Performance evaluation method of unmanned aerial vehicle assisted millimeter wave communication network

Abstract

The invention relates to a modeling and performance analysis method for an unmanned aerial vehicle assisted millimeter wave communication network. According to the method, the modeling method of the unmanned aerial vehicles in the emergency communication network is optimized by introducing a Maren hardcore point process, external interference in the emergency network is fully isolated, and the minimum safety distance between the unmanned aerial vehicles is ensured. Meanwhile, each unmanned aerial vehicle is provided with a millimeter wave antenna capable of adjusting the beam width and the radiation direction, so that the signal strength in a specific direction is enhanced, and the signal coverage efficiency and the communication quality are improved. The invention further provides a closed expression of the coverage probability under the Maren hardcore point process distribution, and a theoretical basis is provided for performance analysis of the unmanned aerial vehicle assisted millimeter wave communication network. Through the method, the signal coverage efficiency and the communication quality of the unmanned aerial vehicle in the emergency communication network are improved, scientific decision support is provided for unmanned aerial vehicle assisted millimeter wave communication network performance modeling and analysis, and the method has important practical application value and theoretical significance.

Description

Technical Field

[0001] The present invention belongs to the field of auxiliary emergency communication, and specifically relates to a method for evaluating the performance of an unmanned aerial vehicle (UAV)-assisted millimeter-wave communication network. Background Art

[0002] UAV-assisted communication can quickly respond to disaster sites and provide temporary communication guarantees for affected areas due to its advantages such as high mobility, flexible deployment, and strong line-of-sight. Especially in millimeter-wave (mmWave) emergency communication networks, UAVs can act as relay nodes to effectively expand the network coverage and improve communication quality.

[0003] However, the broadcast characteristic and line-of-sight-dominated air-to-ground channels make UAV-assisted communication networks more vulnerable to interference attacks, posing security challenges. How to ensure its stability and reliability under complex environmental conditions is an urgent problem to be solved. With the rapid development of modern beamwidth tuning technology, recent research has begun to focus on steerable beamwidth directional antennas. Existing research usually adopts an omnidirectional antenna model when modeling UAV-assisted networks. Due to the rapid development of 6G technology and the characteristics of high frequency and short wavelength of millimeter waves, beamforming technology is usually used to improve the signal transmission distance and anti-interference ability. By restricting the antenna beamwidth of UAVs, adjusting their radiation direction and angle to adapt to different environments and applications, the aggregated interference from interfering base stations can be restricted while obtaining a high antenna gain. In recent years, the millimeter-wave band has received particular attention due to the high data rate and bandwidth it can provide, and significant achievements have been made in autonomous driving and near-earth satellites. Compared with traditional UAV-assisted networks, UAV-assisted networks equipped with millimeter-wave antenna arrays have high bandwidth and high data transmission capabilities, can achieve very low network latency, and are a very promising architecture in emergency communication networks.

[0004] Currently, when solving the problems of UAV-assisted millimeter-wave communication network modeling and performance analysis, since UAVs are not in fixed positions and the distance between UAVs and ground users is not constant, stochastic geometry is usually introduced to model and characterize the above characteristics of the network. However, most of the analyses in current literature are based on the Poisson point process (PPP) or the binomial point process (BPP), without considering the mobility of UAVs and their mutual relationships. UAVs need to ensure a minimum safety distance to achieve safe flight, and UAV network deployment also needs to pay attention to the mutual interference caused by over-dense nodes. Summary of the Invention

[0005] The present invention proposes a method for evaluating the performance of a UAV-assisted millimeter-wave communication network, aiming to optimize the accuracy of performance analysis of UAV-assisted millimeter-wave communication networks to improve the coverage efficiency and communication quality of millimeter-wave communication networks.

[0006] The technical solution for achieving the purpose of the present invention is as follows: A method for evaluating the performance of an unmanned aerial vehicle (UAV)-assisted millimeter-wave communication network, including the following aspects:

[0007] Step 1: Model the UAV-assisted millimeter-wave communication network;

[0008] Step 2: Model the signal-to-noise ratio (SNR) of the UAV-assisted millimeter-wave communication network;

[0009] Step 3: Model malicious aerial interference;

[0010] Step 4: Calculate the coverage probability index of the UAV-assisted millimeter-wave network;

[0011] Step 5: Calculate the capacity index of the UAV-assisted millimeter-wave network.

[0012] Preferably, the specific method for modeling the UAV-assisted millimeter-wave communication network is as follows:

[0013] Step 1.1: Scenario modeling:

[0014] Use a rotary-wing UAV as an aerial base station to assist the ground base station to provide services to ground users, and an aerial jammer is used to interrupt the legitimate communication from the aerial base station to the ground users; the UAV hovers at the same height with a transmit power of P t U The distributions of users and ground base stations both follow a Poisson point process Φp, and the aerial base station is modeled as a Matérn hard-core point process Φ U , and the ground base stations, ground users, and jammers all follow a Poisson point process distribution;

[0015] Step 1.2: Millimeter-wave antenna modeling:

[0016] Each UAV is equipped with a variable beamwidth conical antenna model; the ground base station uses a multi-sector antenna, and the antenna radiation direction of the ground base station is vertically directional and horizontally omnidirectional;

[0017] Step 1.3: Channel and element distribution modeling:

[0018] Both the air-to-ground and ground-to-ground channels adopt the Nakagami-m fading model;

[0019] Model the UAV as a Matérn hard-core point process according to the Matérn hard-core point process distribution;

[0020] Step 1.4: Path loss modeling:

[0021] Based on the height of the UAV and the density of ground obstacles, determine the path loss of the air-to-ground channel and the average additional path loss of the air-to-ground channel. Among them, the path loss of the air-to-ground channel is specifically:

[0022]

[0023] where d is the horizontal distance between the user and the UAV, and h U represents the height of the UAV, and η μ and α μ represent the additional path loss and path loss exponent of the LOS and NLOS channels respectively. μ ∈ {L, N}, where μ = L represents the LOS channel and μ = N represents the NLOS channel. and represent the path losses of the air-to-ground LOS and NLOS channels respectively. C and β are the additional path loss and path loss exponent of the ground-to-ground channel;

[0024] The average additional path loss of the air-to-ground channel is specifically:

[0025]

[0026] In the formula, is the probability of establishing a LOS connection when the horizontal distance between the user and the serving aerial base station is d.

[0027] Preferably, the signal-to-noise ratio of the UAV-assisted millimeter-wave communication network is modeled, specifically expressed as:

[0028]

[0029] In the formula, represents the cooperative interference from the base station, represents the cooperative interference from all aerial interferers, and G c is the channel gain, represents the directional antenna gain, and D A (ω) represents the maximum directivity of the aerial base station antenna array, and ω is the directivity parameter of the antenna array. represents the radiation efficiency of the antenna array, is the incident angle. The antenna array gain depends on the directivity parameter ω and the radiation angle. The larger ω is, the higher the directivity of the antenna array and the more concentrated the radiation power; μ ∈ {L, N, G} are the transmit powers of the air-to-ground LOS, air-to-ground NLOS, and ground-to-ground channels respectively, and l A (d, h U ) is the attenuation of the air-to-ground channel, and l G (d) is the attenuation of the ground-to-ground channel.

[0030] Preferably, the malicious aerial interference is modeled, specifically expressed as:

[0031]

[0032] In the formula, o represents the user himself / herself, represents the set of all UAVs, represents the set of all ground base stations, represents the set of all airborne jammers, o represents the serving base station, P t represents the transmit power of the airborne base station or the airborne jammer, represents the channel attenuation between the UAV and the user in the air-to-ground channel, d GBS_GU represents the attenuation magnitude between the ground base station and the user in the ground-to-ground channel, represents the transmit power of the jammer, G a_U is the antenna gain of the UAV, G a_J is the antenna gain of the jammer.

[0033] Preferably, the specific formula for calculating the coverage probability of the UAV-assisted millimeter-wave network is:

[0034]

[0035] where, is the distance-based coverage probability, refers to the power-based association probability under the condition that the serving base station is a UAV or a ground base station.

[0036] Preferably, the distance-based coverage probability includes the system average coverage probability of the air-to-ground channel from the nearest UAV to the line-of-sight and non-line-of-sight channels

[0037]

[0038] In the formula, ε N = 1 - ε L is the probability that a specific user is located in the non-line-of-sight area, is the probability that a specific user is located in the line-of-sight area, represents the probability that the distance between UAVs is less than the minimum safety distance when a specific user is located in the non-line-of-sight area, represents the probability that the distance between UAVs is greater than or equal to the minimum safety distance when a specific user is located in the non-line-of-sight area, represents the coverage probability of users located in the line-of-sight and area, specifically:

[0039]

[0040] In the formula, r is the actual distance between UAVs, ε L represents the probability that a specific user is located in the line-of-sight area;

[0041] and The coverage probability for users in the non-line-of-sight area is specifically as follows:

[0042] When r L ≤ r ≤ δ / 2, the coverage probability for users in the non-line-of-sight area is:

[0043]

[0044] In the formula, r L is the radius of the area that can be covered by the UAV node, r is the distance between UAV nodes, and δ represents the preset minimum safety distance between UAVs under the Matérn hard-core point process distribution. represents the probability that the distance between UAVs is less than the minimum safety distance when a specific user is in the non-line-of-sight area;

[0045] When r > δ / 2, the coverage probability for users in the non-line-of-sight area is:

[0046]

[0047] In the formula, δ represents the preset minimum safety distance between UAVs under the Matérn hard-core point process distribution. represents the probability that the distance between UAVs is greater than the minimum safety distance when a specific user is in the non-line-of-sight area, r is the distance between UAV nodes, and f M2 (r) is the probability density function of the distribution when the distance between UAVs is greater than the minimum safety distance when the user is in the non-line-of-sight area under the Matérn hard-core point process model;

[0048]

[0049] In the formula, respectively represent the received power from the non-line-of-sight air-to-ground, line-of-sight air-to-ground, and ground-to-ground three channels, r N , r L , r G are respectively the distances between the serving base station and the user under the three channel conditions. and are respectively the Laplace transforms of the UAV and the aerial jammer. is the distance between the user and its non-line-of-sight serving UAV. is the distance between the user and its ground serving base station.

[0050] Preferably, calculating the UAV-assisted millimeter-wave network capacity metrics includes:

[0051] Calculating the average throughput:

[0052]

[0053] where $\delta\in\{L,N,G\}$ represents the air-to-ground line-of-sight, air-to-ground non-line-of-sight, and ground-to-ground channels respectively, denotes taking the mean, SIR represents the value of the signal-to-interference ratio, and $r$ is the link distance between the ground user and the serving base station; the average ergodic rate:

[0054]

[0055] where is the average ergodic rate, $\delta\in\{L,N,G\}$ represents three channel conditions, $r$ is the specific link length between the user and its serving base station, and $E[\cdot]$ is the average of the received signal-to-noise ratio distribution and the link length distribution. The average spectral efficiency:

[0056]

[0057] where $\lambda$ m is the node density under the Matérn hard-core point process, and $\lambda$ p is the node density under the Poisson point process, is the data rate under the air-to-ground non-line-of-sight channel, is the data rate under the air-to-ground line-of-sight channel, is the data rate under the ground-to-ground channel.

[0058] Compared with the prior art, the significant advantages of the present invention are:

[0059] (1) The Matérn hard-core point process and the Poisson point process are used to model the distributions of UAVs and ground base stations respectively. To approximately derive the expressions for the coverage probability and network capacity in the UAV-assisted millimeter-wave network, stochastic geometry is considered an effective method. The present invention models the UAV network through the repulsive point process, taking into account the minimum distance constraint between UAVs and isolating the interference between UAVs. In addition, the closed-form expressions for the coverage probability and network capacity typicality metrics of the UAV-assisted millimeter-wave communication network are derived.

[0060] (2) The millimeter-wave antenna array with variable beam width and direction is used to model the UAV antenna configuration. The present invention considers a more realistic angle-dependent millimeter-wave antenna array to simulate the three-dimensional antenna beamforming gain in the millimeter-wave link between the base station and the user to meet the requirements of actual dense or sparse user distributions. Experiments show that by dynamically adjusting the antenna direction factor $\omega$, the coverage probability and capacity of the millimeter-wave network can be significantly improved. In addition, the Nakagami-$m$ model is used to characterize the small-scale fading, and by flexibly adjusting the parameter $m$, the influence of obstacles such as urban buildings and natural terrain can be more accurately simulated;

[0061] (3) An innovative method for measuring the coverage probability of a millimeter-wave mobile network is proposed based on the blocking effect of millimeter waves. Specifically, the coverage probability fully considers the weighted sum of the distance between the base station and the user under three channel conditions and the association probability based on the received power of a specific user, making the trade-off of millimeter-wave network performance more reasonable and accurate.

[0062] The present invention will be further described in detail below with reference to the accompanying drawings. Description of the Drawings

[0063] Figure 1 Schematic diagram of an unmanned aerial vehicle (UAV)-assisted millimeter-wave network model with external interference.

[0064] Figure 2 Schematic diagram of the interaction of UAVs following a Matérn hard-core point process distribution.

[0065] Figure 3 Schematic diagram of the method for selecting service base stations in a UAV-assisted millimeter-wave communication network. Detailed Implementation Manner

[0066] A performance evaluation method for a UAV-assisted millimeter-wave communication network, with the specific concept being:

[0067] (1) Use the Matérn hard-core point process and the Poisson point process to model the distribution of UAVs and ground base stations respectively;

[0068] (2) Use a millimeter-wave antenna array with variable beam width and direction to model the UAV antenna configuration;

[0069] (3) Use the stochastic geometry method to derive the closed-form expressions of the coverage probability and the typicality index of the network capacity of the UAV-assisted millimeter-wave communication network, so as to accurately evaluate the coverage probability and capacity of the UAV-assisted millimeter-wave network.

[0070] The specific steps of the present invention are as follows:

[0071] Step 1: Model each element of the UAV-assisted millimeter-wave communication network.

[0072] Step 1.1: Scene modeling.

[0073] Consider a three-dimensional UAV-assisted millimeter-wave emergency communication network with active aerial interference. The rotor UAV acts as an aerial base station to assist the ground base station in providing services to ground users, and the aerial jammer attempts to interrupt the legitimate communication from the base station to the user. Assume that the UAV has a transmission power of P t UHover at the same height. The distributions of users and ground base stations both follow a Poisson point process (denoted as PPP Φp), with the density represented as λp. The UAVs are equipped with millimeter-wave directional antennas to improve network communication efficiency and isolate interference. Considering the minimum distance constraint between UAVs, the aerial base stations are modeled as a Matérn hard-core point process Φ U , with a density of λ U , and a height of h u . The ground base stations, ground users, and interferers all follow a Poisson point process distribution. R cov is the coverage radius of the UAV antenna, d = h U / tanθ is the horizontal distance between the UAV and the ground user, is the pitch angle, and r represents the Euclidean distance between the typical user and the serving UAV.

[0074] Step 1.2: Millimeter-wave antenna modeling.

[0075] To improve network coverage performance and reduce mutual interference, each UAV is equipped with a variable beamwidth conical antenna model to enhance the signal strength in a specific direction. The gain of the millimeter-wave antenna array can be expressed as:

[0076]

[0077] where, represents the maximum directivity of the UAV antenna array, ω is the directivity parameter of the antenna array, represents the radiation efficiency of the antenna array, represents the incident angle. The array gain depends on the directivity parameter ω and the radiation angle, and is symmetric along the vertical direction. The beam solid angle Ω A (ω) of the antenna array can be expressed as where U ω (ρ) = cos(ρ) / ω represents the normalized radiation intensity of the antenna array under the UAV. Therefore, it can be observed that a larger ω results in a higher directivity of the antenna array, corresponding to a smaller half-power beamwidth. Thus, it allows the radiation power to be focused in a smaller area. For simplicity, the influence of the UAV body on the antenna pattern and radio propagation is ignored here.

[0078] In fact, the antennas of ground base stations usually tilt downward to cover more users. Therefore, multi-sector antennas are used to optimize the radiation range of ground base stations, and it is assumed that the radiation direction of the antennas of ground base stations is vertically directional and horizontally omnidirectional.

[0079] Step 1.3: Channel and element distribution modeling.

[0080] Both the air-to-ground and ground-to-ground channels are described by the Nakagami-m fading model to account for small-scale fading effects. The Nakagami-m fading covers various fading scenarios in realistic wireless applications through the parameter m, which includes Rayleigh fading (m = 1) as a special case. Thus, the channel gain G c is a gamma random variable with the distribution given by:

[0081]

[0082] where denote the Nakagami-m fading parameters for the air-to-ground line-of-sight, air-to-ground non-line-of-sight, and ground-to-ground channels, respectively. Thus, the received power of a specific user from the corresponding ground base station and UAV can be expressed as:

[0083]

[0084] where μ ∈ {L, N} represents the line-of-sight or non-line-of-sight channel, r is the propagation distance between the user and the serving base station, and are the transmit powers of the UAV and the ground base station, respectively.

[0085] For ease of processing, most studies model the distribution of UAVs as a Poisson point process or a binomial point process (BPP). In the present invention, the UAVs are modeled as a Matérn hard-core point process according to the Matérn hard-core point process distribution, which is represented by Φm and density λu. In the case of the Poisson point process, for the parent Poisson point process, λp is the density, and thus the probability that R > r equals the zero probability of the PPP can be given by:

[0086] F G (r) = 1 - exp{-λ p πr 2}

[0087] Thus, the probability density function (PDF) can be obtained as follows:

[0088]

[0089] where the Matérn hard-core point process type II can be obtained by assigning a random label uniformly distributed in [0, 1] to each parent of Φp. Thus, the UAV density of the Matérn hard-core point process distribution can be derived as:

[0090]

[0091] However, for a network modeled using the Matérn hard-core point process, there is currently no known closed-form expression for the PDF of the nearest distance r between two nodes. Due to the repulsive property within the points of the Matérn hard-core point process, the calculation of interference is also very cumbersome. In the present invention, a simple approximate expression is derived. Specifically, the distribution of the Matérn hard-core point process is approximated by the interference-to-signal ratio (ISR) distribution of the PPP, and using the ISR-based gain method, it is given by:

[0092]

[0093] where, when the nodes follow the Matérn hard-core point process distribution, denotes the average interference-to-signal ratio, and G m denotes the average interference-to-signal ratio gain.

[0094] Since the UAVs are deployed according to the Matérn hard-core point process, if the distance between a specific user and the serving base station is r, there is no interfering base station closer to the specific user. The probability density function of r is the potential spatial distribution of the blank space in the Matérn hard-core point process. Using Campbell's theorem, the probability density function (PDF) and cumulative distribution function (CDF) under the Matérn hard-core point process model based on the approximate distance can be approximated as:

[0095]

[0096] where, r is the distance between a specific user and the serving base station, λ m denotes the UAV density based on the Matérn hard-core point process, β is a positive real parameter, and δ is the minimum safety distance between UAVs.

[0097] Step 1.4: Path loss modeling:

[0098] For the UAV millimeter-wave air-to-ground channel, the blockage of the signal needs to consider the height of the UAV and the density of ground obstacles. In the blockage effect modeling, is the probability of establishing a line-of-sight connection when the horizontal distance between the user and the serving aerial base station is d, a and b are environmental factors. At the same time, different path losses are caused by the blockage effect for the line-of-sight and non-line-of-sight channels, so the path loss formula for the air-to-ground channel is:

[0099]

[0100] where, d is the horizontal distance between a specific user and the UAV, h represents the height of the UAV, η μ and α μ (μ ∈ {L, N}) respectively represent the additional path loss and path loss exponent for the line-of-sight and non-line-of-sight channels, and represent the path losses of the air-to-ground LOS and NLOS channels respectively, where η and α represent the path loss and path loss exponent, and their subscripts distinguish LOS and NLOS propagation (denoted by subscripts L and N respectively). The ground-to-ground channel is modeled as e G (d)=C -1 d -β , where C and β are the additional path loss and path loss exponent of the ground-to-ground channel. Therefore, the average additional path loss of the air-to-ground channel is:

[0101]

[0102] Millimeter-wave communication usually requires an antenna array to obtain an ideal antenna gain and overcome the severe path loss experienced at high frequencies. A three-dimensional millimeter-wave antenna model is used to model the aerial base station and the jammer.

[0103] The probabilities of the LOS and NLOS channels maintaining connectivity are represented by and A N (r)=1 - A L (r), where a and b are environment-related parameters, and θ = arctan(h / d) is the degree of the elevation angle. For the UAV-assisted millimeter-wave communication network in the present invention, it is not difficult to obtain that the probability that a specific user is located in the LOS region is The probability of being in the NLOS region is ε N =1 - ε L . To avoid strong LOS signal interference between adjacent UAVs, a guaranteed minimum safe distance δ≥2R between UAVs is set L , and further obtain where then

[0104] Step 2: Modeling the signal-to-noise ratio of the UAV-assisted millimeter-wave network.

[0105] Based on the above settings of the UAV-assisted network and its channels and antennas, the signal-to-interference ratio (denoted as SIR) received by a specific ground user from the serving base station can be expressed as:

[0106]

[0107] In the formula, represents the cooperative interference from the base station, represents the cooperative interference from all aerial jammers. Since the UAV system is usually interference-limited, the influence of thermal noise is ignored in this paper.

[0108] Step 3: Modeling malicious aerial interference.

[0109] For a specific ground user, the cumulative interference from other serving base stations except the service drone and the malicious interference from the airborne jammer can be respectively expressed as:

[0110]

[0111] In the formula, represents the set of all airborne base station nodes, represents the set of all ground base stations, represents the set of all airborne jammers, o represents the serving base station, and P t represents the transmit power of the airborne base station or the airborne jammer.

[0112] Step 4: Calculate the related indicators of the coverage probability of the drone-assisted millimeter-wave network.

[0113] Using stochastic geometry tools, the connectivity rate of the drone-assisted millimeter-wave communication network is defined as the probability that the signal-to-noise ratio is greater than a certain threshold, that is, the coverage rate is the complementary cumulative distribution function of the threshold Θ. Therefore, the connectivity probability of the drone-assisted millimeter-wave communication network can be expressed as the probability that the network signal-to-noise ratio is greater than a certain threshold, which can be expressed by the mathematical formula as

[0114] Step 4.1: Coverage rate based on distance

[0115] For the ground-to-ground channel, under the Nakagami-m fading assumption, the coverage probability can be calculated as

[0116]

[0117] In the air-to-ground channel, the distribution of drones as airborne base stations in the drone-assisted millimeter-wave communication network satisfies the Matérn hardcore point process. Therefore, the system average coverage probability of the air-to-ground channel from the nearest drone to the line-of-sight and non-line-of-sight channels can be expressed as:

[0118]

[0119] Among them, and represent the coverage probabilities of specific users located in the line-of-sight and non-line-of-sight regions, and their formula derivations are as follows.

[0120] Step 4.1.1: When r ≤ r L , the air-to-ground channel corresponds to the line-of-sight network, and the coverage probability can be derived as:

[0121]

[0122] Among them, (a) follows the small-scale fading Gc ~exp(1), (b) follows the independence of the ground base station, line-of-sight UAV, and non-line-of-sight UAV interference. Laplace transform and The expression is as follows.

[0123]

[0124]

[0125] Step 4.1.2: When r L ≤ r ≤ δ / 2, the air-to-ground channel corresponds to a non-line-of-sight network, so the coverage probability under this condition can be further obtained as follows:

[0126]

[0127] Step 4.1.3: When r > δ / 2, the air-to-ground channel also depends on the non-line-of-sight channel, but the coverage area becomes irregular and difficult to analyze by traditional methods. Therefore, using the probability distribution function of the distance r derived from the Poisson point process model for approximate calculation, we can obtain:

[0128]

[0129] where represents the total interference in the network. In step (a), the signal-to-interference ratio gain of the Matérn hard-core point process distribution is approximately expressed using the Poisson point process distribution based on the signal-to-interference ratio gain method, where Θ * = MISR m = Θ / G m is substituted. In an interference-limited network, the coverage probability is equivalent to the complementary cumulative distribution function of the signal-to-interference ratio. By adjusting the signal-to-interference ratio threshold of the corresponding network through the Poisson point process distribution model with the same density, the network coverage probability based on the Matérn hard-core point process can be approximately obtained. Therefore, by approximately calculating the signal-to-interference ratio distribution of the Matérn hard-core point process using the signal-to-interference ratio distribution of the Poisson point process, the signal-to-interference ratio gain G m of the air-to-ground network modeled by the Matérn hard-core point process is

[0130] In the above formula represents the average signal-to-interference ratio. The average signal-to-interference ratio of the UAV-assisted network following the Poisson point process distribution is MISR p = 2 / (α N - 2), and the average signal-to-interference ratio under the Matérn hard-core point process distribution can be approximately expressed as MISR MHCPP (δ) = ae bδ, where a and b are fitting correlation coefficients. Considering the characteristics of the Matérn hard-core point process distribution, for the air-to-ground channel, the minimum safety distance between aerial base stations is set to δ≥2R cov , R cov =h U / tanθ is the coverage radius of the line-of-sight of the aerial base station.

[0131] Research shows that by adjusting the signal-to-interference ratio threshold of the corresponding network through the Poisson point process model with the same density, the network coverage probability based on the non-Poisson point process model can be approximately obtained. Therefore, this method is used to offset the signal-to-interference ratio threshold. In step (b), set σ = 1dB. Compared with the Poisson point process, the additional interference of the network modeled by the Matérn hard-core point process type II never exceeds 1dB.

[0132] Therefore, the coverage probability of the line-of-sight channel UAV can be further expressed as:

[0133]

[0134] The coverage probability of the non-line-of-sight channel UAV can be expressed as:

[0135]

[0136] Use That is, the probability density function of the distance r derived from the Poisson point process model is used to approximately calculate the second integral of the above formula, and further use To adjust The deviation brought.

[0137] Among them, Represents the transmit power of the ground base station, T -1 r -β Represents the path loss function of the ground-to-ground channel, f G (r) is the probability distribution function of the distance between the user and the serving base station based on the Poisson point process distribution. (a) follows the small-scale fading G c ~exp(1), (b) follows the independence of the interference of the ground base station, line-of-sight UAV, and non-line-of-sight UAV.

[0138] Step 4.2: Power-based connectivity probability.

[0139] Due to the sensitivity of the millimeter-wave network to obstacles, when a specific user selects a serving base station, not only the signal coverage range but also the received power of the specific user after channel attenuation needs to be considered.

[0140] According to the received power of the user, the probability that the user connects to the non-line-of-sight UAV can be expressed as:

[0141]

[0142] Among them respectively represent the received power from three channels: non-line-of-sight air-to-ground, line-of-sight air-to-ground, and ground-to-ground. r N , r L , r G are respectively the distances between the serving base station and the user under three channel conditions. (a) reflects the independent distribution of the two-point process, and (b) is based on the fact that the incident angle is When the antenna direction factor is ω, the channel gain is of the fact. (c) is based on the definition of the probability distribution function and the average value of the non-line-of-sight air-to-ground distance r N .

[0143] For simplicity is used to represent the distance between the user and the nearest line-of-sight UAV (or ground base station) other than the serving base station. The distance between the user and its non-line-of-sight serving base station is r. Its matrix can be expressed as follows:

[0144]

[0145] Similarly, it can be concluded that the power-based probability of the line-of-sight UAV and the ground base station can be given by the following formula:

[0146]

[0147] Therefore, the coverage probability of the UAV-assisted millimeter-wave communication network can be expressed as the weighted sum of the coverage probabilities under three channel conditions: air-to-ground line-of-sight, air-to-ground non-line-of-sight, and ground-to-ground, while considering the signal coverage range and the received power of a specific user. Mathematically, it is expressed as:

[0148]

[0149] Among them, is the distance-based coverage probability in the above text, refers to the power-based association probability under the condition that the serving base station is a UAV or a ground base station, and its specific expression has been given in the derivation process.

[0150] Step 5: According to the network signal-to-interference ratio and other modeling contents in Step 4, the network capacity-related indicators of the UAV-assisted millimeter-wave communication network can be further evaluated. In this patent, three indicators, namely the network average throughput, average spectral efficiency, and average ergodic rate, are selected as typical indicators for modeling and derivation to complete the performance evaluation of the UAV-assisted millimeter-wave communication network.

[0151] The channel capacity quantifies the performance based on the average raw throughput, while the coverage probability focuses on outcomes such as the connection failures of ground users and other impacts related to the quality of service and link reliability. Therefore, they are complementary perspectives for evaluating the link quality between the base stations and ground users in a UAV-assisted network. The analysis of network capacity metrics is based on network throughput, which is the highest bit rate that a specific ground user can obtain from the network. The throughput of a specific ground user can be derived from the Shannon formula and is expressed as:

[0152]

[0153] Model the following typical performance metrics of the UAV-assisted millimeter-wave communication network capacity:

[0154] Step 5.1: Average Throughput (ATH)

[0155] The average throughput of the UAV-assisted millimeter-wave communication network can be expressed as:

[0156]

[0157] In the above formula, μ ∈ {L, N, G} respectively represent the air-to-ground line-of-sight, air-to-ground non-line-of-sight, and ground-to-ground channels. represents taking the mean, SIR represents the signal-to-interference ratio, and r is the link distance between the ground user and the serving base station.

[0158] Step 5.2: Average Ergodic Rate (AER)

[0159] When a specific user is associated with its serving base station, the average ergodic rate can be expressed as:

[0160]

[0161] Among them, δ ∈ {L, N, G} represents three channel situations, r is the specific link length between the user and its serving base station, and E[·] is the average of the received signal-to-noise ratio distribution and the link length distribution.

[0162] Therefore, the specific expression of the average ergodic rate can be calculated as follows.

[0163] First, consider the case where a specific mobile user is associated with a line-of-sight UAV. In this case, the power-based formula for the average ergodic rate of the line-of-sight is:

[0164]

[0165] Where when X > 0 Therefore:

[0166]

[0167] In the above formula, the Laplace transform has been given above, du represents the integral of the signal-to-interference ratio, and further, the average ergodic rate of the network under the conditions of air-to-ground line-of-sight, air-to-ground non-line-of-sight, and ground-to-ground channels can be derived, which are represented by and respectively. Define as the average ergodic rate of a specific ground user, where and represent the average ergodic rates of the air-to-ground and ground-to-ground channels respectively. Through derivation, the average ergodic rate of a typical ground user associated with the server's ground base station from the ground-to-ground channel is expressed as:

[0168]

[0169] In the above formula, is the interference value of the air-to-ground line-of-sight and ground-to-ground channels, is the Laplace transform, is the transmit power of the ground-to-ground channel.

[0170] The average ergodic rate of a typical

[0171] ground user associated with the server's ground base station from the air-to-ground line-of-sight and air-to-ground non-line-of-sight channels can be derived respectively as:

[0172]

[0173] Step 5.3: Average Spectral Efficiency (ASE)

[0174] The average spectral efficiency refers to the average amount of data or information that the system can transmit under the given spectral resources. It is one of the important indicators to measure the performance of wireless communication systems. A higher average spectral efficiency means that the system can more effectively utilize the limited spectral resources and achieve higher data transmission rates. It is modeled as follows:

[0175]

[0176] where λ m is the point density under the Matern hard-core point process, λ p is the point density under the Poisson point process, is the data rate under the air-to-ground non-line-of-sight channel, is the data rate under the air-to-ground line-of-sight channel, is the data rate under the ground-to-ground channel.

[0177] In the UAV-assisted millimeter-wave communication network, by modeling the average spectral efficiency, it is possible to study how the sharing of spatial spectral resources between the air and the ground affects the overall spectral efficiency of the UAV-assisted millimeter-wave network.

Claims

1. A performance evaluation method for UAV-assisted millimeter wave communication network, including the following aspects: Step 1: Modeling the UAV-assisted millimeter wave communication network; Step 2: Model the signal-to-noise ratio of the UAV-assisted millimeter wave communication network; Step 3: Modeling malicious aerial interference; Step 4: Calculate the UAV-assisted millimeter wave network coverage probability index; Step 5: Calculate the capacity index of the drone-assisted mmWave network.

2. The performance evaluation method of the UAV-assisted millimeter wave communication network according to claim 1 is characterized in that: The specific method for modeling the UAV-assisted millimeter wave communication network is: Step 1.1: Scene Modeling: A rotary-wing UAV is used as an aerial base station to assist the ground base station in providing services to ground users. The aerial jammer is used to interrupt the legitimate communication from the aerial base station to the ground user. The UAV transmits with a power of P t U Hovering at the same height; the distribution of users and ground base stations follows the Poisson point process Φp, and the aerial base station is modeled as the Matérn hard core point process Φ U , ground base stations, ground users and jammers all obey Poisson point process distribution; Step 1.2: Millimeter-wave antenna modeling: Each drone is equipped with a variable beam width conical antenna model; the ground base station uses a multi-sector antenna, and the antenna radiation direction of the ground base station is vertically directional and horizontally omnidirectional; Step 1.3: Channel and element distribution modeling: The Nakagami-m fading model is used for both air-to-ground and ground-to-ground channels; The UAV is modeled as a Matérn hard-core point process according to the Matérn hard-core point process distribution; Step 1.4: Path loss modeling: Based on the altitude of the UAV and the density of ground obstacles, the path loss of the air-to-ground channel and the average additional path loss of the air-to-ground channel are determined. The path loss of the air-to-ground channel is specifically: Where d is the horizontal distance between the user and the drone, h U represents the height of the drone, η μ and α μ They represent the additional path loss and path loss index of line-of-sight and non-line-of-sight channels, μ∈{L,N}, where μ is L for line-of-sight channels and N for non-line-of-sight channels. and denote the path loss of air-to-ground line-of-sight and non-line-of-sight channels respectively, C and β are the additional path loss and path loss index of ground-to-ground channels; The average additional path loss of the air-to-ground channel is: In the formula, is the probability of establishing a line-of-sight connection when the horizontal distance between the user and the serving aerial base station is d, 3. The performance evaluation method of the UAV-assisted millimeter wave communication network according to claim 1 is characterized in that: The signal-to-noise ratio of the UAV-assisted millimeter wave communication network is modeled as follows: In the formula, represents the cooperative interference from the base station, represents the cooperative interference from all airborne jammers, G c is the channel gain, Denotes the directional antenna gain, D A (ω) represents the maximum directivity of the aerial base station antenna array, ω is the directivity parameter of the antenna array, represents the radiation efficiency of the antenna array, is the incident angle. The antenna array gain depends on the directivity parameter ω and the radiation angle. The larger ω is, the higher the directivity of the antenna array and the more concentrated the radiation power. t μ , μ∈{L,N,G} are the transmission powers of air-to-ground line-of-sight, air-to-ground non-line-of-sight, and ground-to-ground channels, respectively. A (d,h U ) is the attenuation of the air-to-ground channel, l G (d) is the ground-to-ground channel attenuation.

4. The performance evaluation method of the UAV-assisted millimeter wave communication network according to claim 1 is characterized in that: Malicious air interference is modeled as follows: In the formula, o represents the user itself, represents the set of all drones, represents the set of all ground base stations, represents the set of all air jammers, o represents the serving base station, P t Indicates the transmission power of the aerial base station or aerial jammer. represents the channel attenuation between the UAV and the user in the air-to-ground channel, d GBS_GU P represents the attenuation between the ground base station and the user in the ground-to-ground channel. t I Indicates the transmit power of the jammer, G a_U is the antenna gain of the UAV, G a_J is the jammer’s antenna gain.

5. The performance evaluation method of the UAV-assisted millimeter wave communication network according to claim 1 is characterized in that: The specific formula for calculating the coverage probability of UAV-assisted millimeter wave network is: in, is the coverage probability based on distance, Refers to the power-based association probability under the condition that the serving base station is a drone or a ground base station.

6. The performance evaluation method of the UAV-assisted millimeter wave communication network according to claim 5 is characterized in that: The distance-based coverage probability includes the system average coverage probability of the air-to-ground channel from the nearest UAV to line-of-sight and non-line-of-sight channels In the formula, ε N =1-ε L is the probability that a specific user is located in the non-line-of-sight area, is the probability that a specific user is in the line-of-sight area, It indicates the probability that the distance between drones is less than the minimum safety distance when a specific user is in the non-line-of-sight area. It represents the probability that the distance between drones is greater than or equal to the minimum safety distance when a specific user is in the non-line-of-sight area. It represents the coverage probability of users in the line of sight and area, specifically: In the formula, r is the actual distance between the UAVs, ε L represents the probability that a specific user is in the line-of-sight area; and is the coverage probability of users in the non-line-of-sight area, which are: When L When ≤r≤δ / 2, the coverage probability of users in the non-line-of-sight area is: In the formula, r L is the radius of the area that can be covered by the drone node, r is the distance between drone nodes, and δ represents the minimum safe distance between drones preset under the Matérn hard core point process distribution. It indicates the probability that the distance between drones is less than the minimum safety distance when a specific user is in the non-line-of-sight area; When r>δ / 2, the coverage probability of users in the non-line-of-sight area is: Where δ represents the minimum safe distance between UAVs preset under the Matérn hard core point process distribution, It represents the probability that the distance between drones is greater than the minimum safety distance when a specific user is in the non-line-of-sight area, r is the distance between drone nodes, is the probability density function of the distribution when the distance between drones is greater than the minimum safety distance when the user is in the non-line-of-sight area under the Matérn hard-core point process model; Where P t N ,P t L ,P t G They represent the received power from non-line-of-sight air-to-ground, line-of-sight air-to-ground, and ground-to-ground channels, respectively. N ,r L ,r G They are the distances between the service base station and the user under three channel conditions. and are the Laplace transforms of the drone and the aerial jammer, is the distance between the user and his non-line-of-sight service drone, is the distance between the user and its ground service base station.

7. The performance evaluation method of the UAV-assisted millimeter wave communication network according to claim 1 is characterized in that: Calculate drone-assisted mmWave network capacity metrics, including: Calculate the average throughput: Where δ∈{L,N,G} represents the air-to-ground line-of-sight, air-to-ground non-line-of-sight, and ground-to-ground channels, respectively. represents the average value, SIR represents the signal-to-interference ratio value, and r is the link distance between the ground user and the server base station; average traversal rate: In the formula, is the average ergodic rate, δ∈{L,N,G} represents three channel conditions, r is the specific link length between the user and its serving base station, and E[·] is the average of the received signal-to-noise ratio distribution and the link length distribution. Average spectral efficiency: In the formula, λ m is the node density under the Matérn hard core process, λ p is the node density under the Poisson point process, is the data rate in the air-to-ground non-line-of-sight channel, is the data rate in the air-to-ground line-of-sight channel, is the data rate in the ground-to-ground channel.

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