Railway intelligent monitoring network system and method for improving information transmission reliability

Abstract

The present invention belongs to the field of communication technology and discloses a railway intelligent monitoring network system and a method for improving the reliability of information transmission. The railway intelligent monitoring network system is specifically based on a concealed dual-station BackCom network system, comprising: a carrier transmitter CE, which serves as a radio frequency source to generate an incident signal; a tag Tag, which has a backscattering circuit, which absorbs the incident signal or passively transmits information by reflecting the incident signal; a reader Reader, which receives the signal reflected by the tag Tag and obtains the information transmitted by the tag Tag; and an eavesdropper Willie, which is used to monitor whether information is being transmitted between the tag and the reader, thereby providing concealment constraints for the system. The present invention obtains approximate closed expressions for the detection error probability at the eavesdropper and the BackCom interruption probability to evaluate the communication concealment and reliability. At the same time, the problem of minimizing the BackCom transmission interruption probability is solved under high signal-to-noise ratio (SNR) conditions.

Description

Technical Field

[0001] The present invention relates to the field of communication technology, and in particular to a railway intelligent monitoring network system and a method for improving information transmission reliability. Background Art

[0002] As the backbone of the integrated transportation system, the informatization and intelligent development of railways has far-reaching significance for national and regional economic development. The railway Internet of Things (IoT) is currently experiencing rapid development, necessitating the accelerated integration of next-generation communication network technologies with the IoT to ensure reliable and accurate information transmission. This requires the deployment of a large number of IoT devices along railway lines to sense environmental parameters and transmit them to data centers. Frequent information transmission consumes the power of IoT devices. However, due to limitations in device size and production costs, IoT devices are typically powered by limited embedded batteries. Therefore, effectively extending the lifespan of IoT devices is a critical issue that needs to be addressed.

[0003] In recent years, backscatter communication (BackCom) has been proposed as an extremely low-power communication paradigm supporting IoT devices. Using this technology, IoT devices can passively modulate their own information onto the incident RF signal by adjusting the antenna load impedance and reflect the modulated signal to the information receiver. This avoids the use of high-power components such as oscillators, achieving low-power information transmission and thus addressing the high energy consumption caused by information transmission. However, due to the inherent broadcast nature of wireless channels, backscattered information is vulnerable to eavesdroppers, necessitating the urgent research of data transmission security technologies for BackCom networks.

[0004] Data encryption and physical layer security are two common data transmission security technologies. Traditional data encryption uses encryption keys, resulting in high computational complexity, which violates the low-complexity design principle of BackCom transmitters. Physical layer security leverages the physical characteristics of wireless channels to achieve secure data transmission. However, in specialized scenarios such as military communications and high-speed rail monitoring data transmission, in addition to protecting information content, it is also necessary to conceal the communication itself, which physical layer security cannot achieve.

[0005] Most existing research on covert BackCom networks exploits the uncertainty of ambient signal transmission power. While this exploits channel uncertainty, it assumes that an eavesdropper can accurately estimate the instantaneous channel state information (CSI) between the eavesdropper and the BackCom transmitter. However, since there is no collaborative relationship between the BackCom transmitter and the eavesdropper, accurate estimation of the instantaneous CSI between them is difficult in actual communications. Furthermore, as important metrics for measuring network performance, there is a trade-off between stealth and reliability. Therefore, improving network transmission performance while maintaining stealth remains an unresolved issue. Summary of the Invention

[0006] Embodiments of the present invention provide a railway intelligent monitoring network system and a method for improving information transmission reliability to address the low reliability of information transmission in railway intelligent monitoring systems in the prior art. To provide a basic understanding of some aspects of the disclosed embodiments, a brief summary is provided below. This summary is not intended to be a comprehensive review, identify key or important elements, or delineate the scope of protection of these embodiments. Its sole purpose is to present some concepts in a simplified form as a prelude to the detailed description that follows.

[0007] According to a first aspect of an embodiment of the present invention, a railway intelligent monitoring network system is provided, specifically based on a concealed dual-station BackCom network system.

[0008] In one embodiment, the system comprises:

[0009] The carrier transmitter CE acts as a radio frequency source to generate the incident signal;

[0010] The tag has a backscatter circuit that absorbs the incident signal or passively transmits information by reflecting the incident signal;

[0011] The reader receives the signal reflected by the tag and obtains the information transmitted by the tag;

[0012] The eavesdropper Willie is used to monitor whether information is being transmitted between the Tag and the Reader, providing concealment constraints for the system;

[0013] Assume that all channels are quasi-static Rayleigh fading channels, and the channel coefficients between CE-Reader, CE-Tag, CE-Willie, Tag-Reader and Tag-Willie are represented by h cr 、h ct 、h cw 、h tr and h twRepresents; then it obeys the complex Gaussian distribution, that is, h mn ~CN(0,1 / λ mn ), where (mn∈(cr,ct,cw,tr,tw)), which is constant within a time slot but varies independently between different time slots;

[0014] Where CN represents the circularly symmetric complex Gaussian distribution, 1 / λ mn represents the variance of each channel.

[0015] On the basis of the above solution, the carrier transmitter CE generates an incident signal with artificial noise based on a key pre-distributed between CE and Reader.

[0016] According to a second aspect of an embodiment of the present invention, a method for improving information transmission reliability in railway intelligent monitoring is provided.

[0017] In one embodiment, the method includes:

[0018] Based on the channel coefficient, the power reflection coefficient β of the tag and the detection threshold of the eavesdropper Willie, the closed-form expressions of the BackCom interruption probability and the detection error probability ξ are obtained.

[0019] Based on the closed expressions of BackCom outage probability and detection error probability, the reliability optimization problem of the hidden dual-station BackCom network system is formulated and rewritten as a convex optimization problem.

[0020] The reliability optimization problem of the hidden dual-station BackCom network system is decoupled into two convex optimization sub-problems through the BCD algorithm.

[0021] The power reflection coefficient β and the detection threshold τ of the eavesdropper Willie under high SNR conditions are determined by a one-dimensional search algorithm, so that the BackCom interruption probability P out Minimum.

[0022] Based on the above scheme, the BackCom interruption probability P is obtained based on the channel coefficient, the power reflection coefficient β of the tag Tag and the detection threshold τ of the eavesdropper Willie. out The steps of obtaining a closed expression for the probability of error ξ include:

[0023] The detection error probability ξ is used to measure the concealment performance of the tag, which is expressed as:

[0024] ξ=P F +P M (7)

[0025] Among them, P F =Pr(H1|H0) is the false alarm probability, PM =Pr(H0|H1) is the probability of missed detection, H0 represents the null hypothesis that the tag remains silent, and the alternative hypothesis H1 represents that the tag reflects the incident information;

[0026] ξ = 0 means that the eavesdropper Willie can detect the covert signal perfectly, while ξ = 1 means that the eavesdropper Willie cannot detect the covert signal;

[0027] When n→∞, the probability of eavesdropper Willie’s detection error can be expressed as:

[0028]

[0029] in, and τ represents the detection threshold of Willie, represents the Willie noise variance, P represents the CE transmission power, β represents the Tag power reflection coefficient, λ ct ,λ cw and λ tw They represent the inverse of the channel variance between CE-Tag, CE-Willie, and Tag-Willie, respectively, and c0≈0.5772 represents the Euler constant;

[0030] The closed-form expression for the BackCom outage probability is:

[0031]

[0032] in, K0(·) represents the modified Bessel function of the second kind, Θ = -abexp(ab)Ei(-ab) and ab = φλ ct λ tr γ0 / βλ cr , represents the exponential integral function, φ represents the interference elimination coefficient, represents the input signal-to-noise ratio of the reader, λ cr ,λ ct and λ tr They represent the inverse of the channel variance between CE-Reader, CE-Tag and Tag-Reader, γ0 represents the corresponding decoding threshold, |h ct | 2 、|h cr | 2 and |h tr | 2 Represent the channel gains between CE-Tag, CE-Reader, and Tag-Reader, respectively;

[0033] Based on the above formula, the optimization problem can be expressed as:

[0034]

[0035] Among them, C0 is the value range of the detection threshold, C1 ensures the concealment of communication, and C2 constrains the value range of the power reflection coefficient. ξ is the detection error probability of the eavesdropper Willie, β is the power reflection coefficient of the tag Tag, and τ is the detection threshold of the eavesdropper Willie. represents the noise variance at the eavesdropper Willie, P out represents the interruption probability of BackCom, and ε is an arbitrarily small value that determines the concealment level.

[0036] Based on the above solution, the steps of decoupling the reliability optimization problem of the covert dual-station BackCom network system into two convex optimization sub-problems using the BCD algorithm specifically include:

[0037] The detection threshold τ of the eavesdropper Willie and the BackCom interruption probability P out Convex optimization subproblem of ;

[0038] Tag power reflection coefficient β and BackCom interruption probability P out Convex optimization subproblem of .

[0039] Based on the above solution, the power reflection coefficient β of the tag and the BackCom interruption probability P out The steps of the convex optimization subproblem include:

[0040]

[0041] Where ξ is the detection error probability of the eavesdropper Willie, τ is the detection threshold of the eavesdropper Willie, represents the noise variance at the eavesdropper Willie, and ε is an arbitrarily small value that determines the stealth level.

[0042] Based on the above scheme, the detection threshold τ of the eavesdropper Willie and the BackCom interruption probability P out The steps of the convex optimization subproblem include:

[0043]

[0044] Where ξ is the detection error probability of the eavesdropper Willie, P out is the interruption probability of BackCom, ε is an arbitrarily small value that determines the concealment level, τ is the detection threshold of the eavesdropper Willie, P outBoth ξ and β are monotonically decreasing functions of β.

[0045] Based on the above scheme, the power reflection coefficient β of the tag Tag and the detection threshold τ of the eavesdropper Willie under high SNR conditions are determined by a one-dimensional search algorithm, so that the BackCom interruption probability P out The smallest steps include:

[0046] Initialization: β 0 , iteration index k = 1, Flag = 1;

[0047] Setting: d cr , d ct , d cw , d tr , d tw ,P, φ, ε;

[0048] Input: Statistical CSI, h cr , h ct , h cw , h tr , h tw and the maximum error ω;

[0049] Output: β * and τ * ;

[0050] Where, β is the power reflection coefficient of the tag, β 0 is the initial value of β, β * and τ * They represent the optimal power reflection coefficient of the tag and the optimal detection threshold of Willie, respectively. cr d ct and d cw Represents the distance between CE and Reader, Tag, and Willie respectively, d tr and d tw Respectively represent the distance between the tag and the reader and the willie, P represents the transmission power of CE, represents the noise variance at the eavesdropper Willie, φ represents the interference elimination coefficient, ε is an arbitrarily small value that determines the concealment level, and h cr 、h ct 、h cw 、h tr and h tw They represent the channel coefficients between CE-Reader, CE-Tag, CE-Willie, Tag-Reader, and Tag-Willie respectively.

[0051] Based on the above scheme, the initialization: β 0 , the steps of iteration index k=1, Flag=1 specifically include:

[0052] (1) When Flag>0;

[0053] Using β (k) Get τ (k+1) and the minimum value of the objective function in P1

[0054] Using τ (k+1) Get β (k+1) and the minimum value of the objective function in P1

[0055] (2) If

[0056] (a) Flag = 1;

[0057] (b) Make β * =β (k+1) And τ * =τ (k+1) ;

[0058] (c) End the loop and output β * and τ * ;

[0059] Otherwise, update k=k+1 and return to step (1);

[0060] Among them, β k and β (k+1) Represent the power reflection coefficients obtained by the kth and k+1th iterations, τ (k+1) Indicates the detection threshold of Willie obtained in the k+1th iteration, and They represent the interruption probability P of BackCom obtained at the kth and k+1th iterations respectively. out .

[0061] The technical solution provided by the embodiment of the present invention may have the following beneficial effects:

[0062] This paper evaluates communication stealth and reliability by obtaining approximate closed-form expressions for the detection error probability at the eavesdropper and the BackCom outage probability. Furthermore, by jointly optimizing the BackCom transmitter's power reflection coefficient and the eavesdropper's detection threshold, a multidimensional resource allocation problem is established to minimize the BackCom outage probability while satisfying network stealth. Due to the coupled optimization variables involved, the resource allocation problem is highly nonconvex. To this end, the block coordinated descent (BCD) method is used to decouple it into two subproblems. By analyzing the structural characteristics of the transformed problem, an iterative algorithm based on BCD is proposed to solve the original optimization problem. Finally, computer simulations verify the superiority of the proposed algorithm.

[0063] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0065] Figure 1 is a schematic diagram of a concealed dual-station BackCom network system according to an exemplary embodiment;

[0066] Figure 2 is a schematic diagram showing detection error probabilities under different power reflection coefficients according to an exemplary embodiment;

[0067] Figure 3 is a schematic diagram showing outage probabilities under different power reflection coefficients according to an exemplary embodiment;

[0068] Figure 4 is a schematic diagram showing interruption probabilities at different transmission rates according to an exemplary embodiment;

[0069] Figure 5 The figure is a schematic diagram showing successful transmission probabilities under different detection error probabilities according to an exemplary embodiment. DETAILED DESCRIPTION

[0070] The following description and accompanying drawings sufficiently illustrate the specific embodiments herein to enable those skilled in the art to practice them. Portions and features of some embodiments may be included in or substituted for portions and features of other embodiments. The scope of the embodiments herein includes the entire scope of the claims, including all available equivalents thereof. Herein, the terms "first," "second," and the like are used solely to distinguish one element from another and do not require or imply any actual relationship or order between these elements. In practice, the first element can also be referred to as the second element, and vice versa. Furthermore, the terms "comprise," "comprising," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a structure, device, or apparatus comprising a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such structure, device, or apparatus. Without further limitation, an element defined by the phrase "comprising a..." does not preclude the presence of other identical elements in the structure, device, or apparatus comprising the element. The various embodiments herein are described in a progressive manner, with each embodiment focusing on its differences from the other embodiments. Similar or identical parts between the various embodiments can be referenced to each other.

[0071] The terms "longitudinal", "transverse", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like used herein to indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are intended only to facilitate the description of this document and simplify the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the present invention. In the description herein, unless otherwise specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, they can be mechanical or electrical connections, or they can be internal connections between two elements, they can be directly connected, or they can be indirectly connected through an intermediate medium. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to the specific circumstances.

[0072] As used herein, unless otherwise specified, the term "plurality" means two or more.

[0073] In this document, the character " / " indicates that the preceding and following objects are in an "or" relationship. For example, A / B means: A or B.

[0074] In this article, the term "and / or" is used to describe the association relationship between objects, indicating that three relationships can exist. For example, A and / or B means: A or B, or, A and B.

[0075] In the absence of conflict, the embodiments of the present invention and the features thereof may be combined with each other.

[0076] Figure 1 An embodiment of the railway intelligent monitoring concealed dual-station BackCom network system of the present invention is shown.

[0077] The covert dual-station BackCom network system includes: a carrier transmitter CE, which acts as a radio frequency source to generate an incident signal; a tag Tag, which has a backscatter circuit that absorbs the incident signal or passively transmits information by reflecting the incident signal; a reader Reader, which receives the signal reflected by the tag Tag and obtains the information transmitted by the tag Tag; and an eavesdropper Willie, which monitors whether information is being transmitted between the tag and the reader, providing covert constraints for the system. Specifically, the carrier transmitter CE generates an incident signal with artificial noise based on a key pre-assigned between the CE and the reader (the key can be removed at the reader through serial interference cancellation technology);

[0078] Assume that all channels are quasi-static Rayleigh fading channels, and the channel coefficients between CE-Reader, CE-Tag, CE-Willie, Tag-Reader and Tag-Willie are represented by h cr 、h ct 、h cw 、h tr and h tw Represents; then it obeys the complex Gaussian distribution, that is, h mn ~CN(0,1 / λ mn ), where (mn∈(cr,ct,cw,tr,tw)), which remains unchanged within a time slot but varies independently between different time slots.

[0079] Where CN represents the circularly symmetric complex Gaussian distribution, 1 / λ mn represents the variance of each channel.

[0080] As part of the system, the eavesdropper Willie is used to detect whether there is covert information transmission in the Tag-Reader link. Willie's detection error probability is then calculated, and the detection error probability can be used as a constraint in the optimization.

[0081] Specifically, for the Tag, the incident signal from the CE can be expressed as:

[0082]

[0083] Where P is the transmit power of CE, c(i) is the signal carried by CE itself and satisfies E[c(i)c *(i)] = 1. Therefore, the reflected signal at the tag can be expressed as:

[0084]

[0085] Where β (0≤β≤1) represents the power reflection coefficient of the tag, and t(i) is the covert message sent by the tag. In addition, the reader receives signals from both the CE and the tag at the same time, so the signal received at the reader can be expressed as:

[0086]

[0087] in represents the additive white Gaussian noise at the reader, φ∈[0,1] is the interference cancellation coefficient, and φ=0 means perfect interference cancellation.

[0088] An embodiment of the method for improving information transmission reliability in railway intelligent monitoring of the present invention.

[0089] S1: Obtain closed-form expressions for the BackCom interruption probability and detection error probability ξ based on the channel coefficients (between CE-Reader, CE-Tag, CE-Willie, Tag-Reader, and Tag-Willie), the tag's power reflection coefficient β, and the eavesdropper Willie's detection threshold τ.

[0090] Specifically, the following steps are included:

[0091] 1. Detection of covert communications:

[0092] Assume that the eavesdropper (Willie) can obtain the transmission power of CE and h ct 、h tw and h cw The statistical CSI of , but cannot obtain their instantaneous CSI. Therefore, the eavesdropper (Willie) will face h ct 、h tw and h cw The uncertainty of the tag can be used to enhance the concealment of the information reflected by the tag. The eavesdropper (Willie) determines whether the covert transmission from the tag to the reader exists, which can be modeled as the following binary hypothesis test:

[0093]

[0094] Among them, y w (i) represents the observation vector used by the i-th channel. The null hypothesis H0 indicates that the Tag absorbs the incident signal, while the alternative hypothesis H1 indicates that the Tag modulates and reflects the incident signal. represents the additive white Gaussian noise at the eavesdropper (Willie).

[0095] Assuming that the eavesdropper (Willie) uses energy detection, the decision rules are as follows:

[0096]

[0097] Among them, the detection statistic P w (i) is the average power of the signal received by the eavesdropper (Willie), and τ>0 is the detection threshold of the eavesdropper (Willie). When n→∞, the average received power P at the eavesdropper (Willie) is w It can be expressed as:

[0098]

[0099] The detection error probability ξ is used to measure the concealment performance of the Tag, that is,

[0100] ξ=P F +P M (7)

[0101] Among them, P F =Pr(H1|H0) is the false alarm probability, P M = Pr(H0|H1) is the probability of missed detection. H0 represents the null hypothesis that the tag remains silent, while the alternative hypothesis H1 indicates that the tag reflects the incident information; in particular, ξ = 0 means that the eavesdropper (Willie) can detect the covert signal perfectly, while ξ = 1 means that the eavesdropper (Willie) cannot detect the covert signal.

[0102] 2. Covert communication performance

[0103] (a) Detection error probability and optimal detection threshold

[0104] When n→∞, the probability of detection error by the eavesdropper (Willie) can be expressed as:

[0105]

[0106] in, and τ represents the detection threshold of Willie, represents the Willie noise variance, P represents the CE transmission power, β represents the Tag power reflection coefficient, λ ct ,λ cw and λ tw They represent the inverse of the channel variance between CE-Tag, CE-Willie, and Tag-Willie, respectively, and c0≈0.5772 represents the Euler constant.

[0107] The specific derivation process of formula (8) is:

[0108] According to (6) and (7), the false alarm probability can be written as:

[0109]

[0110] Among them, when x≥0, h cw The probability density function of

[0111] The probability of missed detection can be written as:

[0112]

[0113] when hour,

[0114]

[0115] Where K0(x) is the modified Bessel function of the second kind, and step (a) is given by Perform variable substitution to obtain. Step (b) is obtained from K0(x)≈-ln(x / 2)-c0, x→0.

[0116] On this basis, according to The Taylor expansion when u→0 can be obtained under high SNR conditions.

[0117]

[0118] Substituting (1.4) into (1.3), we can obtain

[0119]

[0120] Assume that the eavesdropper (Willie) cannot obtain the instantaneous CSI between it and the tag (Tag), so the eavesdropper (Willie) faces the uncertainty of the link channel, that is, the variable h is introduced tw , which makes the derivation more difficult and leads to more complicated expressions.

[0121] (b) BackCom interruption probability

[0122] According to formula (3), the signal-to-interference-noise ratio at the reader can be expressed as:

[0123]

[0124] in, is the SNR of the transmitter. Assume that R0 is the predetermined transmission rate from the tag to the reader. When R < R0, the system is interrupted, where R = log2(1 + γr ) represents the achievable transmission rate from Tag to Reader. Therefore, the probability of backscatter communication interruption can be expressed as:

[0125]

[0126] in, K0(·) represents the modified Bessel function of the second kind, Θ = -abexp(ab)Ei(-ab) and ab = φλ ct λ tr γ0 / βλ cr , represents the exponential integral function, φ represents the interference elimination coefficient, represents the input signal-to-noise ratio of the reader, λ cr ,λ ct and λ tr They represent the inverse of the channel variance between CE-Reader, CE-Tag and Tag-Reader, γ0 represents the corresponding decoding threshold, |h ct | 2 、|h cr | 2 and |h tr | 2 Indicates the channel gains between the CE-Tag, CE-Reader, and Tag-Reader, respectively.

[0127] Considering that the tag can be deployed at a location far away from the reader, its channel coefficient obeys the complex Gaussian distribution, and the complex term |h is introduced in the derivation process. ct | 2 |h tr | 2 , which increases the difficulty of deriving the interruption probability.

[0128] 3. Covert communication algorithm design:

[0129] Based on the above discussion, a resource allocation method is designed to jointly optimize the tag power reflection coefficient β and the Willie detection threshold τ to minimize the system interruption probability while ensuring communication concealment, thereby improving the communication transmission rate. The specific optimization problem can be modeled as:

[0130]

[0131] Among them, C0 is the value range of the detection threshold, C1 ensures the concealment of communication, and C2 constrains the value range of the power reflection coefficient. ξ is the detection error probability of the eavesdropper Willie, ε is an arbitrarily small value that determines the concealment level, β is the power reflection coefficient of the tag Tag, and τ is the detection threshold of the eavesdropper Willie. represents the noise variance at the eavesdropper Willie, P out Indicates the interruption probability of BackCom.

[0132] S2: Based on the closed expressions of BackCom outage probability and detection error probability ξ, the optimization problem of the reliability of the hidden two-station BackCom network system is listed and rewritten as a convex optimization problem;

[0133] Observing P1, we can see that β and τ are coupled in the constraint C1. Therefore, P1 is non-convex. To solve this problem, we use the BCD algorithm to decouple P1 into two sub-problems.

[0134] S3: Using the BCD algorithm, the reliability optimization problem of the hidden dual-station BackCom network system is decoupled into two convex optimization sub-problems, namely Willie's detection threshold and BackCom interruption probability P out The convex optimization subproblem and the Tag power reflection coefficient and BackCom interruption probability P out Convex optimization subproblem of ;

[0135] As shown in P(1.1) and P(1.2), we then solve these two subproblems separately.

[0136]

[0137] In (P1.1), τ is fixed and β needs to be optimized. From (8), we can see that the constraint C1 of the optimization problem (P1.1) contains some complex terms that are difficult to handle. and in The existence of these complex terms makes it difficult to obtain a closed expression for the optimal power reflection coefficient through theoretical derivation. out Both ξ and β are monotonically decreasing functions of β, so a one-dimensional search algorithm can be used to solve (P1.1).

[0138] S4: Determine the power reflection coefficient β of the Tag and the detection threshold τ of Willie under high SNR conditions through a one-dimensional search algorithm (or other methods), so that the BackCom interruption probability P out Minimum.

[0139] The optimal power reflection coefficient under high SNR conditions can be determined by a one-dimensional search algorithm. The specific steps are shown in Table 1:

[0140] Table 1 Solving β * One-dimensional search algorithm

[0141]

[0142]

[0143] In (P1.2), β is fixed, and τ needs to be optimized. It is worth noting that in the high SNR region, ξ is a convex function of τ. Therefore, the optimal detection threshold at high SNR can be determined using a one-dimensional search algorithm (such as gradient descent). Based on the above discussion, we propose an iterative algorithm based on BCD to solve (P1). The specific steps are shown in Table 2.

[0144] Table 2 BCD-based iterative algorithm

[0145]

[0146] To prove that ξ is a convex function of τ, we can do the following:

[0147] The second-order derivative of ξ with respect to τ can be written as:

[0148]

[0149] On this basis, according to exist The Taylor expansion of , under high SNR conditions, can be obtained

[0150]

[0151] To prove this, in the high SNR region, ξ is a monotonically decreasing function of β as follows:

[0152] The first-order derivative of ξ with respect to β can be written as

[0153]

[0154] On this basis, according to exist The Taylor expansion of , under high SNR conditions, can be obtained

[0155]

[0156] This embodiment conducts simulation experiments in the following simulation scenarios to verify the derivation results. The simulation parameters provided in the simulation are set as follows: β = 0.4, φ = 0.01, P = 30dBm, d ct=10m,d cr =10m,d cw =10m,d tr =10m,d tw = 10. The receiver noise is -130dBm.

[0157] Figure 2 The relationship between the detection error probability ξ and the power reflection coefficient β at different transmit power levels is depicted. The figure shows a good fit between the simulated value curve and the theoretical value curve, verifying the accuracy of the derivation of the detection error probability. The correct detection probability can be defined as 1 minus the detection error probability. It can be observed that the detection error probability decreases monotonically with increasing power reflection coefficient, validating the proof of the monotonicity of the detection error probability and the power reflection coefficient. This phenomenon occurs because when a backscattering node reflects more covert information, an eavesdropper can more easily detect the existence of covert communications and is less likely to miss detection, thereby reducing the detection error probability.

[0158] Figure 3 The relationship between the power reflection coefficient and the interruption probability is shown. According to formula (10), the main system selects three different interference elimination coefficients to verify the accuracy of the derivation, namely φ = 0.1, 0.01, and 0.001. As can be seen from the figure, the theoretical value curve and the simulation value curve are relatively close under different interference elimination coefficients, thereby verifying the accuracy of the derivation of the main system interruption probability. It can be found that with the increase of the power reflection coefficient β, the interruption probability shows a monotonically decreasing trend. Combined with the proof, the detection error probability decreases with the increase of the power reflection coefficient. Therefore, for a covert communication network that takes into account both system interruption performance and concealment, it is very important to optimize β.

[0159] Figure 4 The figure shows how the outage probability varies with the transmission rate in the above scenario. It can be seen that both the proposed scheme and the baseline scheme increase with increasing transmission rate, because higher transmission rates increase the likelihood of outages. Furthermore, it can be observed that the proposed scheme achieves a lower outage probability than the baseline scheme.

[0160] Figure 5 The relationship between the probability of successful transmission and the probability of detection error ξ for different interference cancellation coefficients is depicted. The probability of successful transmission is defined as 1 minus the probability of outage. It can be seen that the probability of successful transmission decreases as the probability of detection error ξ increases, indicating a trade-off between stealth and outage performance. Furthermore, it can be seen that increasing φ reduces the trade-off region in the vertical direction.

[0161] In summary, the performance of a covert two-station BackCom network was studied from the perspectives of detection error probability and outage probability. Assuming the network operates under high signal-to-noise ratio (SNR) conditions, the detection error probability of the eavesdropper, Willie, was derived. Furthermore, the BackCom outage probability was derived. Finally, under the concealment constraint, the detection threshold of the eavesdropper (Willie) and the power reflection coefficient of the tag were jointly optimized to minimize the BackCom outage probability. An iterative algorithm based on BCD was designed to solve the optimization problem. Compared with a baseline scheme, the proposed BCD-based iterative algorithm achieves higher transmission performance under the same concealment constraint.

[0162] The present invention is not limited to the structures described above and shown in the drawings, and various modifications and changes can be made without departing from the scope thereof. The scope of the present invention is limited only by the appended claims.

Claims

1. A method for improving information transmission reliability in railway intelligent monitoring, characterized in that: Use a railway intelligent monitoring network system, specifically based on a concealed dual-station BackCom network system, including: The carrier transmitter CE acts as a radio frequency source to generate the incident signal; The tag has a backscatter circuit that absorbs the incident signal or passively transmits information by reflecting the incident signal; The reader receives the signal reflected by the tag and obtains the information transmitted by the tag; The eavesdropper Willie is used to monitor whether information is being transmitted between the Tag and the Reader, providing concealment constraints for the system; Assume that all channels are quasi-static Rayleigh fading channels, and the channel coefficients between CE-Reader, CE-Tag, CE-Willie, Tag-Reader and Tag-Willie are represented by h cr 、h ct 、h cw 、h tr and h tw Represents; then it obeys the complex Gaussian distribution, that is, h mn ~CN(0,1 / λ mn ), where (mn∈(cr,ct,cw,tr,tw)), which is constant within a time slot but varies independently between different time slots; Where CN represents the circularly symmetric complex Gaussian distribution, 1 / λ mn represents the variance of each channel; The carrier transmitter CE generates an incident signal with artificial noise based on a key pre-distributed between the CE and the Reader; The following steps are involved: Based on the channel coefficient, the power reflection coefficient β of the tag Tag and the detection threshold τ of the eavesdropper Willie, the BackCom interruption probability P is obtained. out and a closed-form expression for the probability of detection error ξ; Based on the BackCom interruption probability P out and the closed expression of the detection error probability ξ, the optimization problem of the reliability of the covert two-station BackCom network system is listed and rewritten as a convex optimization problem; The reliability optimization problem of the hidden dual-station BackCom network system is decoupled into two convex optimization sub-problems through the BCD algorithm. The power reflection coefficient β and the detection threshold τ of the eavesdropper Willie under high SNR conditions are determined by a one-dimensional search algorithm, so that the BackCom interruption probability P out Minimum.

2. The method for improving information transmission reliability in railway intelligent monitoring according to claim 1, characterized in that: The BackCom interruption probability P is obtained based on the channel coefficient, the power reflection coefficient β of the tag Tag and the detection threshold τ of the eavesdropper Willie. out The steps of obtaining a closed expression for the probability of error ξ include: The detection error probability ξ is used to measure the concealment performance of the tag, which is expressed as: ξ=P F +P M (7) Among them, P F =Pr(H1|H0) is the false alarm probability, P M =Pr(H0|H1) is the probability of missed detection, H0 represents the null hypothesis that the tag remains silent, and the alternative hypothesis H1 represents that the tag reflects the incident information; ξ = 0 means that the eavesdropper Willie can detect the covert signal perfectly, while ξ = 1 means that the eavesdropper Willie cannot detect the covert signal; When n→∞, the probability of eavesdropper Willie’s detection error can be expressed as: in, and τ represents the detection threshold of Willie, represents the Willie noise variance, P represents the CE transmission power, β represents the Tag power reflection coefficient, λ ct ,λ cw and λ tw They represent the inverse of the channel variance between CE-Tag, CE-Willie, and Tag-Willie, respectively, and c0≈0.5772 represents the Euler constant; The closed-form expression for the BackCom outage probability is: in, K0(·) represents the modified Bessel function of the second kind, Θ = -abexp(ab)Ei(-ab) and ab = φλ ct λ tr γ0 / βλ cr , represents the exponential integral function, φ represents the interference elimination coefficient, represents the input signal-to-noise ratio of the reader, λ cr ,λ ct and λ tr They represent the inverse of the channel variance between CE-Reader, CE-Tag and Tag-Reader, γ0 represents the corresponding decoding threshold, |h ct | 2 、|h cr | 2 and |h tr | 2 Represent the channel gains between CE-Tag, CE-Reader, and Tag-Reader, respectively; Based on the above formula, the optimization problem can be expressed as: Among them, C0 is the value range of the detection threshold, C1 ensures the concealment of communication, and C2 constrains the value range of the power reflection coefficient. ξ is the detection error probability of the eavesdropper Willie, β is the power reflection coefficient of the tag Tag, and τ is the detection threshold of the eavesdropper Willie. represents the noise variance at the eavesdropper Willie, P out Indicates the interruption probability of BackCom.

3. The method for improving information transmission reliability in railway intelligent monitoring according to claim 2, characterized in that: The step of decoupling the reliability optimization problem of the covert dual-station BackCom network system into two convex optimization sub-problems using the BCD algorithm specifically includes: Tag power reflection coefficient β and BackCom interruption probability P out Convex optimization subproblem of ; The detection threshold τ of the eavesdropper Willie and the BackCom interruption probability P out Convex optimization subproblem of .

4. The method for improving information transmission reliability in railway intelligent monitoring according to claim 3, characterized in that: The power reflection coefficient and β of the tag and the BackCom interruption probability P out The steps of the convex optimization subproblem include: Where ξ is the probability of detection error of the eavesdropper Willie, ε is an arbitrarily small value that determines the stealth level, and P out is the interruption probability of BackCom, and β is the power reflection coefficient of Tag.

5. The method for improving information transmission reliability in railway intelligent monitoring according to claim 3, characterized in that: The detection threshold τ of the eavesdropper Willie and the BackCom interruption probability P out The steps of the convex optimization subproblem include: Where ξ is the detection error probability of the eavesdropper Willie, P out is the interruption probability of BackCom, ε is an arbitrarily small value that determines the concealment level, τ is the detection threshold of the eavesdropper Willie, P out Both ξ and β are monotonically decreasing functions of β.

6. The method for improving information transmission reliability in railway intelligent monitoring according to claim 1, characterized in that: The power reflection coefficient β and the detection threshold τ of the eavesdropper Willie under high SNR conditions are determined by a one-dimensional search algorithm, so that the BackCom interruption probability P out The smallest steps include: Initialization: β 0 , iteration index k = 1, Flag = 1; Settings: d cr ,d ct ,d cw ,d tr ,d tw ,P, f, e; Input: Statistical CSI, h cr , h ct , h cw , h tr , h tw and the maximum error ω; Output: β * and τ * ; Where, β is the power reflection coefficient of the tag, β 0 is the initial value of β, β * and τ * They represent the optimal power reflection coefficient of the tag and the optimal detection threshold of Willie, respectively. cr d ct and d cw Represents the distance between CE and Reader, Tag, and Willie respectively, d tr and d tw Respectively represent the distance between the tag and the reader and the willie, P represents the transmission power of CE, represents the noise variance at the eavesdropper Willie, φ represents the interference elimination coefficient, ε is an arbitrarily small value that determines the concealment level, and h cr 、h ct 、h cw 、h tr and h tw They represent the channel coefficients between CE-Reader, CE-Tag, CE-Willie, Tag-Reader, and Tag-Willie respectively.

7. The method for improving information transmission reliability in railway intelligent monitoring according to claim 6, characterized in that: The initialization: β 0 , the steps of iteration index k=1, Flag=1 specifically include: (1) When Flag>0; Using β (k) Get τ (k+1) and the minimum value of the objective function in P1 Using τ (k+1) Get β (k+1) and the minimum value of the objective function in P1 (2) If (a) Flag = 1; (b) Make β * = β (k+1) and τ * = τ (k+1) ; (c) End the loop and output β * and τ * ; Otherwise, update k=k+1 and return to step (1); Among them, β k and β (k+1) Represent the power reflection coefficients obtained by the kth and k+1th iterations, τ (k+1) Indicates the detection threshold of Willie obtained in the k+1th iteration, and They represent the interruption probability P of BackCom obtained at the kth and k+1th iterations respectively. out .

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