A covert communication system and optimization method based on environmental signal reflection

Abstract

The application belongs to the technical field of communication, analyzes the reflection signal covert transmission of a single antenna environment backscatter communication system (Ambient backscatter communications, AmBC), and proposes an environmental signal reflection based covert communication system and optimization method. The main steps of the method are as follows: (1) initializing relevant parameters; (2) according to the limit conditions that the communication system needs to meet, the initial optimization interval that the optimization variables need to meet is obtained; (3) in the initial optimization interval, according to the convex-concave characteristics of the optimization function, the convex-concave procedure idea is used to iteratively update the optimization variables, and the optimal reflection channel communication capacity under the limit condition is obtained. The application innovatively analyzes the AmBC system from the perspective of safe covert communication, integrates the CCCP idea, and uses a lower complexity iterative algorithm to improve the communication capacity of the reflection channel.

Description

Technical Field

[0001] This invention belongs to the field of communication technology. It analyzes the communication concealment of a single-antenna AmBC system from the perspective of secure and covert communication, and presents a covert communication system and optimization method based on environmental signal reflection. Background Technology

[0002] Ambient backscatter communications (AmBC) is one of the core technologies for the future Internet of Things (IoT). Using this technology, IoT devices can absorb energy from ambient radio frequency (RF) signals to activate their circuitry, and then transmit information by switching antenna impedance to change the amplitude and phase of the reflected signal. It does not require high-power active RF modules, thus meeting the low-power and long-battery-time requirements of IoT devices. Furthermore, since it does not require dedicated RF excitation and communication carriers, AmBC can share frequency bands with traditional active communications, thereby improving the spectral efficiency of communication.

[0003] With the rapid development of electronic countermeasures and eavesdropping technologies, wireless communication security has become more important than ever in modern civilian communications and information warfare. The characteristic of AmBC technology, which transmits information by reflecting ambient electromagnetic signals, means that other ambient electromagnetic signals naturally exist in its wireless channel, thus possessing the potential to achieve constant-rate covert communication.

[0004] In an ideal scenario, where the transmitter's RFS transmits at a constant power and the monitoring party Willie has complete channel information, covert communication is not possible.

[0005] For the problem of optimizing the communication capacity of the reflection channel, since the objective problem is non-convex, it is difficult to solve using traditional convex optimization algorithms such as Newton's method and gradient descent. Recently, some scholars have proposed solutions similar to alternating gradient descent or the point-scattering method, but these solutions are mostly applied to engineering problems and lack a rigorous theoretical convergence. The CCCP algorithm proposed by Yuille and Rangarajan has had its convergence rigorously proven. We innovatively apply this algorithm to solve our optimization problem to optimize the communication capacity of the reflection channel in a single-antenna AmBC system. Summary of the Invention

[0006] To address the aforementioned shortcomings of existing technologies, this invention provides a covert communication system based on environmental signal reflection. The covert communication system includes: a full-duplex single-antenna environmental radio frequency source (RFS) that transmits signals; a single-antenna legitimate user (User) that receives the signals transmitted by the RFS, requiring a minimum signal-to-noise ratio for legitimate communication; a single-antenna reflector (Alice) that transmits information by reflecting environmental signals; a single-antenna receiver (Bob) that receives the signals reflected by Alice and obtains the information transmitted by Alice; and a single-antenna eavesdropper (Willie) that monitors whether Alice and Bob are transmitting information, providing a covert constraint for the system. The system is further defined by h... RU h RA h RW h RB h AU h AB h AW This represents the channel gain between devices; in a full-duplex single-antenna environment, the transmit power of the RF source RFS is variable, and is P. min ~P max The reflection coefficient at the single-antenna reflecting device Alice is Γ∈[0,1]; the ambient noise at the single-antenna receiving device Bob is: n B (i)~CN(0,δ b 2 ), where δ b 2 Let CN represent the noise power at the receiving device Bob, and let CN denote the circularly symmetric complex Gaussian distribution. The environmental signal transmitted by the full-duplex single-antenna environmental radio frequency source RFS and the concealed signal reflected by the single-antenna reflecting device Alice satisfy: c(i) and x(i) ~ CN(0,1), where c(i) is the environmental signal and x(i) is the reflected signal, both of which satisfy the circularly symmetric complex Gaussian distribution.

[0007] The communication capacity C between Alice (single-antenna reflector) and Bob (single-antenna receiver) B for:

[0008]

[0009]

[0010] Where K represents the period of x(i) being K times that of c(i);

[0011] Constraints:

[0012] (1) Reflection coefficient: 0≤|Γ| 2 ≤1

[0013] (2) Given a concealment rate of ε P Under the given conditions, the following must be satisfied:

[0014]

[0015]

[0016] (3) The signal-to-noise ratio during traversal at the User level must be greater than the given value.

[0017]

[0018] This application also relates to an optimization method for a covert communication system based on environmental signal reflection. The predetermined parameters in the covert communication system include: the distance between objects in the covert communication system; and the maximum transmit power P of the full-duplex single-antenna environmental radio frequency source RFS. max Antenna gain; the required stealth rate ε for a reflective communication system. P The minimum signal-to-noise ratio γ required for normal communication at the User level. u ;

[0019] System optimization parameters: reflection coefficient Γ of the single-antenna reflector Alice; minimum transmit power P of the full-duplex single-antenna environment RF source RFS. min ;

[0020] The constraints of a covert communication system include: the reflection coefficient Γ of the reflecting device is within the range [0,1]; and the reflective communication concealment rate ε meets the system settings. P Requirements: The minimum signal-to-noise ratio ε required by the legitimate user (User) must be met. P ;

[0021] The optimization method specifically includes the following steps:

[0022] Step S1: Determine the initial feasible interval and judge the reflection coefficient |Γ| within different feasible intervals. 2 The expression;

[0023] Step S2: Place |Γ| 2 Substituting the expression into the optimization objective function, the objective function is transformed into one that depends only on the variable P. min The function of P; min Determine whether the objective function is related to the optimization variable P within different intervals. min A monotonic function;

[0024] Step S3: If it is a monotonic function, find its value at the endpoints of the feasible interval and record it;

[0025] Step S4: If it is not a monotonic function of the optimization variable, then find the local maximum within the given interval through an iterative algorithm;

[0026] Step S5: Compare all the values ​​obtained in Steps 3 and 4, and take the largest value as the optimal value for the communication capacity of the reflection channel.

[0027] Preferably, the specific steps of determining the initial feasible interval in step S1 are as follows: based on the given maximum transmit power P... max The required concealment coefficient ε of the system P And channel gain, comparison The magnitudes of 1 and 2, and the relationship between the three, depend on P. min It changes with the changes, and P is divided into... min In different intervals, the minimum of the three is taken as |Γ|. 2 Substitute the value into the objective function.

[0028] Preferably, in step S2, P min The criteria for judging different intervals are:

[0029] S21: When we take |Γ| 2 When 1 is substituted into the objective function, it becomes a monotonic function.

[0030] S22: When we will or When substituting into the objective function, we consider the following in the objective function: Part about P min By taking the second derivative, we can prove that the second derivative has a unique zero in (0,+∞), denoted as M. Then the objective function is a non-monotonic function in the interval to the left of M and a monotonic function in the interval to the right of M.

[0031] Preferably, the iterative steps in step S4 are as follows:

[0032] S41: |Γ| 2 By P min After substitution, an initial point is obtained within the feasible interval, denoted as p(i);

[0033] S42: At this point, the objective function is in the form of a concave function + a convex function, where the concave function part is... The convex function part is We transform it into the form of concave function-concave function, that is, the objective function is

[0034] S43: Our views on Find the slope at p(i), and... Find P that satisfies the condition that the slope is equal to its value. min Its value is denoted as p(i+1);

[0035] S44: We replace p(i) in S43 with p(i+1) and repeat the process until the distance between p(i+1) and p(i) is less than a given value or p(i+1) exceeds the feasible interval, then the iteration ends and we obtain the optimal P. min .

[0036] The contribution of this invention lies in analyzing the covert communication performance of a single-antenna AmBC system under the premise of uncertain transmitter power, and achieving covert communication while meeting a certain covertness rate. Simultaneously, for the communication capacity of the reflection channel, we propose a method incorporating CCCP principles to optimize it, thereby maximizing communication capacity under certain conditions. Attached Figure Description

[0037] Figure 1 This is a model diagram of a single-antenna AmBC system;

[0038] Figure 2 The graph shows the uncertainty of communication concealment rate as a function of transmission power under different reflection coefficients.

[0039] Figure 3 Communication capacity varies with maximum transmit power P under different concealment levels max Change curve graph;

[0040] Figure 4 This is a graph showing the change in communication capacity with concealment rate at different code rates K. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to embodiments and specific implementation methods. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0042] Single-antenna AmBC system model as follows Figure 1 As shown, the AmBC system contains a full-duplex single-antenna environmental radio frequency source RFS, a single-antenna legitimate user User, a single-antenna reflector Alice, a single-antenna receiver Bob, and a single-antenna unauthorized eavesdropper Willie. These are represented by h... RU h RA h RW h RB h AU h AB h AW Indicates the channel gain between devices; h RU This represents the channel gain between the radio frequency source RFS in a full-duplex single-antenna environment and the single-antenna legitimate user User; h RA This represents the channel gain between the radio frequency source RFS in a full-duplex single-antenna environment and the single-antenna reflector Alice; hRW This represents the channel gain between the radio frequency source RFS in a full-duplex single-antenna environment and Willie, a single-antenna illegal eavesdropper; h RB This represents the channel gain between the radio frequency source RFS and the single-antenna receiving device Bob in a full-duplex single-antenna environment; h AU This represents the channel gain between the single-antenna reflector Alice and the single-antenna legitimate user User; h AB This represents the channel gain between Alice, a single-antenna reflector, and Bob, a single-antenna receiver; h AW This represents the channel gain between Alice, the single-antenna reflector, and Willie, the single-antenna eavesdropper; the transmit power of RFS is variable, and is P. min ~P max The reflection coefficient at Alice is Γ∈[0,1]; the ambient noise at Bob is: n B (i)~CN(0,δ b 2 The environmental signal emitted by RFS and the covert signal reflected by Alice satisfy: c(i) and x(i) ~ CN(0,1).

[0043] The case discussed in this article is when the symbol period of x(i) is K times that of c(i), which is a relatively common situation; generally, the reflection rate of the signal by the reflective communication device Alice is less than the transmission rate of the signal source RFS.

[0044] In this case, the signal received at Bob's location needs to be demodulated using maximum ratio combining. Therefore, the received signal at Bob's location during the i-th Alice symbol period can be expressed as follows:

[0045]

[0046] The signal-to-noise ratio can be expressed as:

[0047] By Shannon's theorem, the channel ergodic capacity from Alice to Bob is:

[0048]

[0049] Using an energy detector as the optimal detector at Willie's location, let H0 represent the period when Alice and Bob are not communicating, and H1 represent the period when Alice and Bob are communicating. Then, the received power during the i-th symbol period of Alice can be expressed as:

[0050]

[0051] The expression for the received signal at the User location is:

[0052]

[0053] Its ergodic signal-to-noise ratio is:

[0054]

[0055] Analysis of the stealth of reflected communication:

[0056] For Willie, the eavesdropper, there are two types of detection errors: one is judging Alice as having reflected a signal when Alice did not reflect the RFS signal, i.e., the false alarm probability, denoted by P. FA Another possibility is that Alice reflected the signal but was judged not to have reflected it; this is the probability of a missed detection, denoted by P. MD The overall probability of a detection error is expressed as:

[0057] P e =pP FA +(1-p)P MD =1-ε P (Formula 7)

[0058] P e The larger the value, the better the concealment.

[0059] P FA and P MD The expressions are as follows:

[0060]

[0061] λ is the detection threshold, α = |h RW | 2 , β=|h RW | 2 +|h RA | 2 |Γ| 2 |h AW | 2

[0062]

[0063] Make P e (λ) is the largest at this time

[0064]

[0065] Communication capacity optimization:

[0066] We are considering the scenario at maximum transmit power P. max Under fixed conditions, for P minOptimization is performed, and the optimization issues are as follows:

[0067] Optimization goal: Communication capacity from Alice to Bob:

[0068]

[0069]

[0070] Constraints:

[0071] (1) Reflection coefficient: 0≤|Γ| 2 ≤1

[0072] (2) Given a concealment rate of ε P Under the given conditions, the following must be satisfied:

[0073]

[0074]

[0075] (3) The signal-to-noise ratio during traversal at the User level must be greater than the given value.

[0076]

[0077] The issues to be identified and optimized are as follows:

[0078]

[0079]

[0080] st0≤|Γ| 2 ≤1

[0081]

[0082]

[0083]

[0084] Because ① increases monotonically with θ, and ② increases monotonically with our optimization variable Γ, we can define |Γ| that satisfies the constraints. 2 Substitute the upper bound into ②, and then discuss P separately. min Regarding the changes in our objective function.

[0085] Furthermore, we can prove that when we substitute ③ or ④ into ②, its Part about P minThe second derivative of has a unique zero on (0,+∞), denoted as M. Furthermore, its second derivative is less than 0 on (0,M) and greater than 0 on (M,+∞). This indicates that the overall concavity of equation ② is related to P. max It is a piecewise function, which is of the form of (concave function + convex function) on (0,M) and concave on (M,+∞). It can be optimized using the methods described above.

[0086] In the simulation, we assume that the fading channels involved are all independent and identically distributed Rayleigh channels, and the channel gain of all the direct channels involved is given by equation ctL. -2 Given that the channel gain of all cascaded channels is given by equation ctL -3.5 Given, where c = 0.01, t follows an exponential distribution with parameter 1, and L is the distance between the two endpoints of the channel. In this simulation, the positions of each reference point in the system model are determined by polar coordinates, with RFS as the pole, and the distance between each reference point and RFS is determined by a random function. We also assume that the noise power at Bob is δ. B = -110dBm, system bandwidth is 5MHz.

[0087] In the simulation example, attached Figure 2 This is a graph showing the relationship between stealth rate and transmission power. We can see that P max With P min The larger the ratio, the greater the uncertainty of the transmission power, the better the concealment, and the higher the reflectivity |Γ|. 2 The smaller it is, the better it is concealed.

[0088] Appendix Figure 3 The Alice-Bob communication capacity and maximum transmit power P max From the relationship diagram, we can see that, overall, communication capacity increases with P. max The increase in capacity shows a trend of increasing, but the growth trend gradually slows down, and the higher the requirement for system concealment, the smaller the communication capacity of Alice-Bob.

[0089] Appendix Figure 4 This is a graph showing the relationship between Alice-Bob communication capacity and stealth rate. From the graph, we can see that at a fixed maximum transmit power P... max In this context, as the requirements for system concealment become increasingly stringent, Alice-Bob's communication capacity is also decreasing.

Claims

1. A covert communication system based on environmental signal reflection, characterized in that, The covert communication system includes: a full-duplex single-antenna environmental radio frequency source (RFS) that transmits signals; a single-antenna legitimate user (User) that receives signals transmitted by the RFS, requiring a minimum signal-to-noise ratio for legitimate communication; a single-antenna reflector (Alice) that transmits information by reflecting environmental signals; a single-antenna receiver (Bob) that receives signals reflected by Alice and obtains the information transmitted by Alice; and a single-antenna eavesdropper (Willie) that monitors whether Alice and Bob are transmitting information, providing covert constraints for the system. Use respectively , This represents the channel gain between devices; in a full-duplex single-antenna environment, the transmit power of the RF source RFS varies. The reflection coefficient at Alice, the location of the single-antenna reflector, is... The ambient noise at Bob's location, the single-antenna receiving device, is: ,in Let CN represent the noise power at the receiving device Bob, and let CN denote a circularly symmetric complex Gaussian distribution. The environmental signal transmitted by the full-duplex single-antenna environment RF source RFS and the covert signal reflected by the single-antenna reflection device Alice satisfy the following: c(i) is the environmental signal and x(i) is the reflected signal, both of which satisfy a circularly symmetric complex Gaussian distribution; Communication capacity from single-antenna reflector Alice to single-antenna receiver Bob for: ; Where K represents the period of x(i) being K times that of c(i); Constraints: (1) Reflection coefficient: ; (2) Given a concealment rate Under the given conditions, the following must be satisfied: ; ; (3) The traversal signal-to-noise ratio at the User location must be greater than the given value. : ； The predetermined parameters in a covert communication system include: the distance between objects in the covert communication system; and the maximum transmit power of the radio frequency source (RFS) in a full-duplex single-antenna environment. Antenna gain; the required stealth rate for a reflective communication system. The minimum signal-to-noise ratio required for normal communication at the User level. ; System optimization parameters: Reflection coefficient of the single-antenna reflector Alice Minimum transmit power of RF source RFS in full-duplex single-antenna environment ; The limitations of covert communication systems include: the reflectivity of the reflecting devices. In the interval Within the range; meets the system settings for reflective communication concealment rate. Requirements: Meet the minimum signal-to-noise ratio requirements specified by the authorized user (User). ; The optimization method specifically includes the following steps: Step S1: Determine the initial feasible interval and judge the reflection coefficient within different feasible intervals. The expression; Step S2: Substituting the expression into the optimization objective function transforms the objective function into one that depends only on the variables. Functions; in relation to Determine whether the objective function is about the optimization variable within different intervals. A monotonic function; Step S3: If it is a monotonic function, find its value at the endpoints of the feasible interval and record it; Step S4: If it is not a monotonic function of the optimization variable, then find the local maximum within the given interval through an iterative algorithm; Step S5: Compare all the values ​​obtained in Steps 3 and 4, and take the largest value as the optimal value for the communication capacity of the reflection channel; In step S2 The criteria for judging different intervals are: S21: When we will When substituted into the objective function, it becomes a monotonic function; S22: When we will or When substituting into the objective function, we consider the following in the objective function: Part of the information Find the second derivative and prove that its second derivative is in If the objective function has a unique zero point, let it be M, then the objective function is a non-monotonic function in the interval to the left of M and a monotonic function in the interval to the right of M. The iterative steps in step S4 are as follows: S41: Will Depend on After substitution, an initial point is obtained within the feasible interval, denoted as p(i); S42: At this point, the objective function is in the form of a concave function + a convex function, where the concave function part is... The convex function part is We transform it into the form of a concave function-concave function, that is, the objective function is ; S43: Our views on Find the slope at p(i), and... Find the condition that satisfies the slope being equal to it. Its value is denoted as p(i+1); S44: We replace p(i) in S43 with p(i+1) and repeat the process until the distance between p(i+1) and p(i) is less than a given value or p(i+1) is outside the feasible interval, then the iteration ends, and the optimal value is obtained. .

2. The optimization method for a covert communication system based on environmental signal reflection according to claim 1, characterized in that, The specific steps for determining the initial feasible interval in step S1 are as follows: based on the given maximum transmit power... The required concealment coefficient of the system And channel gain, comparison , The size of 1 and the relationship between the three sizes follow... It changes with the changes, and is divided into In different intervals, the smallest of the three is taken as the minimum value. Substitute the value into the objective function.

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