A multi-UAV relay laser / RF aviation communication method based on a mobile platform

Abstract

This paper proposes a mobile-based, multi-UAV relay laser / RF aviation communication method, comprising the following steps: system model construction and transmission signal analysis; relay scheme selection; channel modeling; and evaluation metric development. This paper employs a mobile-based, multi-UAV relay aviation communication system that connects airborne early warning aircraft (AEW&Cs) with mobile ground stations using a hybrid laser / RF link. This method can effectively improve the reliability and availability of air-to-ground laser links in mobile scenarios.

Description

Technical Field

[0001] The present invention belongs to the technical field of free-space optical communication and airborne optical communication, and specifically relates to a multi-UAV relay laser / radio frequency hybrid aviation communication method based on a mobile platform. Background Art

[0002] In recent years, the application of free-space optical communication technology in aviation communication systems has received widespread attention. Compared with traditional RF aviation communications in the shortwave or ultra-shortwave frequency bands, laser communication overcomes the shortcomings of bandwidth limitations, low transmission capacity, and susceptibility to interference, making it a viable solution for meeting the needs of massive data transmission. Laser communication signals are affected by three important factors: atmospheric attenuation, turbulence, and pointing errors, all of which are related to distance. In addition, laser transceivers are subject to strict line-of-sight alignment requirements. Therefore, aerial relay-assisted communication has become a key factor affecting the application and development of airborne laser communications. Drones are flexible and highly maneuverable. Using drones as aerial relay nodes in aviation communication systems can provide better line-of-sight connections for ground users and other aircraft, meeting the needs of reliable long-distance transmission.

[0003] Unlike traditional fixed-node networks, aviation communication networks are characterized by complex atmospheric environments and high platform mobility, both of which affect communication reliability. Therefore, when applying laser communication technology to aviation communications, it is necessary to analyze the impact of platform mobility on system performance. Summary of the Invention

[0004] To overcome the above-mentioned deficiencies of the prior art, the present invention provides a multi-UAV relay laser / RF aviation communication method based on a mobile platform, the specific steps of which are as follows:

[0005] Step 1: System model construction and transmission signal analysis;

[0006] The multi-UAV relay laser / RF aviation communication system based on mobile platform includes: the early warning aircraft as the source node of information transmission, represented by S; the mobile ground station as the destination node, represented by D; N parallel UAV relays, represented by R i ,i=1,2,…N, where N is the number of drone relays; the drone divides the link into two hops; the first hop is the AWACS-drone relay i link, denoted as SR i The second hop is the drone relay i-ground station link, denoted as R i D. Under complex atmospheric conditions, the system adopts a laser / RF hybrid transmission scheme, in which the laser link is used as the main link. When the laser link cannot meet the signal-to-noise ratio requirements, the RF backup link is activated. Assuming that the AWACS maintains a constant cruising altitude H AWACS , all drones have the same height H UAV and elevation angle ξ UAV, the elevation angle of the ground station is ξ GS ;

[0007] (1) Laser link

[0008] The instantaneous received signal-to-noise ratio of the laser link at the UAV relay i is expressed as:

[0009]

[0010] Where, is the average signal-to-noise ratio of the source node to the relay laser link, is the average transmission optical power of the source node, η is the detector response, is the channel coefficient of the first hop, is the variance of the additive white Gaussian noise signal;

[0011] The UAV relay i adopts the decoding and forwarding mode, so that the instantaneous receiving signal-to-noise ratio of the destination node is expressed as:

[0012]

[0013] Where, is the average transmission optical power of the relay, represents the second hop channel coefficient, is the average signal-to-noise ratio of the laser link from the relay to the destination node;

[0014] (2) RF link

[0015] When using RF link transmission, the instantaneous received signal-to-noise ratio at drone relay i is expressed as:

[0016]

[0017] in, is the average signal-to-noise ratio of the radio frequency link from the source node to the relay node, is the radio frequency power transmitted by the source node; the radio frequency channel coefficient of the first hop is represents the path loss of the first hop, is the variance of the Gaussian white noise signal; the instantaneous signal-to-noise ratio expression of the radio frequency link from relay node i to destination node is:

[0018]

[0019] Where, is the average signal-to-noise ratio of the radio frequency link from the relay node to the destination node, is the average RF signal transmission power of the relay, and denote the channel coefficient and path loss of the second hop respectively;

[0020] Step 2: Select relay solution;

[0021] The AWACS selects a node with the best channel quality from among multiple UAV nodes as a relay based on the feedback information from the channel state feedback channel in the system. Four different relay selection modes are available: end-to-end selection, source-relay selection, relay-destination selection, and distributed dual-relay selection.

[0022] 1) End-to-end selection solution

[0023] According to SR i and R i The channel state feedback of the two-hop link D is used to select the best relay based on the signal-to-noise ratio of the channel feedback; the end-to-end signal-to-noise ratio of the i-th link is is the first-hop signal-to-noise ratio of the i-th link, is the second-hop signal-to-noise ratio of the i-th link; the optimal relay I1 is the relay that maximizes the end-to-end signal-to-noise ratio, expressed as:

[0024]

[0025] Where I1∈{1,2…,N} represents the best relay in Scheme 1. i and R i D. Feedback channels are required in both hops of the link. This solution is highly complex.

[0026] 2) Source-Relay Selection Scheme

[0027] Relay selection is based on the first hop SR i The channel quality is selected, and the drone relay node with the highest first-hop signal-to-noise ratio is selected as the relay. At this time, the best relay I2 is the relay that maximizes the signal-to-noise ratio from the source to the relay node, which is expressed as:

[0028]

[0029] Among them, I2∈{1,2…,N} is the best relay in scheme 2, and the selected relay I2 is used for the second-hop communication; in scheme 2, only the first hop requires a feedback channel;

[0030] 3) Relay-destination selection scheme

[0031] This scheme is based on the second hop R i The relay is selected based on the channel quality of D, and the drone node with the highest second-hop signal-to-noise ratio is selected as the relay. At this time, the best relay I3 is the relay that maximizes the signal-to-noise ratio from the relay node to the destination node, which is expressed as:

[0032]

[0033] Where I3∈{1,2…,N} is the best relay in scheme 3, and the first hop uses the selected relay I3 for communication; in this scheme, only the second hop requires a feedback channel;

[0034] 4) Distributed dual relay selection scheme

[0035] The relay nodes are divided into N a and N b Two parts and N a +N b = N; source node and N a relay nodes have feedback channels, the destination node and N b The relay nodes have feedback channels; according to the received feedback information, the source node a Select a relay with the highest instantaneous signal-to-noise ratio among the relays; the destination node is N b Select a relay with the highest instantaneous signal-to-noise ratio among the relay nodes, which is expressed as:

[0036]

[0037] Among them I a ∈{1,2…,N a} is the best relay selected by the source node, I b ∈{1,2…,N b The best relay selected by the destination node is the best relay. During signal transmission, the two selected relays are activated simultaneously, and the two links cooperate to transmit information. After reaching the destination node, the signal is received using a selection combination technique. This solution does not require an end-to-end feedback link, and the number of feedback channels is significantly reduced.

[0038] Step 3: Channel modeling;

[0039] The channel model of each hop transmission is constructed, including the channel model construction of the AWACS-UAV relay and UAV relay-mobile ground station based on laser transmission, the channel model construction of the AWACS-UAV relay and UAV relay-mobile ground station based on RF transmission, and the subscript j∈{SR i ,R i D} denotes the links from AWACS to UAV relay and from UAV relay to mobile ground station respectively;

[0040] (i) Laser channel

[0041] The two hops from the AWACS to the UAV relay and from the UAV relay to the mobile ground station occur within the troposphere, so it is reasonable to assume that the two hops are affected by the same atmospheric conditions;

[0042] (a) Atmospheric attenuation

[0043] Atmospheric attenuation Due to scattering and absorption by particles in the atmosphere, the propagation of the light beam is affected by power loss. Atmospheric attenuation is expressed as:

[0044]

[0045] in, and SR i and R i D is the distance of the link; ω is the atmospheric attenuation coefficient;

[0046] (b) Atmospheric turbulence

[0047] The weak to strong turbulence model is characterized by Gamma-Gamma distribution, atmospheric turbulence h j The probability density function of t is expressed as:

[0048]

[0049] Where Γ(·) is the Gamma function, K v (·) is the modified Bessel function of the second kind, and the subscript v represents α j -β j ; α j represents the large-scale fading parameter, β j represents the small-scale fading parameter; Γ(α j ), Γ(β j ) represent α j and β j The corresponding Gamma function value; middle, The whole is The coefficient of

[0050] (c) Pointing error

[0051] AWACS-UAV relay link:

[0052] The combined radial displacement vector from the center of the UAV detector to the center of the beam footprint at the UAV receiver aperture is expressed as where r S =[x s ,y s ] is the displacement vector of the early warning aircraft, x s ,y s r S The vector components on the x-axis and y-axis; r R =[x R ,y R ] is the displacement vector of the UAV, x R ,y R r RThe vector components on the x-axis and y-axis; this fluctuation caused by a large number of random events obeys the normal distribution, and the component of the combined radial displacement vector on the x-axis The mean is 0 and the variance is The normal distribution of Combined radial displacement vector component on the y-axis The mean is 0 and the variance is The normal distribution of The position deviation of the AWACS is caused by a sudden change in its speed, which is recorded as v S =[v Sx ,v Sy ], the speed change component v of the AWACS on the x-axis and y-axis Sx and v Sy Normal distribution with mean zero is the speed variance of the AWACS; assuming that the speed of the AWACS does not change much in a very short time interval Δt, the displacement distance is expressed as x S =v Sx Δt / 2 and y S =v Sy Δt / 2; r R =[x R ,y R ] Position fluctuation component x on the x-axis and y-axis R and y R They have mean zero and variance Normal distribution The sum has a mean of zero and a variance of Normal distribution The variance of the displacement vector of the combined radial displacement on the x-axis and y-axis and Expressed as:

[0053]

[0054] UAV relay-mobile ground station link:

[0055] The combined radial displacement vector from the center of the mobile ground station detector to the center of the beam footprint at the ground station receiver aperture is expressed as The displacement vector of the combined radial displacement on the x-axis is The mean is 0 and the variance is The normal distribution of Displacement vector of combined radial displacement on the y-axis The mean is 0 and the variance is The normal distribution of r θ =[xθx ,x θy ] is the displacement vector caused by the direction fluctuation of the hovering drone. Assume that the shaking angle θ of the drone on the x-axis x and the jitter angle θ on the y-axis y is small enough, then the displacement vector on the x-axis Displacement vector on the y-axis Among them L RD is the launch distance, the jitter angles on the x-axis and y-axis have a mean of 0 and a variance of The normal distribution of r D =[x D ,y D ] is the displacement vector of the mobile ground station, x D ,y D r D Vector components on the x-axis and y-axis; the position deviation of a mobile ground station with unsteady velocity is caused by a sudden change in its velocity, which is denoted by v D =[v Dx ,v Dy ], its velocity change component v on the x-axis and y-axis Dx and v Dy Normal distribution is the velocity variance of the ground station, and the displacement distance on the x-axis and y-axis within Δt is expressed as x D =v Dx Δt / 2 and y D =v Dy Δt / 2; therefore, the variance of the displacement vectors of the combined radial displacement on the x-axis and y-axis is and Expressed as:

[0056]

[0057] Pointing error The probability density function of is expressed as:

[0058]

[0059] Where A 0,j =[erf(v j )] 2 is the fraction of the light power collected when the difference between the center of the light spot and the center of the detector is zero, erf(·) is the error function, is the distance L j The aperture radius a and beam width ω z,j Pointing error coefficient in is the equivalent beamwidth; To correct the jitter standard deviation, the first jump j = SR i , is the corrected jitter standard deviation of the AWACS-UAV relay link; the second hop j = R i D, is the corrected jitter standard deviation of the UAV-mobile ground station link;

[0060] (d) Angle of arrival jitter

[0061] When the incident laser has a certain incident angle θ a,j When arriving at the receiving plane, the Airy pattern may exceed the detection range of the detector due to the obvious deviation in direction; arrival angle jitter The probability density function of is expressed as:

[0062]

[0063] in, is the UAV jitter angle variance, θ FoV,j is the field of view of the receiver, δ(·) is the Dirac function;

[0064] (e) Doppler effect

[0065] The relative motion between the mobile ground station and the UAV relay causes the Doppler frequency shift between the UAV relay and the mobile ground station link, which is expressed as Δf = vf FSO cos(ξ GS ) / c, where v is the relative speed between the UAV and the mobile ground station, f FSO is the optical carrier frequency, c is the speed of light; the UAV relay-mobile ground station link can ignore the influence of the Doppler effect;

[0066] (f) Overall channel statistical characteristics

[0067] The coefficients of the laser transmission channel are respectively composed of atmospheric attenuation, atmospheric turbulence, pointing error and arrival angle jitter; the combined channel coefficient is expressed as:

[0068]

[0069] Combined channel coefficient h j The probability density function of is expressed as:

[0070]

[0071] Where, the combined channel coefficients of attenuation, turbulence, and pointing error are for The probability density function of , according to equations (9), (10), (15), and (16), and substituting equation (17) into equation (18), performs integral operation and obtains:

[0072]

[0073] in, is the Meijer-G function, m, n, p, q are non-negative integers representing the number of variables;

[0074] Combining the relationship between channel coefficient and signal-to-noise ratio in equations (1) and (2), and using h j The signal-to-noise ratio of the laser link between the AWACS and the UAV relay and the laser link between the UAV relay and the mobile ground station is obtained by integrating the probability density function of The cumulative distribution function is:

[0075]

[0076] in, is the laser link signal-to-noise ratio threshold; is the probability density function of the signal-to-noise ratio of the AWACS-UAV relay optical link and the UAV relay-mobile ground station optical link;

[0077] (ii) Radio frequency channel

[0078] RF channel coefficient I j ,j∈{SR i ,R i D} is modeled using Nakagami-m distribution, whose probability density function is:

[0079]

[0080] Where m is the RF fading factor of the Nakagami-m distribution, is the average signal-to-noise ratio of the RF; Γ(m) represents the Gamma function value corresponding to m; combining the relationship between the channel coefficient and the signal-to-noise ratio in equations (3) and (4), the signal-to-noise ratio of the AWACS-UAV relay RF link and the UAV relay-mobile ground station RF link is obtained by integration: The cumulative distribution function of is:

[0081]

[0082] Where Γ(α,x) is the incomplete gamma function, and in equation (22) the parameter α = m, and the parameter G j is the path loss, is the signal-to-noise ratio threshold of the radio frequency link;

[0083] Step 4: Construction of evaluation indicators:

[0084] Construct dual evaluation indicators of interruption probability and bit error rate;

[0085] I. Interruption Probability

[0086] The outage probability is defined as the probability that the link cannot transmit data due to the signal-to-noise ratio falling below a certain threshold. The outage probability is expressed as:

[0087]

[0088] Where Pr(·) represents the probability, γ SD represents the system end-to-end signal-to-noise ratio, γ th is the signal-to-noise ratio threshold, Represents γ SD The cumulative distribution function of

[0089] (A) End-to-end selection scheme interruption probability

[0090] In scheme 1, the link that UAV relay i relays is the i-th link; the instantaneous signal-to-noise ratio of the end-to-end link of the i-th link is is the first hop signal-to-noise ratio of the i-th link and the second hop signal-to-noise ratio of the i-th link The minimum value of According to formula (5), the drone I1 with the best end-to-end signal-to-noise ratio is selected as the relay. At this time, the maximum end-to-end instantaneous signal-to-noise ratio of scheme 1 is:

[0091]

[0092] Therefore, the outage probability of scenario 1 is expressed as:

[0093]

[0094] Where, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay laser link, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay radio frequency link i, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay i-mobile ground station laser link, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay i-mobile ground station RF link; Substituting equations (20) and (22) into equation (25), we can obtain the outage probability of scheme 1;

[0095] (B) Outage probability of source-relay selection scheme

[0096] In scheme 2, the best relay i=I2 is selected based on the first-hop signal-to-noise ratio, as shown in formula (6). The instantaneous signal-to-noise ratio between the AWACS-UAV relay I2 link in scheme 2 is:

[0097]

[0098] Scheme 2: Signal-to-noise ratio of the UAV relay I2-mobile ground station link Signal-to-noise ratio of the laser link from the drone relaying I2 to the mobile ground station Signal-to-noise ratio of the RF link from the drone relay I2 to the mobile ground station The maximum value of is expressed as:

[0099]

[0100] The end-to-end instantaneous signal-to-noise ratio of solution 2 is:

[0101]

[0102] in, When i=I2 The value of

[0103] The outage probability of scenario 2 is:

[0104]

[0105] in, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay I2-mobile ground station laser link, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay I2-mobile ground station RF link; Substitute equations (20) and (22) into equation (29) to calculate the outage probability of scheme 2;

[0106] (C) Interruption probability of relay-destination selection scheme

[0107] Scheme 3 selects the best relay i=I3 based on the second-hop signal-to-noise ratio, as shown in Equation (7). The instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 link in Scheme 3 is:

[0108]

[0109] Where, is the instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 laser link, is the instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 radio frequency link; the signal-to-noise ratio of the UAV relay I3-mobile ground station link is:

[0110]

[0111] The end-to-end instantaneous signal-to-noise ratio of solution 3 is:

[0112]

[0113] Therefore, the outage probability of scenario 3 is expressed as:

[0114]

[0115] in, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay I3 laser link, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay I3 radio frequency link; Substitute equations (20) and (22) into equation (33) to calculate the interruption probability of scheme 3;

[0116] (D) Distributed Dual-Relay Selection Scheme Interruption Probability

[0117] In scheme 4, the signal passes through relay i=I a The transmission is called path 1, using drone relay I a Signal-to-noise ratio of the link being relayed for:

[0118]

[0119] in, For AWACS-UAV relay I a The instantaneous signal-to-noise ratio, Relay for drones I a - the instantaneous signal-to-noise ratio of the mobile ground station, Relay for drones I a - the instantaneous signal-to-noise ratio of the mobile ground station laser link, Relay for drones I a -Instantaneous signal-to-noise ratio of the mobile ground station radio frequency link;

[0120] The signal passes through relay i=I b The transmission is called path 2, using drone relay I b Signal-to-noise ratio of the link being relayed Expressed as:

[0121]

[0122] in, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio of the laser link, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio of the RF link, Relay for drones I b -Instantaneous signal-to-noise ratio of the mobile ground station;

[0123] When two signals arrive at the mobile ground station and the receiver uses selective combining technology, the end-to-end instantaneous signal-to-noise ratio of Scheme 4 is:

[0124]

[0125] Therefore, the outage probability expression of scheme 4 is:

[0126]

[0127] in, Relay for drones I a - Cumulative distribution function of the signal-to-noise ratio of the mobile ground station laser link, Relay for drones I a - the cumulative distribution function of the signal-to-noise ratio of the RF link of the mobile ground station S, For AWACS-UAV relay I b Cumulative distribution function of the laser link signal-to-noise ratio, For AWACS-UAV relay I b Cumulative distribution function of the RF link signal-to-noise ratio,Substitute equations (20) and (22) into equation (37) to calculate the outage probability of scheme 4;

[0128] 2. Average bit error rate

[0129] The average bit error rate of the laser link is:

[0130]

[0131] The closed-form expression for the average bit error rate of the RF link is:

[0132]

[0133] in, Indicates the RF signal-to-noise ratio m-1 power; when binary modulation is used, coefficient A = 1, coefficient B = 1; when multi-base modulation is used, coefficient A = 2 / log2M, coefficient B = sin(π / M);

[0134] The average bit error rate of the parallel laser / RF link is:

[0135]

[0136] in, is the probability of using a laser link to transmit information, is the probability of using the RF link, the link selection probability can be expressed as:

[0137]

[0138] In the parallel UAV relay system, when the states of each path are independently distributed, the average bit error rate of the first and second hops of the system is B SR and B RD , which is equal to the average bit error rate of a single path, expressed as and and are the average bit error rates of the first-hop single path and the second-hop single path, respectively. In this case, the average bit error rates of the four relay modes are the same. Considering the system as a serial two-hop system with decode-and-forward relay, its end-to-end average bit error rate is expressed as:

[0139]

[0140] Substituting equations (38), (39), (40), and (41) into (42) yields the end-to-end average bit error rate of the system.

[0141] In one embodiment of the present invention, the method further comprises step five: simulation results;

[0142] The simulation parameters are shown in Table 1;

[0143] Table 1 Simulation parameter settings

[0144]

[0145] Assume that all UAV relays experience the same atmospheric conditions and P f,j =P r,j =P t , P t is the signal transmission power.

[0146] In a specific embodiment of the present invention, the total number of drone relays does not exceed 4.

[0147] In another embodiment of the present invention, in a multi-UAV relay system, the performance of the end-to-end selection scheme is the best; when Smaller and When the value is large, use solution 2-4 to replace the end-to-end solution; Larger and When the value is small, the source-relay selection scheme is adopted; when and When both are large, a distributed dual-relay selection scheme is adopted.

[0148] The present invention combines the communication characteristics of airborne platforms to deploy parallel relays on UAVs and proposes four relay selection schemes; constructs a radio frequency data link backup communication method and performs laser / radio frequency hybrid transmission to improve system reliability; and analyzes the impact of platform mobility performance on the interruption probability and bit error rate of the overall communication system.

[0149] This paper constructs an airborne optical communication system based on multiple parallel drone relay nodes. This system establishes an airborne laser / radio frequency hybrid air-to-ground communication link from an airborne early warning aircraft to a mobile ground station, and uses hard switching for link switching. Furthermore, the system focuses on the impact of changes in the speed variance of the two mobile platforms, the early warning aircraft and the mobile ground station, and constructs two evaluation indicators, namely, interruption probability and bit error rate, to conduct system performance evaluation and analysis. Furthermore, four relay selection schemes are designed, and the applicability of the four schemes is analyzed under different platform mobility performances. The optimal number and deployment height of drone relays are determined. Finally, a system design guide is provided. BRIEF DESCRIPTION OF THE DRAWINGS

[0150] Figure 1 Schematic diagram of the hybrid laser / RF link aviation communication system model based on multi-UAV relay in the present invention;

[0151] Figure 2 Gaussian beam footprint at the receiver aperture: (a) receiver on the UAV relay; (b) receiver on the mobile ground station;

[0152] Figure 3 Shows that when H UAV =0.5km, The relationship between the outage probability and the transmission power under the four relay selection schemes; (a) Scheme 1; (b) Scheme 2; (c) Scheme 3; (d) Scheme 4;

[0153] Figure 4 Shows that when H UAV =0.3km, P t =25dBm under different relay selection schemes and the relationship between the interruption probability and the speed variance of the early warning aircraft; (a) N = 3 (N a =2,N b =1), (b) N = 3 (N a =2,N b =1), (c) N = 4 (N a =2,N b =2),

[0154] Figure 5 Shows that when H UAV =0.3km, P t =25dBm under different relay selection schemes and the relationship between the outage probability and the speed variance of the mobile ground station; (a) N = 3 (N a =1,N b =2), (b) N = 3 (N a=1,N b =2), (c) N = 4 (N a =2,N b =2),

[0155] Figure 6 Schematic diagram of the impact of drone relay deployment height on interruption probability;

[0156] Figure 7 Schematic diagram of the impact of speed variance between the early warning aircraft and the mobile ground station on the bit error rate. DETAILED DESCRIPTION

[0157] The present invention will be further described below with reference to the accompanying drawings.

[0158] The present invention proposes a multi-UAV relay laser / RF aviation communication system based on a mobile platform, and the specific steps are as follows.

[0159] Step 1: System model construction and transmission signal analysis;

[0160] The present invention is based on a multi-UAV relay laser / RF aviation communication system on a mobile platform. Figure 1 The system consists of an early warning aircraft as the source node of information transmission, represented by S; a mobile ground station as the destination node, represented by D; N parallel drone relays, represented by R i ,i=1,2,…N, where N is the number of drone relays. In this system, to ensure reliable information transmission from air to ground, the drone divides the link into two hops. The first hop is the AWACS-UAV relay i link, denoted as SR i The second hop is the drone relay i-ground station link, denoted as R i D. Considering the complex atmospheric conditions, the system adopts a laser / RF hybrid transmission scheme, in which the laser link is used as the main link. When the laser link cannot meet the signal-to-noise ratio requirements, the RF backup link is activated. Assume that the AWACS maintains a constant cruising altitude H AWACS , all drones have the same height H UAV and elevation angle ξ UAV , the elevation angle of the ground station is ξ GS .

[0161] (1) Laser link

[0162] The laser link uses on-off keying modulation, intensity modulation, and direct detection technology. The instantaneous received signal-to-noise ratio of this link at the UAV relay i can be expressed as:

[0163]

[0164] Where, is the average signal-to-noise ratio of the source node to the relay laser link, is the average transmission optical power of the source node, η is the detector response, is the channel coefficient of the first hop, is the variance of the additive white Gaussian noise signal.

[0165] The UAV relay i adopts the decoding and forwarding mode, and the instantaneous receiving signal-to-noise ratio of the destination node can be expressed as:

[0166]

[0167] Where, is the average transmission optical power of the relay, represents the second hop channel coefficient, is the average signal-to-noise ratio of the laser link from the relay to the destination node.

[0168] (2) RF link

[0169] When using RF link transmission, the instantaneous received signal-to-noise ratio at the drone relay i can be expressed as:

[0170]

[0171] in, is the average signal-to-noise ratio of the radio frequency link from the source node to the relay node, is the radio frequency power transmitted by the source node. The radio frequency channel coefficient of the first hop is represents the path loss of the first hop, is the variance of the Gaussian white noise signal. The instantaneous signal-to-noise ratio expression of the radio frequency link from relay node i to destination node is:

[0172]

[0173] Where, is the average signal-to-noise ratio of the radio frequency link from the relay node to the destination node, is the average RF signal transmission power of the relay, and represent the channel coefficient and path loss of the second hop respectively.

[0174] Step 2: Select relay solution;

[0175] The AWACS selects a node that provides the best channel quality from among multiple UAV nodes as a relay based on the feedback information from the channel status feedback channel in the system. The present invention considers four different relay selection modes: end-to-end selection, source-relay selection, relay-destination selection, and distributed dual-relay selection.

[0176] 1) End-to-end selection solution

[0177] In this mode, according to SR i and R i The channel state feedback of the two-hop link D is used to select the best relay based on the signal-to-noise ratio of the channel feedback. The end-to-end signal-to-noise ratio of the i-th link is is the first-hop signal-to-noise ratio of the i-th link, is the second-hop signal-to-noise ratio of the i-th link. The optimal relay I1 is the relay that maximizes the end-to-end signal-to-noise ratio, expressed as:

[0178]

[0179] Where I1∈{1,2…,N} represents the best relay in Scheme 1. i and R i Feedback channels are required for both hops of the D link. In this case, the source node requires a feedback link that connects to all nodes. However, since there may not be a direct line-of-sight connection between the source and destination nodes, relay nodes may even be required to provide feedback on the link's channel status back to the source node, which leads to a highly complex system.

[0180] 2) Source-Relay Selection Scheme

[0181] In this mode, relay selection is based on the first hop SR i The channel quality is selected, and the drone relay node with the highest first-hop signal-to-noise ratio is selected as the relay. At this time, the best relay I2 is the relay that maximizes the signal-to-noise ratio from the source to the relay node, which is expressed as:

[0182]

[0183] Where I2∈{1,2…,N} is the best relay in Scheme 2, and the selected relay I2 is used for the second-hop communication. Unlike Scheme 1, in Scheme 2, only the first hop requires a feedback channel.

[0184] 3) Relay-destination selection scheme

[0185] This scheme is based on the second hop R i The relay is selected based on the channel quality of D, and the drone node with the highest second-hop signal-to-noise ratio is selected as the relay. At this time, the best relay I3 is the relay that maximizes the signal-to-noise ratio from the relay node to the destination node, which is expressed as:

[0186]

[0187] Where I3∈{1,2…,N} is the optimal relay in Scheme 3. The first hop uses the selected relay I3 for communication. In this scheme, only the second hop requires a feedback channel.

[0188] 4) Distributed dual relay selection scheme

[0189] In this scheme, the relay nodes are divided into N a and N b Two parts and N a +N b = N. Source node and N a relay nodes have feedback channels, the destination node and N b The relay nodes have feedback channels. According to the feedback information received, the source node a Select a relay with the highest instantaneous signal-to-noise ratio among the relays. Similarly, the destination node is in N b Select a relay with the highest instantaneous signal-to-noise ratio among the relay nodes, which is expressed as:

[0190]

[0191] Among them I a ∈{1,2…,N a} is the best relay selected by the source node, I b ∈{1,2…,N b} is the best relay selected by the destination node. During signal transmission, the two selected relays are activated simultaneously, and the two links coordinate information transmission. After reaching the destination node, the signal is received using a selection combination technique (Zhang X, Zhao S, Wang Y, et al. A weather-dependent UAV relay-assisted hybrid FSO / RF airborne communication system [J]. Optics Communications, 2024, 554: 130196.). Compared with Scheme 1, this scheme does not require an end-to-end feedback link and significantly reduces the number of feedback channels.

[0192] Step 3: Channel modeling;

[0193] This step constructs a channel model for each hop transmission, including the channel model construction of the AWACS-UAV relay and UAV relay-mobile ground station based on laser transmission, and the channel model construction of the AWACS-UAV relay and UAV relay-mobile ground station based on RF transmission. i ,R i D} denote the links from the AWACS to the UAV relay and from the UAV relay to the mobile ground station, respectively.

[0194] (i) Laser channel

[0195] The cruising altitude of AWACS aircraft is typically around 10,000 meters, so both hops—from the AWACS to the UAV relay and from the UAV relay to the mobile ground station—occur within the troposphere. Therefore, it is reasonable to assume that both hops are subject to the same atmospheric conditions.

[0196] (a) Atmospheric attenuation

[0197] Atmospheric attenuation Due to scattering and absorption by particles in the atmosphere, the propagation of the light beam is affected by power loss. Atmospheric attenuation can be expressed as:

[0198]

[0199] in, and SR i and R i D is the distance of the link. ω is the atmospheric attenuation coefficient.

[0200] (b) Atmospheric turbulence

[0201] The presence of turbulence leads to power loss and unpredictable fluctuations in signal strength and phase. The model of weak to strong turbulence is usually characterized by Gamma-Gamma distribution. The probability density function of is expressed as:

[0202]

[0203] Where Γ(·) is the Gamma function, K v (·) is the modified Bessel function of the second kind, and the subscript v represents α j -β j α j represents the large-scale fading parameter, β j represents the small-scale fading parameter. Γ(α j ), Γ(β j ) represent α j and β j The corresponding Gamma function value can be directly calculated using MATLAB software. middle, The whole is The coefficient of .

[0204] (c) Pointing error

[0205] The primary contributors to pointing errors are the speed variations of the AWACS and mobile ground station, as well as fluctuations in the relative position and orientation of the UAV caused by random air disturbances and vibrations within the surrounding atmosphere. It is worth noting that the pointing-acquisition-tracking systems on the UAV and mobile ground station dynamically adjust the orientation of the transmit and receive lenses to maintain nearly constant beam alignment. However, this system is insufficient to compensate for random position fluctuations caused by sudden changes in the speed of the AWACS and mobile ground station.

[0206] AWACS-UAV relay link:

[0207] For this link, the combined radial displacement vector from the center of the UAV detector to the center of the beam footprint at the UAV receiver aperture is expressed as where r S =[x s ,y s ] is the displacement vector of the early warning aircraft, x s ,y s r S The vector components on the x-axis and y-axis. R =[x R ,y R ] is the displacement vector of the UAV, x R ,y R r R The vector components on the x-axis and y-axis, such as Figure 2 (a) This fluctuation caused by a large number of random events obeys the normal distribution, and the component of the combined radial displacement vector on the x-axis The mean is 0 and the variance is The normal distribution of Combined radial displacement vector component on the y-axis The mean is 0 and the variance is The normal distribution of The position deviation of the AWACS is caused by a sudden change in its speed, which is recorded as v S =[v Sx ,v Sy ], the speed change component v of the AWACS on the x-axis and y-axis Sx and v Sy Normal distribution with mean zero is the speed variance of the AWACS. Assuming that the speed of the AWACS does not change much in a very short time interval Δt, the displacement distance can be expressed as x S =v Sx Δt / 2 and y S =v Sy Δt / 2; r R =[x R ,yR ] Position fluctuation component x on the x-axis and y-axis R and y R They have mean zero and variance Normal distribution and has a mean of zero and a variance of Normal distribution The variance of the displacement vector of the combined radial displacement on the x-axis and y-axis and It can be expressed as:

[0208]

[0209] UAV relay-mobile ground station link:

[0210] For this link, the combined radial displacement vector from the center of the mobile ground station detector to the center of the beam footprint at the ground station receiver aperture is expressed as The displacement vector of the combined radial displacement on the x-axis is The mean is 0 and the variance is The normal distribution of Displacement vector of combined radial displacement on the y-axis The mean is 0 and the variance is The normal distribution of is the displacement vector caused by the directional fluctuation of the hovering drone. Assume that the shaking angle θ of the drone on the x-axis x and the jitter angle θ on the y-axis y is small enough, then the displacement vector on the x-axis Displacement vector on the y-axis Among them L RD is the launch distance, the jitter angles on the x-axis and y-axis have a mean of 0 and a variance of The normal distribution of r D =[x D ,y D ] is the displacement vector of the mobile ground station, x D ,y D r D The vector components on the x-axis and y-axis, such as Figure 2 (b) The position deviation of a mobile ground station with unsteady velocity is caused by a sudden change in its velocity, which is denoted by v. D =[v Dx ,v Dy ], its velocity change component v on the x-axis and y-axis Dx and v Dy Normal distribution is the velocity variance of the ground station, and the displacement distance on the x-axis and y-axis within Δt can be expressed as x D =v Dx Δt / 2 and y D =v Dy Δt / 2. Therefore, the variance of the displacement vector of the combined radial displacement on the x-axis and y-axis is and It can be expressed as:

[0211]

[0212] Pointing error The probability density function of is expressed as:

[0213]

[0214] Where A 0,j =[erf(v j )] 2 is the fraction of the light power collected when the difference between the center of the light spot and the center of the detector is zero, erf(·) is the error function, is the distance L j The aperture radius a and beam width ω z,j Pointing error coefficient in is the equivalent beamwidth. To correct the jitter standard deviation, the first jump j = SR i , is the corrected jitter standard deviation of the AWACS-UAV relay link; the second hop j = R i D, is the corrected jitter standard deviation of the UAV-mobile ground station link.

[0215] (d) Angle of arrival jitter

[0216] Due to the vibration of the hovering drone, the beam is no longer orthogonal to the receiving plane. a,j When the beam reaches the receiving plane, the Airy pattern may be outside the detector's detection range due to significant deviation in direction. The probability density function can be expressed as:

[0217]

[0218] in, is the UAV jitter angle variance, θ FoV,jis the field of view angle of the receiver, and δ(·) is the Dirac function (Wang JY, Ma Y, et al. Hovering UAV-based FSO communications: Channel modelling, performance analysis, and parameter optimization[J]. IEEE Journal on Selected Areas in Communications, 2021, 39(10): 2946-2959.).

[0219] (e) Doppler effect

[0220] In the scenario of the present invention, to ensure the information transmission of the AWACS, the relay formation composed of drones and the AWACS remain relatively stationary at all times. Therefore, the Doppler effect between the AWACS-UAV relay link is not considered. The relative motion between the mobile ground station and the drone relay causes the Doppler frequency shift between the drone relay and the mobile ground station link, which is expressed as Δf = vf FSO cos(ξ GS ) / c, where v is the relative speed between the UAV and the mobile ground station, f FSO is the optical carrier frequency, and c is the speed of light. Currently designed optical receivers can correct for frequency shifts up to ±15 GHz. That is, for an optical signal with λ = 1550 nm, the resulting Doppler shift can be corrected if v < 6458 km / h. The relative speed between current drone relays and mobile ground stations (i.e., vehicles) cannot exceed this value, so the Doppler effect can be ignored in the drone relay-mobile ground station link.

[0221] (f) Overall channel statistical characteristics

[0222] The coefficients of the laser transmission channel are composed of atmospheric attenuation, atmospheric turbulence, pointing error and arrival angle jitter. The combined channel coefficients can be expressed as:

[0223]

[0224] Combined channel coefficient h j The probability density function can be expressed as:

[0225]

[0226] Where, the combined channel coefficients of attenuation, turbulence, and pointing error are for The probability density function of . According to equations (9), (10), (15), and (16), and substituting equation (17) into equation (18), we can obtain the following integral operation:

[0227]

[0228] in, is the Meijer-G function, which can be used to represent most special functions. m, n, p, and q are non-negative integers representing the number of variables.

[0229] Combining the relationship between channel coefficient and signal-to-noise ratio in equations (1) and (2), and using h j The signal-to-noise ratio of the laser link between the AWACS and the UAV relay and the laser link between the UAV relay and the mobile ground station is obtained by integrating the probability density function of The cumulative distribution function of is:

[0230]

[0231] in, is the laser link signal-to-noise ratio threshold, The signal-to-noise ratio of the optical link between the AWACS and the UAV and the optical link between the UAV and the mobile ground station is The probability density function of .

[0232] (ii) Radio frequency channel

[0233] RF channel coefficient I j ,j∈{SR i ,R i D} can be modeled using the Nakagami-m distribution (Usman M, Yang HC, Alouini MS. Practical switching-based hybrid FSO / RF transmission and its performance analysis [J]. IEEE Photonics journal, 2014, 6(5): 1-13.), which is closer to the actual fading of the AWACS-UAV relay channel and the UAV relay-mobile ground station channel. Its probability density function is:

[0234]

[0235] Among them, m is the Nakagami-m parameter, also known as the radio frequency fading factor, is the average signal-to-noise ratio of the RF.

[0236] Γ(m) represents the Gamma function value corresponding to m, which can be directly calculated using MATLAB software. Combining the relationship between the channel coefficient and the signal-to-noise ratio in equations (3) and (4), the signal-to-noise ratio of the AWACS-UAV relay RF link and the UAV relay-mobile ground station RF link is obtained by integration: The cumulative distribution function of is:

[0237]

[0238] Among them, Γ(α,x) is an incomplete gamma function, which can be directly calculated using MATLAB software. In formula (22), parameter α = m, parameter G j is the path loss, is the signal-to-noise ratio threshold of the RF link.

[0239] Step 4: Construction of evaluation indicators:

[0240] The present invention constructs dual evaluation indicators of outage probability and bit error rate. By analyzing the overall statistical characteristics of the proposed system, the expressions of outage probability and average bit error rate under four relay selection schemes are derived.

[0241] I. Interruption Probability

[0242] The outage probability is defined as the probability that the link cannot transmit data due to the signal-to-noise ratio falling below a certain threshold. The outage probability is expressed as:

[0243]

[0244] Where Pr(·) represents the probability, γ SD represents the system end-to-end signal-to-noise ratio, γ th is the signal-to-noise ratio threshold, Represents γ SD The cumulative distribution function of .

[0245] (A) End-to-end selection scheme interruption probability

[0246] In scheme 1, the link that UAV relay i relays is link i. The instantaneous signal-to-noise ratio of the end-to-end link of link i is is the first hop signal-to-noise ratio of the i-th link and the second hop signal-to-noise ratio of the i-th link The minimum value of According to formula (5), the drone I1 with the best end-to-end signal-to-noise ratio is selected as the relay. At this time, the maximum end-to-end instantaneous signal-to-noise ratio of scheme 1 is:

[0247]

[0248] Therefore, the outage probability of scenario 1 is expressed as:

[0249]

[0250] Where, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay laser link, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay radio frequency link i, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay i-mobile ground station laser link, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay i-mobile ground station RF link. Substituting Equations (20) and (22) into Equation (25), we can obtain the outage probability of Scheme 1.

[0251] (B) Outage probability of source-relay selection scheme

[0252] In scheme 2, the best relay i=I2 is selected based on the first-hop signal-to-noise ratio, as shown in formula (6). The instantaneous signal-to-noise ratio between the AWACS-UAV relay I2 link in scheme 2 is:

[0253]

[0254] Scheme 2: Signal-to-noise ratio of the UAV relay I2-mobile ground station link Signal-to-noise ratio of the laser link from the drone relaying I2 to the mobile ground station Signal-to-noise ratio of the RF link from the drone relay I2 to the mobile ground station The maximum value of is expressed as:

[0255]

[0256] The end-to-end instantaneous signal-to-noise ratio of solution 2 is:

[0257]

[0258] in, When i=I2 The value of .

[0259] The outage probability of scenario 2 is:

[0260]

[0261] in, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay I2-mobile ground station laser link, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay I2-mobile ground station RF link. Substituting Equations (20) and (22) into Equation (29), the outage probability of Scheme 2 can be calculated.

[0262] (C) Interruption probability of relay-destination selection scheme

[0263] Scheme 3 selects the best relay i=I3 based on the second-hop signal-to-noise ratio, as shown in Equation (7). The instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 link in Scheme 3 is:

[0264]

[0265] Where, is the instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 laser link, is the instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 radio frequency link. The signal-to-noise ratio of the UAV relay I3-mobile ground station link is:

[0266]

[0267] The end-to-end instantaneous signal-to-noise ratio of solution 3 is:

[0268]

[0269] Therefore, the outage probability of scenario 3 is expressed as:

[0270]

[0271] in, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay I3 laser link, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay I3 radio frequency link. Substituting equations (20) and (22) into equation (33), the outage probability of scheme 3 can be calculated.

[0272] (D) Distributed Dual-Relay Selection Scheme Interruption Probability

[0273] In scheme 4, the signal passes through relay i=I a The transmission is called path 1, using drone relay I a Signal-to-noise ratio of the link being relayed for:

[0274]

[0275] in, For AWACS-UAV relay I a The instantaneous signal-to-noise ratio, Relay for drones I a - the instantaneous signal-to-noise ratio of the mobile ground station, Relay for drones I a - the instantaneous signal-to-noise ratio of the mobile ground station laser link, Relay for drones I a-Instantaneous signal-to-noise ratio of the mobile ground station RF link.

[0276] Similarly, the signal passes through relay i=I b The transmission is called path 2, using drone relay I b Signal-to-noise ratio of the link being relayed Expressed as:

[0277]

[0278] in, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio of the laser link, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio of the RF link, Relay for drones I b -Instantaneous signal-to-noise ratio of the mobile ground station.

[0279] When two signals arrive at the mobile ground station and the receiver uses selective combining technology, the end-to-end instantaneous signal-to-noise ratio of Scheme 4 is:

[0280]

[0281] Therefore, the outage probability expression of scheme 4 is:

[0282]

[0283] in, Relay for drones I a - Cumulative distribution function of the signal-to-noise ratio of the mobile ground station laser link, Relay for drones I a - the cumulative distribution function of the signal-to-noise ratio of the RF link of the mobile ground station S, For AWACS-UAV relay I b Cumulative distribution function of the laser link signal-to-noise ratio, For AWACS-UAV relay I b Cumulative distribution function of the RF link signal-to-noise ratio. Substituting equations (20) and (22) into equation (37), the outage probability of scheme 4 can be calculated.

[0284] 2. Average bit error rate

[0285] The average bit error rate of the laser link is:

[0286]

[0287] The closed-form expression for the average bit error rate of the RF link is:

[0288]

[0289] in, Indicates the RF signal-to-noise ratio m-1th power. When binary modulation is used, coefficient A = 1, coefficient B = 1. When multi-level modulation is used, coefficient A = 2 / log2M, coefficient B = sin(π / M).

[0290] The average bit error rate of the parallel laser / RF link is:

[0291]

[0292] in, is the probability of using a laser link to transmit information, is the probability of using the RF link, the link selection probability can be expressed as:

[0293]

[0294] In the parallel UAV relay system, when the states of each path are independently distributed, the total average bit error rate B of the first and second hops of the system is SR and B RD , which is equal to the average bit error rate of a single path, can be expressed as and and are the average bit error rates of the first-hop single path and the second-hop single path, respectively. In this case, the average bit error rates of the four relay modes are the same, and the system can be regarded as a serial two-hop system with decode-and-forward relay. Its end-to-end average bit error rate can be expressed as:

[0295]

[0296] Substituting equations (38), (39), (40), and (41) into (42) yields the end-to-end average bit error rate of the system.

[0297] Step 5: Simulation results.

[0298] In order to verify the effectiveness and feasibility of the present invention, the method proposed in the present invention was analyzed using MATLAB simulation software, and the simulation parameters are shown in Table 1.

[0299] Table 2 Simulation parameter settings

[0300]

[0301] Assume that all UAV relays experience the same atmospheric conditions and P f,j =P r,j =Pt , P t is the signal transmission power.

[0302] Figure 3 (a), (b), (c) and (d) show the relationship between the outage probability and the average transmission power of different numbers of drone relays in Scheme 1, Scheme 2, Scheme 3 and Scheme 4, respectively. As shown in the figure, the increase in transmission power significantly improves the overall outage probability performance. In addition, Figure 3 The simulation results in (a), (c), and (d) show that the outage probability generally decreases as the number of drone relays increases. However, in scenario 2, the outage probability is unaffected by the number of drone relays. Notably, in all four scenarios, N = 5 shows no significant improvement in outage probability performance compared to N = 4. Therefore, for prudent cost management, the number of drone relays deployed should not exceed four.

[0303] exist Figure 4 When the transmission power is 25dBm, the interruption performance of the four proposed schemes is observed. As the value of increases, the standard deviation of the AWACS-UAV link jitter increases, which leads to an increase in the pointing error and a deterioration of the overall interruption performance. Figure 4 In (a), when When it is less than 8, solution 1 shows the best end-to-end interruption performance, and the range is about 10 -20 to 10 -10 It is worth noting that when When it exceeds 8, the outage probability curves of Scheme 1 and Scheme 4 overlap. In addition, when When it exceeds 15, the curve of Scheme 2 is consistent with the curves of Scheme 1 and Scheme 4. That is, when When the value is greater than 8, solution 4 can be used instead of solution 1 to reduce the system's demand for feedback channels. When the number of relay selection schemes exceeds 15, Scheme 2 can be used to replace both Scheme 4 and Scheme 1. In practical applications, some trade-offs need to be made between the complexity and performance of these relay selection schemes.

[0304] like Figure 4 As shown in (b), When it increases to 10, the overall probability of end-to-end outage increases, and the outage performance of different relay selection schemes changes. As can be seen from the figure, when When it is less than 2, the optimal end-to-end interruption performance of Scheme 1 and Scheme 3 is about 10 -8 , but with As increases, the interruption performance of Scheme 3 deteriorates rapidly. Figure 4 (a) is different. The interruption performance of scheme 2 is always poor, maintaining at 10-3 Around. When the outage probability of Scheme 4 is approximately 10 -5 , and with And, with the increase of With the increase of , the outage probability curve of Scheme 4 is very close to that of Scheme 1. However, since the speed variance of the AWACS and the mobile ground station is large at this time, the overall outage performance of the system is poor.

[0305] and Figure 4 (b) Compared with Figure 4 (c) Add a drone relay. Obviously, the additional relay significantly improves the overall interruption performance of the system. When it is less than 2, the interruption probability of Scheme 1 and Scheme 3 is reduced to 10 -11 The outage probability of Scheme 4 is reduced to 10 -8 However, the increase in the number of drones in Scheme 2 does not cause a significant change in the interruption performance. The interruption probability of scheme 1 is stable at 10 -5 The interruption probability of scheme 4 is similar to that when N=3, and is stable at 10 -4 about.

[0306] Figure 5 Display outage probability and It can be observed that The larger the value, the worse the interrupt performance. Figure 4 Same, larger This will result in a large pointing error. The performance analysis of different solutions is as follows: Figure 5 (a). When it exceeds 3, the outage probability curve of Scheme 4 coincides with that of Scheme 1, indicating that Scheme 4 can be used as a feasible alternative to the complex Scheme 1. When it exceeds 6, the outage probability curve of Scheme 3 is consistent with the curves of Schemes 1 and 4, indicating that Scheme 3 can be used as a simpler alternative relay selection mode.

[0307] like Figure 5 As shown in (b), when When the speed variance increases to 10, the speed variance of the AWACS and the mobile ground station increases simultaneously, resulting in a significant deterioration in the interruption performance. As can be seen from the figure, the interruption probability of Scheme 1 and Scheme 2 is the smallest compared to other schemes, about 10 -9 However, the performance of solution 2 decreases as This is different from the response of Scheme 4, which shows the smallest outage probability at the initial moment, but as The interruption performance changes relatively slowly with the increase of -3 Around, with There was no significant increase.

[0308] In addition, if Figure 5 As shown in (c), the outage probability performance of schemes 1, 2, and 4 improves with the increase in the number of relay nodes. However, the outage probability of case 3 remains relatively unchanged compared to when N=3.

[0309] exist Figure 6 In comparison, H UAV The impact of changes in H on the interruption performance of the four relay schemes. It can be seen that as H UAV As H increases, the outage probability of Schemes 1, 2, and 4 increases rapidly and then reaches a stable state. UAV The change in the outage probability is not obvious when the distance is less than 0.5 km. This is because the scheme significantly enhances the outage performance of the second hop by using diversity technology in the link from the UAV relay to the ground station, while the overall end-to-end outage performance of the system is limited by the first hop from the AWACS to the UAV relay. In other words, if the system is required to have an outage probability not exceeding the specified value (10 -10 For example, the drone altitude in options 1 and 3 should be limited to a maximum of 700 meters. The drone altitude in option 4 should not exceed 500 meters, while the drone altitude in option 2 should not exceed 300 meters.

[0310] Figure 7 show The impact of changes on the system average bit error rate performance. The increase in , makes the overall bit error rate performance worse. In addition, it can be seen that When the value is small, The increase of makes the average bit error rate increase significantly. On the contrary, the bit error rates of the three curves are It tends to converge when it is larger. Similarly, hour The increase in bit error rate from 10 -5 Rapidly rise to 10 -1 , however, when Although with With the increase of , the bit error rate still changes, but only shows a slight increase.

[0311] Design Guidelines:

[0312] 1. Using drone relays improves overall system performance. Increasing the number of relays reduces the probability of outages to a certain extent. However, when N > 4, increasing the number of drones has no significant impact on the outage probability. Therefore, for cost-effectiveness, it is recommended that the total number of drone relays in the system should not exceed 4.

[0313] 2. In mobile scenarios, the speed variance of AWACS and mobile ground stations directly impacts the outage and average bit error rate performance of the laser / RF hybrid aviation communication system. Increased speed variance in both the AWACS and mobile ground stations leads to decreased system performance.

[0314] 3. In a multi-UAV relay system, different relay selection modes have different effects on interruption performance. Generally speaking, the end-to-end selection scheme has the best performance, but it requires the most feedback channels and is the most complex. In fact, when Smaller and When is large, a simpler relay-destination selection scheme can replace the end-to-end selection scheme. Larger and When the value is small, the source-relay selection scheme can replace the end selection scheme. and When both are large, the distributed dual-relay selection scheme can also be regarded as a feasible alternative to the end-to-end selection scheme. The choice of relay scheme depends on the trade-off between scheme complexity and system performance in actual use cases.

[0315] 4. The system end-to-end interruption probability is affected by the deployment altitude of the drone relay. Within the acceptable range of drone flight characteristics, a lower flight altitude will improve the interruption performance. To ensure that the interruption probability is controlled within 10 -5 Within the range, the drone relay flight altitude in Schemes 1 and 3 should not exceed 1km, in Scheme 4 it should not exceed 800m, and in Scheme 2 it should not exceed 500m.

Claims

1. A multi-UAV relay laser / RF aviation communication method based on a mobile platform, characterized in that: The specific steps are as follows: Step 1: System model construction and transmission signal analysis; The multi-UAV relay laser / RF aviation communication system based on mobile platform includes: the early warning aircraft as the source node of information transmission, represented by S; the mobile ground station as the destination node, represented by D; N parallel UAV relays, represented by R i ,i=1,2,…N, where N is the number of drone relays; the drone divides the link into two hops; the first hop is the AWACS-drone relay i link, denoted as SR i The second hop is the drone relay i-ground station link, denoted as R i D. Under complex atmospheric conditions, the system adopts a laser / RF hybrid transmission scheme, in which the laser link is used as the main link. When the laser link cannot meet the signal-to-noise ratio requirements, the RF backup link is activated. Assuming that the AWACS maintains a constant cruising altitude H AWACS , all drones have the same height H UAV and elevation angle ξ UAV , the elevation angle of the ground station is ξ GS ; (1) Laser link The instantaneous received signal-to-noise ratio of the laser link at the UAV relay i is expressed as: Where, is the average signal-to-noise ratio of the source node to the relay laser link, is the average transmission optical power of the source node, η is the detector response, is the channel coefficient of the first hop, is the variance of the additive white Gaussian noise signal; The UAV relay i adopts the decoding and forwarding mode, so that the instantaneous receiving signal-to-noise ratio of the destination node is expressed as: Where, is the average transmission optical power of the relay, represents the second hop channel coefficient, is the average signal-to-noise ratio of the laser link from the relay to the destination node; (2) RF link When using RF link transmission, the instantaneous received signal-to-noise ratio at drone relay i is expressed as: in, is the average signal-to-noise ratio of the radio frequency link from the source node to the relay node, is the radio frequency power transmitted by the source node; the radio frequency channel coefficient of the first hop is , represents the path loss of the first hop, is the variance of the Gaussian white noise signal; the instantaneous signal-to-noise ratio expression of the radio frequency link from relay node i to destination node is: Where, is the average signal-to-noise ratio of the radio frequency link from the relay node to the destination node, is the average RF signal transmission power of the relay, and denote the channel coefficient and path loss of the second hop respectively; Step 2: Select relay solution; The AWACS selects a node with the best channel quality from among multiple UAV nodes as a relay based on the feedback information from the channel state feedback channel in the system. Four different relay selection modes are available: end-to-end selection, source-relay selection, relay-destination selection, and distributed dual-relay selection. 1) End-to-end selection solution According to SR i and R i The channel state feedback of the two-hop link D is used to select the best relay based on the signal-to-noise ratio of the channel feedback; the end-to-end signal-to-noise ratio of the i-th link is is the first-hop signal-to-noise ratio of the i-th link, is the second-hop signal-to-noise ratio of the i-th link; the optimal relay I1 is the relay that maximizes the end-to-end signal-to-noise ratio, expressed as: Where I1∈{1,2…,N} represents the best relay in Scheme 1. i and R i D. Feedback channels are required in both hops of the link. This solution is highly complex. 2) Source-Relay Selection Scheme Relay selection is based on the first hop SR i The channel quality is selected, and the drone relay node with the highest first-hop signal-to-noise ratio is selected as the relay. At this time, the best relay I2 is the relay that maximizes the signal-to-noise ratio from the source to the relay node, which is expressed as: Among them, I2∈{1,2…,N} is the best relay in scheme 2, and the selected relay I2 is used for the second-hop communication; in scheme 2, only the first hop requires a feedback channel; 3) Relay-destination selection scheme This scheme is based on the second hop R i The relay is selected based on the channel quality of D, and the drone node with the highest second-hop signal-to-noise ratio is selected as the relay. At this time, the best relay I3 is the relay that maximizes the signal-to-noise ratio from the relay node to the destination node, which is expressed as: Where I3∈{1,2…,N} is the best relay in scheme 3, and the first hop uses the selected relay I3 for communication; in this scheme, only the second hop requires a feedback channel; 4) Distributed dual relay selection scheme The relay nodes are divided into N a and N b Two parts and N a +N b = N; source node and N a relay nodes have feedback channels, the destination node and N b The relay nodes have feedback channels; according to the received feedback information, the source node a Select a relay with the highest instantaneous signal-to-noise ratio among the relays; the destination node is N b Select a relay with the highest instantaneous signal-to-noise ratio among the relay nodes, which is expressed as: Among them I a ∈{1,2…,N a } is the best relay selected by the source node, I b ∈{1,2…,N b The best relay selected by the destination node is the best relay. During signal transmission, the two selected relays are activated simultaneously, and the two links cooperate to transmit information. After reaching the destination node, the signal is received using a selection combination technique. This solution does not require an end-to-end feedback link, and the number of feedback channels is significantly reduced. Step 3: Channel modeling; The channel model of each hop transmission is constructed, including the channel model construction of the AWACS-UAV relay and UAV relay-mobile ground station based on laser transmission, the channel model construction of the AWACS-UAV relay and UAV relay-mobile ground station based on RF transmission, and the subscript j∈{SR i ,R i D} denotes the links from AWACS to UAV relay and from UAV relay to mobile ground station respectively; (i) Laser channel The two hops from the AWACS to the UAV relay and from the UAV relay to the mobile ground station occur within the troposphere, so it is reasonable to assume that the two hops are affected by the same atmospheric conditions; (a) Atmospheric attenuation Atmospheric attenuation Due to scattering and absorption by particles in the atmosphere, the propagation of the light beam is affected by power loss. Atmospheric attenuation is expressed as: in, and SR i and R i D is the distance of the link; ω is the atmospheric attenuation coefficient; (b) Atmospheric turbulence The weak to strong turbulence model is characterized by the Gamma-Gamma distribution, atmospheric turbulence The probability density function of is expressed as: Where Γ(·) is the Gamma function, K v (·) is the modified Bessel function of the second kind, and the subscript v represents α j -β j ; α j represents the large-scale fading parameter, β j represents the small-scale fading parameter; Γ(α j ), Γ(β j ) represent α j and β j The corresponding Gamma function value; middle, The whole is The coefficient of (c) Pointing error AWACS-UAV relay link: The combined radial displacement vector from the center of the UAV detector to the center of the beam footprint at the UAV receiver aperture is expressed as where r S =[x s ,y s ] is the displacement vector of the early warning aircraft, x s ,y s r S The vector components on the x-axis and y-axis; r R =[x R ,y R ] is the displacement vector of the UAV, x R ,y R r R The vector components on the x-axis and y-axis; this fluctuation caused by a large number of random events obeys the normal distribution, and the component of the combined radial displacement vector on the x-axis The mean is 0 and the variance is The normal distribution of Combined radial displacement vector component on the y-axis The mean is 0 and the variance is The normal distribution of The position deviation of the AWACS is caused by a sudden change in its speed, which is recorded as The speed change component v of the AWACS on the x-axis and y-axis Sx and v Sy Normal distribution with mean zero is the speed variance of the AWACS; assuming that the speed of the AWACS does not change much in a very short time interval Δt, the displacement distance is expressed as x S =v Sx Δt / 2 and y S =v Sy Δt / 2; r R =[x R ,y R ] Position fluctuation component x on the x-axis and y-axis R and y R They have mean zero and variance Normal distribution and has a mean of zero and a variance of Normal distribution The variance of the displacement vector of the combined radial displacement on the x-axis and y-axis and Expressed as: UAV relay-mobile ground station link: The combined radial displacement vector from the center of the mobile ground station detector to the center of the beam footprint at the ground station receiver aperture is expressed as The displacement vector of the combined radial displacement on the x-axis is The mean is 0 and the variance is The normal distribution of The displacement vector y of the combined radial displacement on the y-axis RiD The mean is 0 and the variance is The normal distribution of r θ =[x θx ,x θy ] is the displacement vector caused by the direction fluctuation of the hovering drone. Assume that the shaking angle θ of the drone on the x-axis x and the jitter angle θ on the y-axis y is small enough, then the displacement vector on the x-axis Displacement vector on the y-axis Among them L RD is the launch distance, the jitter angles on the x-axis and y-axis have a mean of 0 and a variance of The normal distribution of r D =[x D ,y D ] is the displacement vector of the mobile ground station, x D ,y D r D Vector components on the x-axis and y-axis; the position deviation of a mobile ground station with unsteady velocity is caused by a sudden change in its velocity, which is denoted by v D =[v Dx ,v Dy ], its velocity change component v on the x-axis and y-axis Dx and v Dy Normal distribution is the velocity variance of the ground station, and the displacement distance on the x-axis and y-axis within Δt is expressed as x D =v Dx Δt / 2 and y D =v Dy Δt / 2; therefore, the variance of the displacement vectors of the combined radial displacement on the x-axis and y-axis is and Expressed as: Pointing error The probability density function of is expressed as: Where A 0,j =[erf(v j )] 2 is the fraction of the light power collected when the difference between the center of the light spot and the center of the detector is zero, erf(·) is the error function, is the distance L j The aperture radius a and beam width ω z,j Pointing error coefficient in is the equivalent beamwidth; To correct the jitter standard deviation, the first jump j = SR i , is the corrected jitter standard deviation of the AWACS-UAV relay link; the second hop j = R i D, is the corrected jitter standard deviation of the UAV-mobile ground station link; (d) Angle of arrival jitter When the incident laser has a certain incident angle θ a,j When arriving at the receiving plane, the Airy pattern may exceed the detection range of the detector due to the obvious deviation in direction; arrival angle jitter The probability density function of is expressed as: in, is the UAV jitter angle variance, θ FoV,j is the field of view of the receiver, δ(·) is the Dirac function; (e) Doppler effect The relative motion between the mobile ground station and the UAV relay causes the Doppler frequency shift between the UAV relay and the mobile ground station link, which is expressed as Δf = vf FSO cos(ξ GS ) / c, where v is the relative speed between the UAV and the mobile ground station, f FSO is the optical carrier frequency, c is the speed of light; the UAV relay-mobile ground station link can ignore the influence of the Doppler effect; (f) Overall channel statistical characteristics The coefficients of the laser transmission channel are respectively composed of atmospheric attenuation, atmospheric turbulence, pointing error and arrival angle jitter; the combined channel coefficient is expressed as: Combined channel coefficient h j The probability density function of is expressed as: Where, the combined channel coefficients of attenuation, turbulence, and pointing error are for The probability density function of , according to equations (9), (10), (15), and (16), and substituting equation (17) into equation (18), performs integral operation and obtains: in, is the Meijer-G function, m, n, p, q are non-negative integers representing the number of variables; Combining the relationship between channel coefficient and signal-to-noise ratio in equations (1) and (2), and using h j The signal-to-noise ratio of the laser link between the AWACS and the UAV relay and the laser link between the UAV relay and the mobile ground station is obtained by integrating the probability density function of The cumulative distribution function is: in, is the laser link signal-to-noise ratio threshold; is the probability density function of the signal-to-noise ratio of the AWACS-UAV relay optical link and the UAV relay-mobile ground station optical link; (ii) Radio frequency channel RF channel coefficient I j ,j∈{SR i ,R i D} is modeled using Nakagami-m distribution, whose probability density function is: Where m is the RF fading factor of the Nakagami-m distribution, is the average signal-to-noise ratio of the RF; Γ(m) represents the Gamma function value corresponding to m; combining the relationship between the channel coefficient and the signal-to-noise ratio in equations (3) and (4), the signal-to-noise ratio of the AWACS-UAV relay RF link and the UAV relay-mobile ground station RF link is obtained by integration: The cumulative distribution function of is: Where Γ(α,x) is the incomplete gamma function, and in equation (22) the parameter α = m, and the parameter G j is the path loss, is the signal-to-noise ratio threshold of the radio frequency link; Step 4: Construction of evaluation indicators: Construct dual evaluation indicators of interruption probability and bit error rate; I. Interruption Probability The outage probability is defined as the probability that the link cannot transmit data due to the signal-to-noise ratio falling below a certain threshold. The outage probability is expressed as: P out =Pr(γ SD <γ th )=F γSD (γ th ) (23) Where Pr(·) represents the probability, γ SD represents the system end-to-end signal-to-noise ratio, γ th is the signal-to-noise ratio threshold, F γSD (γ th ) represents γ SD The cumulative distribution function of (A) End-to-end selection scheme interruption probability In scheme 1, the link that UAV relay i relays is the i-th link; the instantaneous signal-to-noise ratio of the end-to-end link of the i-th link is is the first hop signal-to-noise ratio of the i-th link and the second hop signal-to-noise ratio γ of the i-th link RiD The minimum value of According to formula (5), the drone I1 with the best end-to-end signal-to-noise ratio is selected as the relay. At this time, the maximum end-to-end instantaneous signal-to-noise ratio of scheme 1 is: Therefore, the outage probability of scenario 1 is expressed as: Where, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay laser link, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay radio frequency link i, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay i-mobile ground station laser link, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay i-mobile ground station RF link; Substituting equations (20) and (22) into equation (25), we can obtain the outage probability of scheme 1; (B) Outage probability of source-relay selection scheme In scheme 2, the best relay i=I2 is selected based on the first-hop signal-to-noise ratio, as shown in formula (6). The instantaneous signal-to-noise ratio between the AWACS-UAV relay I2 link in scheme 2 is: Scheme 2: Signal-to-noise ratio of the UAV relay I2-mobile ground station link Signal-to-noise ratio of the laser link from the drone relaying I2 to the mobile ground station Signal-to-noise ratio of the RF link from the drone relay I2 to the mobile ground station The maximum value of is expressed as: The end-to-end instantaneous signal-to-noise ratio of solution 2 is: in, When i=I2 The value of The outage probability of scenario 2 is: in, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay I2-mobile ground station laser link, is the cumulative distribution function of the signal-to-noise ratio of the UAV relay I2-mobile ground station RF link; Substitute equations (20) and (22) into equation (29) to calculate the outage probability of scheme 2; (C) Interruption probability of relay-destination selection scheme Scheme 3 selects the best relay i=I3 based on the second-hop signal-to-noise ratio, as shown in Equation (7). The instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 link in Scheme 3 is: Where, is the instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 laser link, is the instantaneous signal-to-noise ratio of the AWACS-UAV relay I3 radio frequency link; the signal-to-noise ratio of the UAV relay I3-mobile ground station link is: The end-to-end instantaneous signal-to-noise ratio of solution 3 is: Therefore, the outage probability of scenario 3 is expressed as: in, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay I3 laser link, is the cumulative distribution function of the signal-to-noise ratio of the AWACS-UAV relay I3 radio frequency link; Substitute equations (20) and (22) into equation (33) to calculate the interruption probability of scheme 3; (D) Distributed Dual-Relay Selection Scheme Interruption Probability In scheme 4, the signal passes through relay i=I a The transmission is called path 1, using drone relay I a Signal-to-noise ratio of the link being relayed for: in, For AWACS-UAV relay I a The instantaneous signal-to-noise ratio, Relay for drones I a - the instantaneous signal-to-noise ratio of the mobile ground station, Relay for drones I a - the instantaneous signal-to-noise ratio of the mobile ground station laser link, Relay for drones I a -Instantaneous signal-to-noise ratio of the mobile ground station radio frequency link; The signal passes through relay i=I b The transmission is called path 2, using drone relay I b Signal-to-noise ratio of the link being relayed Expressed as: in, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio of the laser link, For AWACS-UAV relay I b The instantaneous signal-to-noise ratio of the RF link, Relay for drones I b -Instantaneous signal-to-noise ratio of the mobile ground station; When two signals arrive at the mobile ground station and the receiver uses selective combining technology, the end-to-end instantaneous signal-to-noise ratio of Scheme 4 is: Therefore, the outage probability expression of scheme 4 is: in, Relay for drones I a - Cumulative distribution function of the signal-to-noise ratio of the mobile ground station laser link, Relay for drones I a - the cumulative distribution function of the signal-to-noise ratio of the RF link of the mobile ground station S, For AWACS-UAV relay I b Cumulative distribution function of the laser link signal-to-noise ratio, For AWACS-UAV relay I b Cumulative distribution function of the RF link signal-to-noise ratio,Substitute equations (20) and (22) into equation (37) to calculate the outage probability of scheme 4; II. Average Bit Error Rate The average bit error rate of the laser link is: The closed-form expression for the average bit error rate of the RF link is: in, Indicates the RF signal-to-noise ratio m-1 power; when binary modulation is used, coefficient A = 1, coefficient B = 1; when multi-base modulation is used, coefficient A = 2 / log2M, coefficient B = sin(π / M); The average bit error rate of the parallel laser / RF link is: in, is the probability of using a laser link to transmit information, is the probability of using the RF link, the link selection probability can be expressed as: In the parallel UAV relay system, when the states of each path are independently distributed, the average bit error rate of the first and second hops of the system is B SR and B RD , which is equal to the average bit error rate of a single path, expressed as and and are the average bit error rates of the first-hop single path and the second-hop single path, respectively. In this case, the average bit error rates of the four relay modes are the same. Considering the system as a serial two-hop system with decode-and-forward relay, its end-to-end average bit error rate is expressed as: Substituting equations (38), (39), (40), and (41) into (42) yields the end-to-end average bit error rate of the system.

2. The mobile platform-based multi-UAV relay laser / RF aviation communication method according to claim 1, characterized in that: The method further comprises step five, simulation results; The simulation parameters are shown in Table 1; Table 1 Simulation parameter settings Assume that all UAV relays experience the same atmospheric conditions and P f,j =P r,j =P t , P t is the signal transmission power.

3. The mobile platform-based multi-UAV relay laser / RF aviation communication method according to claim 1, characterized in that: The total number of drone relays shall not exceed 4.

4. The mobile platform-based multi-UAV relay laser / RF aviation communication method according to claim 1, characterized in that: In the multi-UAV relay system, the performance of the end-to-end selection scheme is the best; when Smaller and When the value is large, use solution 2-4 to replace the end-to-end solution; Larger and When the value is small, the source-relay selection scheme is adopted; when and When both are large, a distributed dual-relay selection scheme is adopted.

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