adjusting its own reflection coefficient, thereby transmitting its confidential information to the destination node. All wireless channels are modeled as quasi-static Rayleigh fading.

3. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, characterized in that, The tag access strategy for the sequential statistics includes: The destination node sorts the tags according to their backscatter link channel gain.

4. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, characterized in that, The outdated channel state information model is as follows: ； in, This represents the actual channel coefficients during data transmission. This represents the channel coefficient at the tag selection time. express Circularly symmetric complex Gaussian random variables with the same variance express and The correlation coefficient between them.

5. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, characterized in that, Performing the backscatter transmission includes: The destination further compares the backscatter link channel gain of the selected tag with its corresponding eavesdropping link channel gain; if Then the tag is allowed. Perform backscatter transmission; otherwise, the tag remains silent; where, This represents the channel coefficient at the tag selection time. This indicates the corresponding eavesdropping link channel gain.

6. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, characterized in that, The first preset formula is: ； in, Represents a node via link The received signal-to-noise ratio, This represents the average transmitted signal-to-noise ratio of the links to D and E. This represents the variance of the complex Gaussian noise at points D and E. This indicates the forward link channel gain from the RF source to the selected tag. Represents the reflection coefficient at a fixed power. This indicates the transmit power of the RF source, and D and E represent the destination node and the eavesdropping node, respectively. The channel coefficients at the tag selection time; The second preset formula is: ； in, This indicates the signal-to-noise ratio received by the eavesdropping node. This indicates the corresponding eavesdropping link channel gain.

7. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, wherein the third preset formula is: ； in, Indicates the selected label Actual backscatter link gain during data transmission phase The cumulative distribution function, This represents the sorted label index. This indicates removing an index from the tag index set. The resulting set Indicates the total number of tags; Indicates the process of inclusion-exclusion expansion from set Any subset of the tag indexes selected from the list. This represents the third auxiliary parameter determined by the outdated correlation coefficient. This represents the first auxiliary parameter determined by the outdated correlation coefficient, the power gain of the backscatter link of the selected tag, and the average power gain of the backscatter link of other tags. This represents a second auxiliary parameter determined by the outdated correlation coefficient, the power gain of the backscatter link of the selected tag, and the average power gain of the backscatter link of other tags.

8. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, characterized in that, The closed-form expression for the system's strictly confidentiality interruption probability is: ； in, This indicates the probability of a system interruption requiring strict confidentiality. This represents the sorted label index; This indicates removing an index from the tag index set. The resulting set; Indicates the total number of tags; Indicates the process of inclusion-exclusion expansion from set Any subset of the tag indexes selected from; Represents a set T Tag index in; Indicates the correlation coefficient due to obsolescence. Selected tag backscatter link power gain The first auxiliary parameter is determined together with the average power gain of the backscattering link of other tags; Indicates the correlation coefficient due to obsolescence. Selected tag backscatter link power gain The second auxiliary parameter is determined together with the average power gain of the backscattering link of other tags; This represents the secrecy interruption decision threshold determined by the target secrecy rate; Indicates the target secrecy rate; This represents the third auxiliary parameter determined by the outdated correlation coefficient; This represents the correlation coefficient between the channel coefficients during the label selection phase and the actual channel coefficients during the data transmission phase. This represents the variance of the forward link channel coefficients from the radio frequency source to the selected tag; This represents the variance of the backscatter link channel coefficients from the selected tag to the destination node; This represents the variance of the channel coefficients of the eavesdropping link from the selected tag to the eavesdropping node; Represents the reflection coefficient at a fixed power. Represents a first-order modified Bessel function; The asymptotic expression for the high signal-to-noise ratio of the system's strict security interruption probability is: ； in, The high signal-to-noise ratio asymptotic value representing the probability of a system's strict security interruption.

9. The method for evaluating the security performance of a bi-station backscatter communication system under outdated channel state information according to claim 1, characterized in that, The closed-form expression for traversing the secret capacity is: ； in, This indicates traversing the confidential capacity. This represents the instantaneous signal-to-noise ratio under strict confidentiality standards. express The probability density function, Represents the integral variable. Represents the differential with respect to the variable u. express The cumulative distribution function, Represents the secant function. Denotes the order of the Gauss-Chebyshev product. This represents the index of a Gauss-Chebyshev quadrature node. Indicates the first Gauss-Chebyshev integration nodes Indicates the product of the quadrature nodes The variables obtained from the mapping.

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