Device-to-Device Covert Communication System and Method Jointly Assisted by Unmanned Aerial Vehicle and Intelligent Reflecting Surface

Abstract

The present invention discloses a device-to-device covert communication system assisted by a drone and an intelligent reflecting surface, establishes a drone and intelligent reflecting surface UIRS joint-assisted D2D covert communication model, including communication links between various entities, calculates the average minimum error detection probability and the maximum communication rate; the sender sends a covert signal to the UIRS, and the UIRS forwards it to the receiver. Among them, the UIRS changes the angles of the corresponding incident covert signal and the reflected covert signal through its constituent elements; the spectrum-sharing cellular user sends a cellular signal to the base station, and at the same time the base station sends an interference signal, introducing an uncertainty factor at the receiver of the eavesdropper Willie to achieve the covertness of the UIRS joint-assisted D2D communication link; the eavesdropper Willie monitors whether the UIRS joint-assisted D2D communication link transmits a covert signal; the covertness is measured by the average minimum error detection probability; under the multiple constraints of satisfying the average minimum error detection probability, the cellular communication link outage probability, the transmission power, and the transmission power of the interference signal, etc., the maximum communication rate of the UIRS joint-assisted D2D communication link is obtained, and the communication rate of the system is effectively improved under the joint assistance of the drone and the intelligent reflecting surface UIRS.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technology, and particularly relates to a device-to-device covert communication system assisted by a drone and an intelligent reflecting surface. Background Art

[0002] Device-to-device (D2D) communication allows direct communication between end users without the need for a base station or access device for forwarding, thereby effectively improving the spectrum utilization efficiency of the network. In a harsh communication environment, relay-assisted D2D communication has become an effective solution to expand the communication range and alleviate connection obstacles. Due to the limitations of traditional ground relays in terms of flexibility and mobility, drone relay-assisted D2D communication has gradually received more and more attention and research.

[0003] A drone (UAV) can establish a line-of-sight link with a ground communication node, and has advantages such as high mobility and on-demand deployment capabilities, and is widely used in wireless communication networks. However, due to the complex environment, drone communication may be blocked and eavesdropped in actual scenarios. By adjusting the angles of the constituent elements of an intelligent reflecting surface (IRS) to change the incident signal and the reflected signal, and reconfiguring the transmission environment, the transmission signal can be effectively enhanced and the communication quality can be improved. Therefore, by loading the IRS on the UAV, the drone and intelligent reflecting surface UIRS-assisted D2D communication system can expand the wireless communication range and improve the communication quality by combining the mobility of the UAV and the beamforming ability of the IRS, and is widely used in fields such as disaster relief, the Internet of Things, and intelligent transportation.

[0004] The D2D link assisted by a drone and an intelligent reflecting surface is vulnerable to monitoring by eavesdroppers due to the open characteristics and visibility of signal propagation. Traditional encryption measures and physical layer security methods focus on protecting the communication content, but the existence of the link is still exposed to the wireless environment. Covert communication is dedicated to protecting the existence of the link or the signal. Therefore, by combining drone- and intelligent-reflecting-surface-assisted D2D communication and covert communication, the communication link between the sender and the receiver in the D2D pair can be effectively hidden, and at the same time, the cellular user link can send interference signals, which can effectively confuse the monitoring of eavesdroppers, thereby enhancing the concealment of the communication link.

[0005] Patent CN2021102655224 discloses a joint power control and channel allocation method for D2D communication based on unmanned aerial vehicles. Patent 2024104223106 discloses a multi-resource joint optimization method for maximizing energy efficiency in intelligent reflecting surface-assisted D2D communication. Patent CN2024107232978 relates to an intelligent reflecting surface-based D2D covert communication method, which improves the covert communication performance and enhances the performance of the D2D system. However, patents 2021102655224 and CN2024104223106 use unmanned aerial vehicles and intelligent reflecting surfaces to assist D2D communication, but do not consider the channel concealment; patent CN2024107232978 uses intelligent reflecting surfaces to assist D2D covert communication. However, the deployment flexibility of the IRS fixed on the ground is limited and it cannot adapt to changing environmental conditions.

[0006] Therefore, it is necessary and feasible to study the device-to-device covert communication system jointly assisted by unmanned aerial vehicles and intelligent reflecting surfaces and its communication method, and to optimize and analyze its concealment and communication rate. Summary of the Invention

[0007] Object of the Invention: The object of the present invention is to solve the deficiencies existing in the prior art and provide a device-to-device covert communication system jointly assisted by unmanned aerial vehicles and intelligent reflecting surfaces.

[0008] Technical Solution: A device-to-device covert communication system jointly assisted by unmanned aerial vehicles and intelligent reflecting surfaces according to the present invention involves entities including unmanned aerial vehicles and intelligent reflecting surface UIRS, a full-duplex base station B s and half-duplex communication terminals. The half-duplex communication terminals include half-duplex cellular users C using single antennas u , half-duplex D2D senders D t , half-duplex D2D receivers D r and half-duplex eavesdroppers Willie; the following communication links are formed between each entity;

[0009] Link 1), the UIRS jointly assists the D2D covert link D t →UIRS→D r ; in this link, the sender D t sends a covert signal to the unmanned aerial vehicle and intelligent reflecting surface UIRS, and the UIRS forwards the covert signal sent by the sender D t to the receiver D r ; the cellular user C u sends a cellular signal to the base station B s , forming an uplink cellular link C u →B s ; the cellular user C uBoth the uplink and downlink use orthogonal spectrum resources and there is no interference between them; and the covert link D t →UIRS→D r shares spectrum resources with the uplink cellular link C u →B s ;

[0010] Link 2), the base station B s To counter the eavesdropping of the eavesdropper Willie and improve the system's covertness, artificial noise is sent to the eavesdropper Willie to construct an artificial noise link B s →Willie; the base station B s The artificial noise emitted also interferes with the receiver D r and forms a link B s →D r , and causes self-interference to the base station B s and constitutes a link B s →B s ; In link 2), the base station B s uses the same spectrum resource to send and receive information simultaneously;

[0011] Link 3), the randomly distributed eavesdropper Willie attempts to eavesdrop on the UIRS-assisted D2D covert link D t →UIRS→D r to detect whether a covert signal is being sent, involving the eavesdropping links D t →Willie and UIRS→Willie;

[0012] Link 4), the base station B s sends information to the sender D t and forms a downlink cellular link B s →D t ;

[0013] Calculate the average minimum error detection probability of the eavesdropper Willie in link 3 Use the average minimum error detection probability to measure the covertness of link 1) the UIRS-assisted D2D covert link D t →UIRS→D r ;

[0014] At the same time, calculate the outage probability of the uplink cellular link C u →B s ;

[0015] Finally, calculate to meet the average minimum error detection probability and the cellular communication link C u →Bs Interruption probability Constrained communication rate R r , and perform constrained optimization on the communication rate R r to obtain the maximum communication rate of link 1)

[0016] Furthermore, calculate the minimum error detection probability ξ * and the average minimum error detection probability as follows:

[0017] Consider that the error detection probability of the eavesdropper Willie satisfies ξ = P FA +P MD ;

[0018]

[0019] P FA is the false alarm probability of the eavesdropper Willie, and P MD is the miss alarm probability of the eavesdropper Willie;

[0020] H0 indicates that the UIRS joint-assisted D2D communication link does not transmit concealed signals, and H1 indicates that the UIRS joint-assisted D2D communication link transmits concealed signals; P b is the transmission power of the interference signal of the full-duplex base station B s , P t is the transmission power of the sender D t , h bw is the small-scale fading parameter of the interference signal communication link B s →Willie, h ur is the small-scale fading parameter of the UIRS→D r communication link, h tu is the small-scale fading parameter of the D t →UIRS communication link, h tw is the small-scale fading parameter of the D t →Willie communication link; τ is the detection threshold of Willie, is the noise power received by the eavesdropper Willie;

[0021] Next, calculate the minimum error detection probability ξ * including two cases:

[0022]

[0023] Case 1): If the intermediate parameter ψ1 = ψ2, then the average minimum error detection probability is equal to the fixed value 1-(1 / e);

[0024] Among them,

[0025]

[0026] The intermediate parameter ψ1 reflects the interference signal strength between the full-duplex base station B s and the eavesdropper Willie, considering the transmission power P s of the interference signal from the full-duplex base station B b , the distance from the full-duplex base station B s to the eavesdropper Willie, and the path loss exponent α bw ; The intermediate parameter ψ2 reflects the signal strength between the UAV-IRS-assisted D2D communication link and the eavesdropper Willie, considering the distance d r from the UAV and intelligent reflecting surface UIRS to the receiver D ur , the distance d t from the UAV and intelligent reflecting surface UIRS to the sender D tu , the distance d t from the sender D tw to the eavesdropper Willie, the transmission power P t , and the path loss exponents α r from the UAV and intelligent reflecting surface UIRS to the receiver D t , the path loss exponents α t from the UAV and intelligent reflecting surface UIRS to the sender D ur and α tu from the sender D tw to the eavesdropper Willie. d bw is the distance from the full-duplex base station B s to the eavesdropper Willie, d ur is the distance from the UAV and intelligent reflecting surface UIRS to the receiver D r , d tu is the distance from the UAV and intelligent reflecting surface UIRS to the sender D t , d tw is the distance from the sender D t to the eavesdropper Willie; α bw , α ur , α tu and α tw are the path loss exponents from the full-duplex base station B s to the eavesdropper Willie, from the UAV and intelligent reflecting surface UIRS to the receiver D r , from the UAV and intelligent reflecting surface UIRS to the sender D t and from the sender D t to the eavesdropper Willie respectively; α bw = α ur = αtu = α tw ; g ur 、g tu and g tw Each element of follows an independent complex Gaussian distribution; β0 is the channel gain at a reference distance of 1 m;

[0027] Case 2), if the intermediate parameter ψ1 ≠ ψ2, the average minimum error detection probability is further divided into the following two cases: Case A), if the priority communication protection area O of the cellular link b is within the coverage area O centered on the sender D t , calculate the corresponding average minimum error detection probability t Case B), if the priority communication protection area O of the cellular link

[0028] is outside the coverage area O centered on the sender D b , then calculate the corresponding average minimum error detection probability t The expression is as follows: t where ξ is the minimum error detection probability of the eavesdropper Willie, which is a function of the transmission power P of the sender D

[0029]

[0030] and the transmission power P of the interference signal of the full-duplex base station B * , d t is the distance from the eavesdropper Willie to the sender D of D2D t , d s is the distance from the full-duplex base station B b to the sender D tw , r t is the straight-line distance from the eavesdropper Willie, θ bt is the azimuth angle of the eavesdropper Willie, R s is the radius of the coverage area O centered on the sender D t , r w is the radius of the priority communication protection area O of the cellular communication link C w → B t t . t Radius b For the cellular communication link C u → B s Priority communication protection area O b Radius

[0031] Furthermore, obtain the average minimum error detection probability that satisfies and the outage probability of the cellular communication link C u → B s ​​ Constrained communication rate R r After that, according to the half-duplex D2D sender D t 's transmission power P t and the transmission power P of the interference signal b as well as the cellular communication link C u →B s outage probability and the average minimum error detection probability of the half-duplex eavesdropper Willie's receiver These four constraints are finally used to optimize and obtain the maximum communication rate

[0032] Furthermore, during the D2D communication between the drone and the intelligent reflecting surface UIRS-assisted sender D t and receiver D r assuming that the UIRS hovers at a height H, the IRS is equipped with K reflecting elements, and the effective phase shift of all reflecting elements of the IRS is Θ; then for the UIRS joint-assisted D2D covert link D t →UIRS→D r The modeling is as follows:

[0033]

[0034] j is represented as a complex number, and θ i represents the phase shift of the i-th element, and θ i ∈[0, 2π], i = 1, 2,..., K; h tu is the small-scale fading parameter of the D t →UIRS communication link, and h ur is the small-scale fading parameter of the UIRS→D r communication link, β0 is the channel gain at a reference distance of 1 m, and d tu is the distance between the drone and the intelligent reflecting surface UIRS to the sender D t and d ur is the distance between the drone and the intelligent reflecting surface UIRS to the receiver D r and λ is the carrier wavelength, d is the distance between the reflecting elements, and φ tu and φ ur are the cosines of the emission angles from the sender D t to the drone and the intelligent reflecting surface UIRS, and α tu and α ur are the path loss exponents from the drone and the intelligent reflecting surface UIRS to the sender D t and from the drone and the intelligent reflecting surface UIRS to the receiver D r respectively.

[0035] Furthermore, the eavesdropping link UIRS→Willie in link 3) is modeled as follows:

[0036]

[0037] In the above formula, d uw is the distance from the UAV and the intelligent reflecting surface UIRS to the half-duplex eavesdropper Willie, and α uw is the path loss exponent from the UAV and the intelligent reflecting surface UIRS to the eavesdropper Willie and from the sender D t to the eavesdropper Willie. Each element of g uw follows an independent complex Gaussian distribution, that is where m represents the m-th element of the communication link from the UAV and the intelligent reflecting surface UIRS to the half-duplex eavesdropper Willie, m = 1, 2, …, K, and K refers to the IRS being equipped with K reflecting elements.

[0038] Furthermore, the full-duplex base station B s is configured with two antennas. One antenna receives the cellular signal sent by the half-duplex cellular user C u , and the other is for the downlink cellular link and sending interference signals. Self-interference is generated between the two antennas and cannot be eliminated. represents the self-interference coefficient;

[0039] The full-duplex base station B s interferes with the covert communication detection of the eavesdropper Willie on the UIRS joint-assisted D2D covert link D t →UIRS→D r by sending interference signals, and the transmission power of the interference signals follows a uniform distribution;

[0040] The outage probability of the uplink cellular link C u →B s is calculated as:

[0041]

[0042] In the above formula, P c is the transmission power of the half-duplex cellular user C u , h cb is the small-scale fading parameter of the communication link C u →B s , h bb is the small-scale fading parameter of the communication link B s →B s , h bt is the small-scale fading parameter of the communication link B s →D t ; For half-duplex cellular user C u Received noise power; R c is the target communication rate.

[0043] Furthermore, the maximum communication rate is obtained The specific method is as follows:

[0044] Step (1), calculate the cellular communication link C u →B s Probability of interruption

[0045]

[0046] Among them, P c For cellular user C u The transmission power, h cb C u →B s Small-scale fading parameter of the communication link, h bb For B s →B s Small-scale fading parameter of the communication link, h bt For B s →D t Small-scale fading parameters of the communication link, For cellular user C u Received noise power; R c is the target communication rate, η is the intermediate auxiliary amount, η=2 Rc -1;

[0047] Step (2): Calculate the maximum communication rate

[0048] Step (2.1), according to Solve for the half-duplex D2D sender D t The transmission power P t And the transmission power of the interference signal P b ;γ is the given target interruption probability;

[0049] Step (2.2), based on the given allowed error detection probability ∈, according to the average minimum error detection probability For sender D t The transmission power P t The monotonically decreasing function and the transmission power P of the interference signal b A monotonically increasing function to solve the sender D t The maximum transmit power P that can be obtained tm and full-duplex base station B s The maximum transmit power P of the interference signal that can be obtainedbm ; The calculation formula is as follows:

[0050]

[0051] Step (2.3): Use a search algorithm in the interval (0, P tm and to obtain the optimal transmission power t of the half - sender D and the optimal transmission power of the interference signal such that formula (8) achieves the maximum value, that is, the maximum communication rate

[0052] R * r = maxR r , (8)

[0053] In the above formula, R r refers to the communication rate that satisfies the average minimum error detection probability and the outage probability u of the cellular communication link C s → B constraint;

[0054]

[0055] Among them, P t is the transmission power of the sender D t , P b is the transmission power of the interference signal of the full - duplex base station B s , h ur is the small - scale fading parameter of the UIRS→D r communication link, h tu is the small - scale fading parameter of the D t →UIRS communication link, h br is the small - scale fading parameter of the B s →D r communication link, Θ is the effective phase shift of all elements of the IRS, is the noise power received by the receiver D r .

[0056] Furthermore, the constraints on the maximum communication rate are as follows:

[0057]

[0058] Among them, Θ is the effective phase shift of all elements of the IRS, h br is the small - scale fading parameter of the B s →D r communication link, For receiver D r Received noise power For sender D t The maximum transmission power determined by itself For full-duplex base station B s The maximum transmission power of the interference signal determined by itself

[0059] Beneficial effects: The present invention obtains the maximum communication rate under multiple constraints such as satisfying the average minimum error detection probability, the cellular communication link interruption probability, the transmission power, and the transmission power of the interference signal With the joint assistance of the unmanned aerial vehicle and the intelligent reflecting surface UIRS, the communication rate of the system is effectively improved. The advantages are as follows:

[0060] 1. The D2D sender Dt of the present invention sends a covert signal to the UIRS, which is forwarded by the UIRS to the half-duplex D2D receiver Dr. The UIRS changes the angles of the corresponding incident covert signal and the reflected covert signal through its components; the spectrum-sharing half-duplex cellular user Cu sends a cellular signal to the full-duplex base station Bs, and at the same time the full-duplex base station Bs sends an interference signal

[0061] 2. The present invention introduces an uncertainty factor at the receiving end of the half-duplex eavesdropper Willie to achieve the concealment of the UIRS-assisted D2D communication link; the half-duplex eavesdropper Willie monitors whether the UIRS-assisted D2D communication link transmits a covert signal

[0062] 3. In the calculation of the average minimum error detection probability, two cases of considering the intermediate parameters ψ1 = ψ2 and ψ1 ≠ ψ2 are considered. In the case of ψ1 ≠ ψ2, the cellular link priority communication protection area O is considered b In the coverage area O centered on the sender Dt t Both inside and outside, the average minimum error detection probability is obtained to measure the concealment

[0063] 4. In the calculation of the maximum communication rate, under the four constraints of satisfying the average minimum error detection probability, the cellular communication link interruption probability, the transmission power, and the transmission power of the interference signal, the maximum communication rate of the UIRS-assisted D2D communication link is obtained, and the communication rate of the system is effectively improved with the joint assistance of the unmanned aerial vehicle and the intelligent reflecting surface UIRS Description of the drawings

[0064] Figure 1 It is a device-to-device covert communication model diagram of the joint assistance of an unmanned aerial vehicle and an intelligent reflecting surface according to the present invention

[0065] Figure 2It is the overall flowchart of the device-to-device covert communication model of the present invention.

[0066] Figure 3 It is the average minimum error detection probability of the device-to-device covert communication model when ψ1 = ψ2 of the present invention Calculation flowchart.

[0067] Figure 4 It is the average minimum error detection probability of the device-to-device covert communication model when ψ1 ≠ ψ2 of the present invention Calculation flowchart.

[0068] Figure 5 It is the calculation flowchart of the maximum communication rate of the device-to-device covert communication model of the present invention.

[0069] Figure 6 It is the full-duplex base station B of the present invention s The transmission power P of the interference signal b And the average minimum error detection probability Relationship simulation diagram.

[0070] Figure 7 It is the half-duplex D2D sender D of the present invention t The transmission power P t And the average minimum error detection probability Relationship simulation diagram.

[0071] Figure 8 It is the half-duplex D2D sender D of the present invention t The transmission power P t And the cellular communication link interruption probability Relationship simulation diagram.

[0072] Figure 9 It is the full-duplex base station B of the present invention s The interference signal P b And the cellular communication link interruption probability Relationship simulation diagram.

[0073] Figure 10 It is the half-duplex D2D sender D of the present invention t The maximum transmission power And the maximum communication rate Relationship simulation diagram.

[0074] Figure 11 It is the cellular link priority communication protection area O of the present invention b In the coverage area O centered on the sender D t Outside the coverage area O t The transmission power P of the half-duplex D2D sender D outside t The transmission power P tRelationship simulation diagram with communication rate R r Relationship simulation diagram

[0075] Figure 12 Is the preferred communication protection area O of the cellular link in the present invention b Within the coverage area centered on the sender D t Coverage area O t Half-duplex D2D sender D within t Transmission power P t Relationship simulation diagram with communication rate R r Relationship simulation diagram Specific implementation manner

[0076] The technical solution of the present invention will be described in detail below, but the protection scope of the present invention is not limited to the described embodiments

[0077] The device-to-device covert communication system jointly assisted by the unmanned aerial vehicle and the intelligent reflecting surface of the present invention involves entities including the unmanned aerial vehicle and the intelligent reflecting surface UIRS, the full-duplex base station B s And half-duplex communication terminals. The half-duplex communication terminals include half-duplex cellular users C using single antennas u Half-duplex D2D sender D t Half-duplex D2D receiver D r And half-duplex eavesdropper Willie; the following several communication links are formed between the entities

[0078] Link 1), UIRS jointly assisted D2D covert link D t →UIRS→D r In this link, the sender D t Sends a covert signal to the unmanned aerial vehicle and the intelligent reflecting surface UIRS, and the UIRS forwards the covert signal sent by the sender D t To the receiver D r Cellular user C u Sends a cellular signal to the base station B s Forming an uplink cellular link C u →B s Cellular user C u The uplink and downlink of use orthogonal spectrum resources and do not interfere with each other; and the covert link D t →UIRS→D r Shares spectrum resources with the uplink cellular link C u →B s ;

[0079] Link 2), the base station B s To counter the eavesdropping of the eavesdropper Willie and improve the system concealment, send artificial noise to the eavesdropper Willie to construct an artificial noise link Bs → Willie; Base Station B s The artificial noise emitted also interferes with the receiver D r to form Link B s → D r and causes self-interference to Base Station B s to form Link B s → B s ; In Link 2), Base Station B s uses the same spectrum resource to send and receive information simultaneously;

[0080] In Link 3), the randomly distributed eavesdropper Willie attempts to eavesdrop on the UIRS-assisted D2D covert link D t → UIRS → D r to detect whether a covert signal is being sent, involving the eavesdropping link D t → Willie and UIRS → Willie;

[0081] In Link 4), Base Station B s sends information to the sender D t to form the downlink cellular link B s → D t .

[0082] The relationships between the communication links are as Figure 1 shown. The UIRS-assisted D2D covert link follows the distributions of Equation (3), Equation (4), and Equation (5), and the remaining terrestrial communication links follow independent quasi-static Rayleigh block fading, with their corresponding small-scale fading parameters being independent and identically distributed circularly symmetric complex Gaussian random variables. The small-scale fading parameters and distances between the communication terminals are respectively expressed as: D t → UIRS is h tu and d tu , UIRS → D r is h ur and d ur , UIRS → Willie is h uw and d uw , C u → B s is h cb and d cb , B s → D t is h bt and d bt , D t → Willie is h tw and d tw , B s → Willie is h bw and d bw, B s → D r is h br and d br , B s → B s is h bb and d bb . The channel noise of each communication link follows a complex Gaussian distribution. The received noise power of the cellular communication link is The received noise power of the UIRS joint-assisted D2D communication link is The received noise power of the half-duplex eavesdropper Willie is The full-duplex base station B s The self-interference coefficient is The full-duplex base station B s The transmitted power of the interference signal transmitted follows a uniform distribution, and its maximum transmitted power is The maximum transmitted power of the half-duplex D2D transmitter D t itself is is the outage probability of the cellular communication link, R r is the communication rate of the UIRS joint-assisted D2D communication link, is its corresponding maximum communication rate.

[0083] Calculate the average minimum error detection probability of the eavesdropper Willie in link 3) Use the average minimum error detection probability to measure the concealment of link 1) the UIRS joint-assisted D2D covert link D t → UIRS → D r ;

[0084] At the same time, calculate the outage probability of the uplink cellular link C u → B s as as Figure 5 shown.

[0085] Finally, calculate the communication rate R that satisfies the average minimum error detection probability and the outage probability of the cellular communication link C u → B s constraint and perform constraint optimization on the communication rate R r , and obtain the maximum communication rate of link 1) r

[0086] Figures 2 to 4 As Figures 2 to 4 shown, the half-duplex eavesdropper Willie collects the signals of a single block fading, and the average value Y of the power of its collected signals wCompare with its detection threshold τ; the second step, based on the power average value Y when n→∞ w , calculate the false alarm probability P under the premise of H0 FA , calculate the missed alarm probability P under the premise of H1 MD ; The third step, according to the formula ξ=P FA +P MD , calculate the error detection probability, and on this basis, find the minimum error detection probability; the fourth step, based on the uncertainty of the half-duplex eavesdropper Willie on the relevant communication link and the cellular link priority communication protection zone O b In half-duplex D2D sender D t The coverage area is centered on O t The average minimum error detection probability is calculated for both the inside and outside cases.

[0087] The false detection probability of the eavesdropper Willie satisfies ξ=P FA +P MD ;

[0088]

[0089] P FA is the false alarm probability of the eavesdropper Willie, P MD is the probability of missed alarm of eavesdropper Willie;

[0090] H0 indicates that the UIRS joint assisted D2D communication link does not transmit concealed signals, and H1 indicates that the UIRS joint assisted D2D communication link transmits concealed signals; P b For full-duplex base station B s The transmission power of the interference signal, P t For sender D t The transmission power, h bw Interference signal communication link B s → Willie's small-scale fading parameter, h ur UIRS→D r Small-scale fading parameter of the communication link, h tu D t →Small-scale fading parameter of UIRS communication link, h tw D t →Small-scale fading parameter of Willie communication link; τ is the detection threshold of Willie, is the noise power received by the eavesdropper Willie;

[0091] Furthermore, the minimum error detection probability ξ is calculated * There are two situations:

[0092]

[0093] Scenario 1): If the intermediate parameter ψ1 = ψ2, the average minimum error detection probability is equal to the fixed value 1 - (1 / e);

[0094] where

[0095]

[0096] d bw is the distance from the full-duplex base station B s to the eavesdropper Willie, d ur is the distance from the UAV and the intelligent reflecting surface UIRS to the receiver D r d tu is the distance from the UAV and the intelligent reflecting surface UIRS to the sender D t d tw is the distance from the sender D t to the eavesdropper Willie; α bw α ur α tu α tw and α s are the path loss exponents from the full-duplex base station B r to the eavesdropper Willie, from the UAV and the intelligent reflecting surface UIRS to the receiver D t from the UAV and the intelligent reflecting surface UIRS to the sender D t and from the sender D bw α ur α tu α tw ; g ur g tu g tw each element of follows an independent complex Gaussian distribution.

[0097] Scenario 2): If the intermediate parameter ψ1 ≠ ψ2, the average minimum error detection probability is further divided into the following two cases: Case A): If the cellular link priority communication protection area O b is within the coverage area O t centered at the sender D t calculate the corresponding average minimum error detection probability

[0098] Case B): If the cellular link priority communication protection area O b is outside the coverage area O t centered at the sender D t then calculate the corresponding average minimum error detection probability The expression is as follows:

[0099]

[0100] Among them, ξ * is the minimum error detection probability of the eavesdropper Willie, which is a function of the transmission power P t of the sender D t and the transmission power P s of the interference signal of the full-duplex base station B b The distance d tw is the distance from the eavesdropper Willie to the sender D of D2D t The distance d bt is the distance from the full-duplex base station B s to the sender D t The straight-line distance r w is the azimuth angle of the eavesdropper Willie, θ w The radius R t is the coverage area O t centered on the sender D t The radius r b is the priority communication protection area O u →B s The radius of the cellular communication link C b Radius.

[0101] This embodiment obtains the average minimum error detection probability and the outage probability u →B s of the cellular communication link C After satisfying the constraint of the communication rate R r According to the transmission power P t of the half-duplex D2D sender D t the transmission power P b of the interference signal, the cellular communication link C u →B s outage probability and the average minimum error detection probability of the half-duplex eavesdropper Willie receiver

[0102] The device-to-device covert communication system jointly assisted by the drone and the intelligent reflecting surface in this embodiment is characterized in that during the D2D communication process assisted by the drone and the intelligent reflecting surface UIRS for the sender Dt and the receiver Dr, assuming that the UIRS hovers at a height H, the IRS is equipped with K reflecting elements, and the effective phase shift of all reflecting elements of the IRS is Θ; then for the UIRS jointly assisting the D2D covert link D t→UIRS→D r The modeling is as follows:

[0103]

[0104]

[0105] j is represented as a complex number, and θ i represents the phase shift of the i-th component, and θ i ∈[0, 2π], i = 1, 2, …, K; h tu is the small-scale fading parameter of the D t →UIRS communication link, and h ur is the small-scale fading parameter of the UIRS→D r communication link. β0 is the channel gain at a reference distance of 1m, and d tu is the distance from the UAV and the intelligent reflecting surface UIRS to the sender D t and d ur is the distance from the UAV and the intelligent reflecting surface UIRS to the receiver D r . λ is the carrier wavelength, d is the distance between the reflecting elements, and φ tu , φ ur is the cosine of the emission angle from the sender D t to the UAV and the intelligent reflecting surface UIRS, and α tu , α ur is the distance from the UAV and the intelligent reflecting surface UIRS to the sender D t and the distance from the UAV and the intelligent reflecting surface UIRS to the receiver D r is the path loss exponent.

[0106] In this embodiment, the eavesdropping link UIRS→Willie in link 3) is modeled as follows:

[0107]

[0108] In the above formula, d uw is the distance from the UAV and the intelligent reflecting surface UIRS to the half-duplex eavesdropper Willie, and α uw is the path loss exponent from the UAV and the intelligent reflecting surface UIRS to the eavesdropper Willie and from the sender D t to the eavesdropper Willie. Each element of g uw follows an independent complex Gaussian distribution, that is where m represents the m-th element of the communication link from the UAV and the intelligent reflecting surface UIRS to the half-duplex eavesdropper Willie, m = 1, 2, …, K, and K refers to the IRS being equipped with K reflecting elements.

[0109] In this embodiment, the full-duplex base station B sConfigure two antennas. One antenna receives the cellular signal sent by the half-duplex cellular user C u and the other is used to perform the downlink cellular link and send interference signals. Self-interference is generated between the two antennas and cannot be eliminated. It represents the self-interference coefficient;

[0110] The full-duplex base station B s interferes with the eavesdropper Willie's detection of the covert communication of the UIRS joint-assisted D2D covert link D t →UIRS→D r by sending interference signals. The transmission power of the interference signals follows a uniform distribution;

[0111] The outage probability of the uplink cellular link C u →B s is calculated as follows: The calculation formula is:

[0112]

[0113] In the above formula, P c is the transmission power of the half-duplex cellular user C u , h cb is the small-scale fading parameter of the communication link from C u →B s , h bb is the small-scale fading parameter of the communication link from B s →B s , h bt is the small-scale fading parameter of the communication link from B s →D t , is the noise power received by the half-duplex cellular user C u ; R c is the target communication rate.

[0114] The specific method to obtain the maximum communication rate in this embodiment is as follows: The specific method is as follows:

[0115] Step (1), calculate the outage probability of the cellular communication link C u →B s

[0116]

[0117] Among them, P c is the transmission power of the cellular user C u , h cb is the small-scale fading parameter of the communication link from C u →B s , h bb is the small-scale fading parameter of Bs →B s Small-scale fading parameter of the communication link, h bt Is B s →D t Small-scale fading parameter of the communication link Is cellular user C u Received noise power; R c Is the target communication rate, η is an intermediate auxiliary quantity, η = 2 Rc -1;

[0118] Step (2), solve for the maximum communication rate

[0119] Step (2.1), according to Solve for the transmit power P t Of the half-duplex D2D transmitter D t And the transmit power P b Of the interference signal; γ is the given target outage probability;

[0120] Step (2.2), based on the given allowable error detection probability ∈, according to the average minimum error detection probability For transmitter D t Of the transmit power P t Is a monotonically decreasing function of and the transmit power P b Of the interference signal, to solve for transmitter D t The maximum achievable transmit power P tm And the full-duplex base station B s The maximum achievable transmit power P bm Of the interference signal; The calculation formula is as follows:

[0121]

[0122] Step (2.3), use a search algorithm in the interval (0, P tm and To obtain the optimal transmit power t Of half-transmitter D And the optimal transmit power Of the interference signal to make formula (17) achieve the maximum value, that is, to obtain the maximum communication rate

[0123] R * r = maxR r , (17)

[0124] In the above formula, R r Refers to satisfying the average minimum error detection probability And the cellular communication link Cu →B s Interruption probability Constrained communication rate;

[0125]

[0126] where P t is the transmission power of the sender D t and P b is the transmission power of the interference signal of the full-duplex base station B s and h ur is the small-scale fading parameter of the UIRS→D r communication link, and h tu is the small-scale fading parameter of the D t →UIRS communication link, and h br is the small-scale fading parameter of the B s →D r communication link, Θ is the effective phase shift of all elements of the IRS, and P r is the noise power received by the receiver D

[0127] The constraint on the maximum communication rate is as follows:

[0128]

[0129] where Θ is the effective phase shift of all elements of the IRS, and h br is the small-scale fading parameter of the B s →D r communication link, and P r is the noise power received by the receiver D and P t is the maximum transmission power determined by the sender D itself, and P s is the maximum transmission power of the interference signal determined by the full-duplex base station B itself

[0130] Example: To verify the performance of the method proposed by the present invention, the following simulation experiments are carried out:

[0131] As Figures 6 to 10 shown, the simulation environment is as follows: The received noise of each communication link follows a complex Gaussian distribution, and it is set that the path loss exponent α = 4

[0132] Figure 6 The transmission power P s of the interference signal of the full-duplex base station B b and the average minimum error detection probability The relationship between the different transmission powers P of the interference signal is studied. b The impact on the average minimum false detection probability. Figure 6 The following conclusions can be drawn: When ψ1=ψ2, the average minimum error detection probability is 1-(1 / e). When ψ1≠ψ2, as the transmission power P of the interference signal increases, b As the average minimum error detection probability increases, it also increases, indicating that in the half-duplex D2D sender D t The transmission power P t When the transmission power of the interference signal is fixed, P b Increasing it will reduce the detection performance of half-duplex eavesdropper Willie.

[0133] Figure 7 Given a half-duplex D2D sender D t Different transmission power P t Average minimum false detection probability In the case of ψ1=ψ2, the average minimum error detection probability is 1-(1 / e). In the case of ψ1=ψ2, the transmission power P of the interference signal is b is a fixed value, with the half-duplex D2D sender D t The transmission power P t As the average minimum error detection probability increases, the half-duplex D2D sender D t The transmission power P t The increase of will make the half-duplex eavesdropper Willie's power at the receiving end relative to the transmission power P of the interference signal b Therefore, the half-duplex D2D sender D t The transmission power P t The increase of will increase the detection probability of the signal and reduce the average minimum false detection probability.

[0134] Figure 8 Given a half-duplex cellular user C u Different transmission powers[ c Half-duplex D2D sender D t Transmit power P t and cellular communication link interruption probability Here we assume that the target communication rate is R c is 1, the transmission power of the interference signal is P b Given as 25dB, the self-interference coefficient is 0.4. It can be obtained that in the half-duplex cellular user C u The transmission power P c The interruption probability of the cellular communication link under the conditions of 25dB, 27.5dB and 30dB respectively With half-duplex D2D sender D t The transmission power P t This indicates that the increase in the transmit power of the IRS-assisted D2D communication link may lead to increased interference to the cellular link, thereby increasing the interruption probability of the cellular communication link.

[0135] Figure 9 The transmission power P of the interference signal under different conditions is studied. b and cellular communication link interruption probability Assuming that the half-duplex D2D sender D t The transmission power P t When the B / s of the half-duplex D2D sender are 29dB and 30dB respectively, t The transmission power P t Increase the probability of causing interruption Assume that the half-duplex D2D sender D t The transmission power P t When the half-duplex cellular user C u The transmission power P c 29dB and 30dB respectively, half-duplex cellular user C u The transmission power P c The smaller the value, the greater the interruption probability. c 0.9 and 1 respectively, which can give a smaller target communication rate R c Reduce the probability of causing interruptions The increase indicates that a stable communication rate can lead to a lower interruption probability.

[0136] Figure 10 Compared with the half-duplex D2D sender D t Maximum transmit power and maximum communication rate The relationship between . Four specific situations are given, respectively. In the cellular link priority communication protection zone O b In half-duplex D2D sender D t The coverage area is centered on O t Within and cellular link priority communication protection zone O b In half-duplex D2D sender D t The coverage area is centered on O t By comparing the other two cases, we can get the half-duplex D2D sender D t The transmission power P t The increase in the value range corresponds to the maximum communication rate will also increase, indicating that the transmission power P of the fixed interference signal b, maximum transmit power is proportional to the maximum communication rate By increasing the transmit power P t of the half-duplex D2D transmitter D t the signal strength can be increased, and the communication rate will also increase relatively when the concealment requirement is reduced.

[0137] Figure 11 and Figure 12 respectively show the relationship diagrams of different transmit powers P t of the half-duplex D2D transmitter Dt and the communication rate R r . Figure 11 Corresponding to the preferred communication protection area O b of the cellular link outside the coverage area O t centered on the transmitter Dt; Figure 12 is the simulation result when the preferred communication protection area O b of the cellular link is within the coverage area O t centered on the transmitter Dt. The two figures respectively compare the performance of four different schemes. The results show that in the trade-off between concealment and communication rate, the communication rate considering concealment is significantly lower than that without considering concealment, but for improving the system concealment, an appropriate reduction in the communication rate is acceptable; compared with the schemes that only consider full-duplex UAV and only consider fixed-position IRS, the method proposed in the present invention significantly improves the communication rate while enhancing the system concealment, demonstrating its effectiveness in optimizing the system performance.

[0138] Figure 6 , Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 and Figure 12 The simulation results show that through the analysis of the average minimum error detection probability and the outage probability of the cellular communication link, the present invention constrains the transmit power and the transmit power of the interference signal, and obtains the maximum communication rate of the UIRS joint-assisted D2D communication link, and the communication rate of the system is effectively improved under the joint assistance of the unmanned aerial vehicle and the intelligent reflecting surface UIRS.

Claims

1. A device-to-device covert communication system assisted by a drone and an intelligent reflective surface, characterized in that: The entities involved include the UAV, the intelligent reflective surface UIRS, and the base station B s and half-duplex communication terminal, base station B s is a full-duplex base station, and the half-duplex communication terminal includes a cellular user C u , D2D sender D t , D2D receiver D r and eavesdropper Willie; cellular user C u , D2D sender D t , D2D receiver D r and the eavesdropper Willie are both half-duplex; The following communication links are formed between various entities; Link 1), UIRS joint assisted D2D hidden link D t →UIRS→D r ; D2D sender D in this link t Send a covert signal to the drone and the intelligent reflective surface UIRS, and UIRS will send the D2D sender D t The concealed signal sent is forwarded to the D2D receiver D r ; Cellular user C u Send cellular signal to base station B s , forming an uplink cellular link C u →B s ; Cellular user C u The uplink and downlink of the D2D network use orthogonal spectrum resources and there is no interference between them. t →UIRS→D r With uplink cellular link C u →B s Shared spectrum resources; Link 2), Base Station B s In order to counter the eavesdropper Willie and improve the system's stealth, artificial noise is sent to the eavesdropper Willie to build an artificial noise link B. s →Willie; Base Station B s The artificial noise emitted also affects the D2D receiver D r Generate interference and form link B s →D r , and causes the base station B s The self-interference of link B s →B s ; Link 2) Base station B s Use the same spectrum resources to send and receive information at the same time; Link 3), the randomly distributed eavesdropper Willie attempts to monitor the UIRS joint assisted D2D covert link D t →UIRS→D r , detect whether a covert signal is being sent, involving eavesdropping on link D t →Willie and UIRS→Willie; Link 4), Base Station B s To D2D sender D t Send information to form a downlink cellular link B s →D t ; Calculate the average minimum false detection probability of the eavesdropper Willie in link 3) Using the mean minimum false detection probability To measure the link 1) UIRS joint assisted D2D hidden link D t →UIRS→D r The concealment of At the same time, the uplink cellular link C is calculated u →B s The probability of interruption Finally, the average minimum false detection probability is calculated and uplink cellular link C u →B s Probability of interruption Constrained communication rate R r , and the communication rate R r Perform constraint optimization to obtain the maximum communication rate of link 1) Calculate the minimum false detection probability ξ * and the average minimum false detection probability The method is as follows: The false detection probability of the eavesdropper Willie satisfies ξ=P FA +P MD ; P FA is the false alarm probability of the eavesdropper Willie, P MD is the missed alarm probability of the eavesdropper Willie; Θ is the effective phase shift of all reflective elements of the IRS; H0 represents the UIRS joint assisted D2D hidden link D t →UIRS→D r No covert signal is transmitted. H1 indicates UIRS joint assisted D2D covert link D t →UIRS→D r There is a hidden signal transmission; P b Base station B s The transmission power of the interference signal, P t D2D sender D t The transmission power, h bw is the artificial noise link B s → Willie's small-scale fading parameter, h ur UIRS→D r Small-scale fading parameter of the communication link, h tu D t →Small-scale fading parameter of UIRS communication link, h tw D t →Small-scale fading parameter of Willie communication link; τ is the detection threshold of Willie, is the noise power received by the eavesdropper Willie; Next, calculate the minimum error detection probability ξ * , including two situations: Case 1), if the intermediate parameter ψ1 = ψ2, then the average minimum error detection probability is equal to the constant value 1-(1 / e); where, The intermediate parameter ψ1 reflects the s The interference signal strength between the eavesdropper Willie and the intermediate parameter ψ2 reflects the UIRS joint assisted D2D covert link D t →UIRS→D r The signal strength between the eavesdropper Willie and the bw Base station B s The distance to the eavesdropper Willie, d ur UIRS to D2D receiver for UAVs with smart reflective surfaces r The distance, d tu UIRS to D2D sender for drones with smart reflective surfaces t The distance, d tw D2D sender D t The distance to the eavesdropper Willie; α bw , α ur , α tu and α tw Base station B s To the eavesdropper Willie, the drone and the intelligent reflective surface UIRS to the D2D receiver D r , UAV and intelligent reflective surface UIRS to D2D sender D t and D2D sender D t Path loss exponent to eavesdropper Willie; α bw =α ur =α tu =α tw ; g ur , g tu and g tw Each element of follows an independent complex Gaussian distribution; β0 is the channel gain at a reference distance of 1m; Case 2), if the intermediate parameter ψ1≠ψ2, the average minimum error detection probability It is divided into the following two cases: Case A), if the cellular link has priority communication protection zone O b In the case of D2D sender D t The coverage area is centered on O t Calculate the corresponding average error detection probability Case B): If the cellular link has priority in communication protection zone O b In the case of D2D sender D t The coverage area is centered on O t Otherwise, the corresponding average error detection probability is calculated The expression is as follows: Among them, d bt Base station B s To D2D sender D t The distance, r w D2D receiver D r The straight-line distance from the eavesdropper Willie, θ w is the azimuth of the eavesdropper Willie, R t D2D sender D t The coverage area is centered on O t Radius, r b C is the uplink cellular link u →B s Priority communication protection zone O b radius; Get the minimum error detection probability that satisfies the average and uplink cellular link C u →B s Probability of interruption Constrained communication rate R r After that, according to the D2D sender D t The transmission power P t , the transmission power of the interference signal P b , Uplink cellular link C u →B s Probability of interruption and the average minimum false detection probability of the eavesdropper Willie at the receiving end These four constraints are finally optimized to obtain the maximum communication rate.

2. The device-to-device covert communication system assisted by a drone and a smart reflective surface according to claim 1, characterized in that: UIRS-assisted D2D transmitter in UAV with smart reflective surface t and D2D receiver D r During D2D communication, assuming that the UIRS is hovering at a height H and the IRS is equipped with K reflective elements, then the UIRS joint assisted D2D covert link D t →UIRS→D r The modeling is as follows: j is a complex number, θ i represents the phase shift of the ith element, θ i ∈[0,2π], i=1,2,…,K; λ is the carrier wavelength, d is the distance between the reflective elements, φ tu D2D sender D t The cosine of the launch angle between the drone and the intelligent reflector UIRS, φ ur UIRS to D2D receiver for UAVs with smart reflective surfaces r Cosine of the launch angle.

3. The device-to-device covert communication system assisted by a drone and a smart reflective surface according to claim 1, characterized in that: The eavesdropping link UIRS→Willie in link 3) is modeled as follows: In the above formula, d uw is the distance from the UAV and the intelligent reflective surface UIRS to the eavesdropper Willie, α uw is the path loss index from the UAV and the intelligent reflective surface UIRS to the eavesdropper Willie, g uw Each element of follows an independent complex Gaussian distribution, that is Where m represents the mth element of the communication link between the UAV and the intelligent reflective surface UIRS to the half-duplex eavesdropper Willie, m = 1, 2, …, K, K means that the IRS is equipped with K reflective elements.

4. The device-to-device covert communication system assisted by a drone and a smart reflective surface according to claim 1, characterized in that: The base station B s Configure two antennas, one antenna receives cellular user C u The antenna transmits the cellular signal, and the other antenna performs the downlink cellular link and sends the interference signal. Self-interference is generated between the two lines and cannot be eliminated. represents the self-interference coefficient; Base Station B s By sending jamming signals, the eavesdropper Willie interferes with the UIRS joint assisted D2D covert link D t →UIRS→D r For covert communication detection, the transmission power of the interference signal obeys uniform distribution; The uplink cellular link C u →B s The probability of interruption The calculation formula is: In the above formula, P c For cellular user C u The transmission power, h cb C u →B s Small-scale fading parameter of the communication link, h bb For B s →B s Small-scale fading parameter of the communication link, h bt For B s →D t Small-scale fading parameters of the communication link, For cellular user C u Received noise power; R c is the target communication rate.

5. The communication method of the device-to-device covert communication system with the joint assistance of a drone and an intelligent reflective surface according to claim 1, characterized in that: Get the maximum communication rate The specific method is as follows: Step (1), calculate the uplink cellular link C u →B s Probability of interruption Among them, P c For cellular user C u The transmission power, h cb C u →B s Small-scale fading parameter of the communication link, h bb For B s →B s Small-scale fading parameter of the communication link, h bt For B s →D t Small-scale fading parameters of the communication link, For cellular user C u Received noise power; R c is the target communication rate, η is the intermediate auxiliary amount, η=2 Rc -1; represents the self-interference coefficient; Step (2): Calculate the maximum communication rate Step (2.1), according to Solve for D2D sender D t The transmission power P t And the transmission power of the interference signal P b ;γ is the given target interruption probability; Step (2.2), based on the given allowed error detection probability ∈, according to the average minimum error detection probability D2D sender D t The transmission power P t The monotonically decreasing function and the transmission power P of the interference signal b A monotonically increasing function is used to solve the D2D sender D t The maximum transmit power P that can be obtained tm and base station B s The maximum transmit power P of the interference signal that can be obtained bm ; The calculation formula is as follows: In the above formula, D2D sender D t The maximum transmit power determined by itself, Base station B s The maximum transmission power of the interference signal determined by itself; Step (2.3), use the search algorithm in the interval (0,P tm ]and In, get the D2D sender D t Optimal transmit power and the optimal transmission power of the interference signal Make formula (8) obtain the maximum value, that is, the maximum communication rate R * r =maxR r ,(8) In the above formula, R r It means that the average minimum false detection probability and uplink cellular link C u →B s Probability of interruption Constrained communication rate; Among them, h br For B s →D r Small-scale fading parameters of the communication link, D2D receiver D r Received noise power.

6. The communication method of the device-to-device covert communication system with the joint assistance of a drone and an intelligent reflective surface according to claim 5, characterized in that: For the maximum communication rate The constraints are as follows: Among them, h br For B s →D r Small-scale fading parameters of communication links.

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