A method for analyzing performance of a cellular network under a high-power electromagnetic pulse attack

Abstract

The application discloses a kind of analysis methods of cellular network performance under strong electromagnetic pulse attack, it is related to wireless communication network performance analysis technical field, the network performance analysis method is analyzed to the coverage probability and regional spectrum efficiency of cellular network under strong electromagnetic pulse attack using random geometry theory, consider that strong electromagnetic pulse attack range is limited and part of base station random destruction in attack area;Strong electromagnetic pulse attack under the spatial distribution model of cellular network surviving base station is constructed based on random geometry theory;Define the influence area and influence radius of strong electromagnetic pulse attack;The estimation formula of network coverage probability and regional spectrum efficiency is deduced, the coverage probability and regional spectrum efficiency of cellular network in strong electromagnetic pulse influence area under different base station destruction probability are calculated;The specific influence of base station initial distribution density and strong electromagnetic pulse attack radius to influence radius can be determined, and the specific influence of base station destruction probability to network coverage performance and regional spectrum efficiency.

Description

Technical Field

[0001] This invention relates to the field of wireless communication network performance analysis technology, and in particular to a method for analyzing the performance of cellular networks under strong electromagnetic pulse attacks. Background Technology

[0002] With the rapid development of 5G / 6G technologies and the widespread application of wireless communication networks, the security of network infrastructure has gradually attracted widespread attention. At the same time, attack methods targeting wireless communication are also increasing, especially the development of powerful electromagnetic pulse (EMP) technologies such as high-power electromagnetic pulses (HMPs), which pose a significant potential threat to wireless communication networks. Therefore, studying the impact of powerful EMP attacks on the performance of wireless communication networks is of great significance.

[0003] In recent years, research on the impact of strong electromagnetic pulse (ESP) attacks on wireless communication has mainly focused on the device and module levels, including the nonlinear effects of passive devices, the damage effects of active devices, and the coupling effects of modules. Although research on the impact of ESP attacks on devices and modules is becoming increasingly comprehensive, quantitative analysis of the impact of ESP attacks on network performance remains lacking. Currently, some researchers have begun to focus on the performance analysis of cellular networks in limited areas and post-disaster network performance recovery, using stochastic geometry to analyze network performance indicators such as coverage probability and ergodic rate. However, these studies neither consider the limited range and impact of ESP attacks nor reveal the true impact of ESP attacks on the performance of wireless communication networks.

[0004] This invention, considering the limited radius of a strong electromagnetic pulse (ESP) attack, provides a method for analyzing the performance of cellular networks under an ESP attack based on random geometry, where some base stations within the attack area are randomly damaged. This method clarifies the impact of the attack radius and the initial distribution density of base stations on the radius of influence of the ESP attack, as well as the impact of the base station damage probability on network coverage performance and regional spectral efficiency. Summary of the Invention

[0005] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and provide a method for analyzing the performance of cellular networks under strong electromagnetic pulse (ESP) attacks. This invention addresses the technical problem that most existing research on ESP attacks focuses on the module and device level, neglecting the network performance analysis caused by infrastructure damage from ESP attacks. It clarifies the impact of the attack radius of the ESP and the initial distribution density of base stations on the scope of the attack, as well as the impact of the base station damage probability on the network coverage probability and regional spectral efficiency within the affected area. This provides insights for studying the comprehensive effects of ESP attacks on information networks and for pre-disaster deployment or post-disaster recovery.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for analyzing cellular network performance under strong electromagnetic pulse attacks, proposed according to the present invention, includes:

[0008] Construct a downlink system model of a cellular network under a strong electromagnetic pulse attack based on stochastic geometry;

[0009] Based on the downlink system model of cellular networks under strong electromagnetic pulse attack, the cumulative distribution function of the shortest distance between a typical user and a surviving base station is calculated, and the probability density function of the shortest distance between a typical user and a surviving base station is calculated based on the cumulative distribution function.

[0010] Based on the downlink system model of a cellular network under a strong electromagnetic pulse attack, the signal-to-interference-to-noise ratio of a typical user is calculated.

[0011] Using the probability density function of the closest distance between a typical user and a surviving base station and the signal-to-interference-to-noise ratio of a typical user, the influence radius of a strong electromagnetic pulse attack is defined to describe the affected area.

[0012] Based on the signal-to-noise ratio and influence radius of a typical user in a cellular network under a strong electromagnetic pulse attack, calculate the probability of a typical user being covered and the probability of cellular network coverage within the affected area under a strong electromagnetic pulse attack.

[0013] Based on the signal-to-interference-to-noise ratio, the probability of being covered, and the radius of influence of typical users in a cellular network under a strong electromagnetic pulse attack, the average reachable rate of users within the coverage area and the regional spectral efficiency of the cellular network within the affected area are calculated.

[0014] This invention provides a further optimization scheme for the cellular network performance analysis method under strong electromagnetic pulse attacks.

[0015] The high electromagnetic pulse (HEP) attack is an omnidirectional HEP attack, emitted from the attack origin o, with an attack radius of r. a The attack range is Base stations within the attack range experience random damage, with a damage probability of p(r). BS ), where r BS Let O be the Euclidean distance between the base station and the attack origin. It is a two-dimensional plane;

[0016] The cellular network is a single-antenna isomorphic cellular network. The initial base stations in the cellular network are distributed in a two-dimensional plane using independent homogeneous Poisson point processes. The initial base station distribution density λ O >0, the initial distribution of base stations is denoted as Φ OMobile users are distributed in a two-dimensional plane using a homogeneous Poisson point process independent of the initial base station distribution, with a user distribution density λ. u >0, the distribution of users is denoted as Φ u The association strategy between users and base stations is the nearest base station association strategy; the base station transmits signals with a constant transmit power of 1 / μ, where μ is the reciprocal of the transmit power; the serving base station and users experience Rayleigh fading and standard path loss, with a path loss exponent α>2; the interference power follows a statistical distribution g.

[0017] As a further optimization of the cellular network performance analysis method under a strong electromagnetic pulse attack described in this invention, the downlink system model of the cellular network under a strong electromagnetic pulse attack includes:

[0018] (1) Distribution density λ of surviving base stations in cellular networks under strong electromagnetic pulse attack S :

[0019]

[0020] Where, λ S Let λ be the distribution density of surviving base stations, 1(·) be the indicator function, and λ be the base station density. O r represents the initial distribution density of base stations. a The attack radius of a strong electromagnetic pulse. For the distribution density of surviving base stations with respect to r BS The function;

[0021] (2) x0 is the location of the surviving service base station, Φ S The set of surviving base station locations, at a distance r from the attack origin o. u Typical users from x0∈Φ S The power P(x0) received by the serving base station and the total interference received from all other surviving base stations in the cellular network. for:

[0022]

[0023] Where h~exp(μ) represents the distance r from the attack origin o. u Typical users from x0∈Φ S The useful signal received by a serving base station transmitting a signal at a constant transmit power of 1 / μ after Rayleigh fading with a mean of 1. This indicates that the location is x0∈Φ S The distance between the service base station and a typical user; and They respectively represent the locations located at x∈Φ SThe distance between the interfering base station and the typical user and the interference channel coefficient; h is the useful signal, x is the location of the surviving interfering base station, and exp(μ) represents an exponential distribution with a mean of 1 / μ.

[0024] As a further optimization scheme for the cellular network performance analysis method under strong electromagnetic pulse attack described in this invention, the calculation formula for the signal-to-interference-to-noise ratio of a typical user is as follows:

[0025]

[0026] Wherein, SINR(r) u () indicates the distance r from the attack origin o. u The signal-to-interference-plus-noise ratio (SNR) of a typical user, σ 2 This represents the power of additive white Gaussian noise;

[0027] The numerator in the formula for calculating the signal-to-interference-plus-noise ratio (SNR) for a typical user is the power received by the typical user from the serving base station, while the denominator is the aggregated interference from all other surviving base stations in the network, excluding the serving base station.

[0028] As a further optimization scheme for the cellular network performance analysis method under strong electromagnetic pulse attack described in this invention, the cumulative distribution function F of the shortest distance between a typical user and a surviving base station is used. R (r,r u ) and probability density function f R (r,r u )for:

[0029]

[0030] Where r is the shortest distance between a typical user and a surviving base station, and R is a random variable representing the shortest distance between a typical user and a surviving base station. u The distance between a typical user and the attack origin o. r represents the distribution density of surviving base stations. BS (r u (w,β) represents the distance between the base station and the attack origin o. w represents the distance between a typical user and the serving base station, and β represents the angle between the straight line drawn from the typical user to the attack origin o and the straight line drawn from the typical user to the serving base station. This represents the complementary cumulative distribution function.

[0031] As a further optimization scheme for the cellular network performance analysis method under strong electromagnetic pulse attack described in this invention, the strong electromagnetic pulse attack radius r a The radius of influence is defined as follows:

[0032]

[0033] Where, r f r represents the radius by which a strong electromagnetic pulse affects network performance. a The radius of attack of a strong electromagnetic pulse is represented by ε, where ε is the minimum value representing precision. λ represents the expected shortest distance between a typical user and a surviving base station. O This represents the initial base station distribution density, and inf{*} represents the infimum.

[0034] As a further optimization scheme for the cellular network performance analysis method under strong electromagnetic pulse attack described in this invention, the distance r from the attack origin o under strong electromagnetic pulse attack... u The probability that a typical user will be covered is:

[0035]

[0036] in, The typical distance between a user and the serving base station is Expectation of the function under given conditions This indicates the distance between a typical user and the serving base station. The probability that the signal-to-interference-plus-noise ratio (SINR) is greater than T under certain conditions, where T is the threshold for the SINR. The typical distance between a user and the serving base station is The probability density function, where e is the natural base. This represents the probability that a typical user will be covered. The Laplace transform of the aggregated interference received by a typical user from other surviving base stations in the cellular network after being served by base station x0 is expressed as:

[0037]

[0038] in, To the expectation of a function that disturbs the statistical distribution g, r is a function of the distribution density of surviving base stations BS (r u (v, γ) represents the distance between the base station and the attack origin o.

[0039] v represents the distance between a typical user and an interfering base station, and γ represents the angle between the straight line formed by the typical user and the attack origin o and the straight line formed by the typical user and the interfering base station.

[0040] The coverage probability P of cellular networks under strong electromagnetic pulse attacks c The calculation formula is:

[0041]

[0042] in, The distance r from the attack origin o BS The probability that a typical user is covered.

[0043] As a further optimization scheme for the cellular network performance analysis method under strong electromagnetic pulse attack described in this invention, the distance r from the attack origin o under strong electromagnetic pulse attack... u Average reachability when users are covered for:

[0044]

[0045] Where C({T}) represents the coverage of a typical user, and y represents the possible threshold under the condition that the signal-to-interference-to-noise ratio is greater than a given threshold T. For the distance r from the attack origin u The probability that the SINR of a typical user is greater than y. Represents the expectation of the function;

[0046] The formula for estimating the regional spectral efficiency (ASE) of a cellular network under a strong electromagnetic pulse attack is as follows:

[0047]

[0048] Where θ represents the distribution angle of the base station in the polar coordinate system with the attack origin o as the origin. The distance r from the attack origin o BS The average reachability rate when users are covered.

[0049] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0050] This invention considers the scenario where a strong electromagnetic pulse (SEP) attack has a limited range and base stations within that range are randomly and completely destroyed. Based on stochastic geometry theory, a spatial distribution model of surviving base stations in a cellular network under such an attack is constructed. The influence radius of the SEP attack is defined to describe the affected area, and the influence radius is calculated under different attack radii and initial base station distribution densities. Estimation formulas for network coverage probability and regional spectral efficiency within the affected area are derived, and the coverage probability and regional spectral efficiency of the cellular network under different base station destruction probabilities are calculated. Based on this analytical method, the impact of the SEP attack radius and initial base station distribution density on the influence radius, as well as the impact of base station destruction probability on network coverage probability and regional spectral efficiency within the affected area, can be clarified. This provides insights for studying the comprehensive effects of SEP attacks on information networks and for pre-disaster deployment or post-disaster recovery. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of a cellular network under a strong electromagnetic pulse attack according to the present invention;

[0052] Figure 2 This is a schematic diagram illustrating the change in the radius of influence of a strong electromagnetic pulse attack under different initial base station distribution densities in an example of the present invention.

[0053] Figure 3 This is a schematic diagram illustrating the change in the radius of influence of a strong electromagnetic pulse attack under different attack radii in this invention example;

[0054] Figure 4 This is a schematic diagram illustrating the change in user coverage probability with user distribution radius under different base station damage probabilities and strong electromagnetic pulse attack radii in an example of the present invention;

[0055] Figure 5 This is a schematic diagram illustrating the change in user coverage probability with user distribution radius under different base station damage probabilities and initial base station distribution densities in an example of the present invention.

[0056] Figure 6 This is a schematic diagram comparing the probability of cellular network coverage in the affected area under different base station damage probabilities in an example of the present invention;

[0057] Figure 7 This is a schematic diagram comparing the regional spectrum efficiency of the cellular network in the affected area under different base station damage probabilities in an example of the present invention.

[0058] Figure 8 This is a flowchart of a method for analyzing the performance of cellular networks under strong electromagnetic pulse attacks according to the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0060] The technical solution adopted in this invention is: a method for analyzing the performance of cellular networks under strong electromagnetic pulse attacks, the process of which is as follows: Figure 8 As shown, the steps are as follows:

[0061] Step 1, according to Figure 1 The diagram shows a cellular network under a strong electromagnetic pulse attack. A downlink system model is constructed based on this diagram.

[0062] The high electromagnetic pulse attack is an omnidirectional high electromagnetic pulse attack, emitted from the attack origin o, with an attack radius of r. a The attack range is Base stations within the attack range experience random damage, with a damage probability of p(r). BS ), where r BS Let O be the Euclidean distance between the base station and the attack origin. It is a two-dimensional plane.

[0063] The cellular network is a single-antenna isomorphic cellular network. Initial base stations in the cellular network are distributed in a two-dimensional plane using independent homogeneous Poisson point processes, with an initial base station distribution density λ. O >0, the initial distribution of base stations is denoted as Φ O Mobile users are distributed in a two-dimensional plane using a homogeneous Poisson point process independent of the initial base station distribution, with a user distribution density λ. u >0, the distribution of users is denoted as Φ u The association strategy between users and base stations is the nearest base station association strategy; the base station transmits signals with a constant transmit power of 1 / μ, where μ is the reciprocal of the transmit power; the serving base station and users experience Rayleigh fading and standard path loss, with a path loss exponent of α>2; the interference power follows a statistical distribution g.

[0064] (1) Distribution density λ of surviving base stations in cellular networks under strong electromagnetic pulse attack S :

[0065]

[0066] Where, λ S Let λ be the distribution density of surviving base stations, 1(·) be the indicator function, and λ be the base station density. O r represents the initial distribution density of base stations. a The attack radius of a strong electromagnetic pulse. For the distribution density of surviving base stations with respect to r BS The function;

[0067] (2) x0 is the location of the surviving service base station, Φ S The set of surviving base station locations, at a distance r from the attack origin o. u Typical users from x0∈Φ S The power P(x0) received by the serving base station and the total interference received from all other surviving base stations in the cellular network.

[0068]

[0069] Where h~exp(μ) represents the distance r from the attack origin o. u Typical users from x0∈Φ S The useful signal received by a serving base station transmitting a signal at a constant transmit power of 1 / μ after Rayleigh fading with a mean of 1. This indicates that the location is x0∈Φ S The distance between the service base station and a typical user; and They respectively represent the locations located at x∈Φ SThe distance between the interfering base station and the typical user and the interference channel coefficient; h is the useful signal, x is the location of the surviving interfering base station, and exp(μ) represents an exponential distribution with a mean of 1 / μ.

[0070] Step 2: Calculate the signal-to-interference-to-noise ratio (SNR) of a typical user based on the downlink system model of a cellular network under a strong electromagnetic pulse attack.

[0071] The formula for calculating the signal-to-interference-to-noise ratio (SNR) for a typical user is as follows:

[0072]

[0073] Wherein, SINR(r) u () indicates the distance r from the attack origin o. u The signal-to-interference-plus-noise ratio (SNR) of a typical user, σ 2 This represents the power of additive white Gaussian noise;

[0074] The numerator in the formula for calculating the signal-to-interference-plus-noise ratio (SNR) for a typical user is the power received by the typical user from the serving base station, while the denominator is the aggregated interference from all other surviving base stations in the network, excluding the serving base station.

[0075] Step 3: Calculate the cumulative distribution function and probability density function of the shortest distance between a typical user and a surviving base station based on the downlink system model of a cellular network under a strong electromagnetic pulse attack.

[0076] The cumulative distribution function F of the shortest distance between a typical user and a surviving base station R (r,r u ) and probability density function f R (r,r u )for:

[0077]

[0078] Where r is the shortest distance between a typical user and a surviving base station, and R is a random variable representing the shortest distance between a typical user and a surviving base station. u The distance between a typical user and the attack origin o. r represents the distribution density of surviving base stations. BS (r u (w,β) represents the distance between the base station and the attack origin o. w represents the distance between a typical user and the serving base station, and β represents the angle between the straight line drawn from the typical user to the attack origin o and the straight line drawn from the typical user to the serving base station. This represents the complementary cumulative distribution function.

[0079] Step 4: Using the probability density function of the shortest distance between a typical user and a surviving base station and the signal-to-interference-to-noise ratio of a typical user, define the influence radius of a strong electromagnetic pulse attack to describe the affected area.

[0080] The radius of a strong electromagnetic pulse attack is r a The radius of influence is defined as follows:

[0081]

[0082] Where, r f r represents the radius by which a strong electromagnetic pulse affects network performance. a The radius of attack of a strong electromagnetic pulse is represented by ε, where ε is the minimum value representing precision. λ represents the expected shortest distance between a typical user and a surviving base station. O This represents the initial base station distribution density, and inf{*} represents the infimum.

[0083] Step 5: Based on the signal-to-noise ratio and influence radius of a typical user in a cellular network under a strong electromagnetic pulse attack, calculate the probability of a typical user being covered and the coverage probability of the cellular network within the affected area under a strong electromagnetic pulse attack.

[0084] Distance r from origin o under strong electromagnetic pulse attack u The probability that a typical user will be covered is:

[0085]

[0086] in, The typical distance between a user and the serving base station is Expectation of the function under given conditions This indicates the distance between a typical user and the serving base station. The probability that the signal-to-interference-plus-noise ratio (SINR) is greater than T under certain conditions, where T is the threshold for the SINR. The typical distance between a user and the serving base station is The probability density function, where e is the natural base. This represents the probability that a typical user will be covered. The Laplace transform of the aggregated interference received by a typical user from other surviving base stations in the cellular network after being served by base station x0 is expressed as:

[0087]

[0088] in, To the expectation of a function that disturbs the statistical distribution g, r is a function of the distribution density of surviving base stations BS (r u (v, γ) represents the distance between the base station and the attack origin o. v represents the distance between a typical user and an interfering base station, and γ represents the angle between the straight line formed by the typical user and the attack origin o and the straight line formed by the typical user and the interfering base station.

[0089] The coverage probability P of cellular networks under strong electromagnetic pulse attacks c The calculation formula is:

[0090]

[0091] in, The distance r from the origin o BS The probability that a typical user is covered;

[0092] Step 6: Based on the signal-to-interference-to-noise ratio, the probability of being covered, and the radius of influence of typical users in a cellular network under a strong electromagnetic pulse attack, calculate the average reachable rate of users within the coverage area and the regional spectral efficiency of the cellular network within the affected area under a strong electromagnetic pulse attack.

[0093] Distance r between the attack origin o and the strong electromagnetic pulse attack u The average reachability rate when a user is covered is:

[0094]

[0095] Where C({T}) represents the coverage of a typical user, and y represents the possible threshold under the condition that the signal-to-interference-to-noise ratio is greater than a given threshold T. For the distance r from the attack origin u The probability that the SINR of a typical user is greater than y. Represents the expectation of the function;

[0096] The formula for estimating the regional spectral efficiency (ASE) of a cellular network under a strong electromagnetic pulse attack is as follows:

[0097]

[0098] Where θ represents the distribution angle of the base station in the polar coordinate system with the attack origin o as the origin. The distance r from the attack origin o BS The average reachability rate when users are covered.

[0099] Example 1

[0100] A method for analyzing the performance of cellular networks under strong electromagnetic pulse attacks, considering noiseless single-antenna isomorphic cellular networks with an initial base station distribution density λ. O =1BS / km 2 User distribution density λ u =8UE / km 2 Strong electromagnetic pulse attack radius ra =5km, path loss index α=4.

[0101] Based on the above-mentioned method for analyzing cellular network performance under strong electromagnetic pulse attacks based on random geometry, the relationship between the influence radius and the initial distribution density of base stations is as follows: Figure 2 and 4 As shown, the relationship between the radius of influence and the radius of attack by a strong electromagnetic pulse is as follows: Figure 3 and 5 As shown. Figure 2 , 4 It can be seen that, given a fixed radius of attack by a strong electromagnetic pulse, the radius of influence decreases with increasing initial base station density, and this decreasing trend gradually slows down. For example... Figure 3 , 5 As shown, with a fixed initial base station distribution density, the influence radius gradually increases with the increase of the attack radius, and the influence radius is always greater than the attack radius.

[0102] The relationship between the probability of network coverage in the affected area and the probability of base station damage and the signal-to-noise ratio threshold in the attacked area is as follows: Figure 6 As shown, the probability of network coverage within the affected area decreases as the base station failure probability and the signal-to-noise ratio threshold increase. Figure 6 It can be seen that when the base station failure probability is 50%, the network coverage probability in the affected area decreases by approximately 10%. The relationship between the network spectral efficiency within the affected area and the base station failure probability and signal-to-noise ratio threshold within the attack area is as follows: Figure 7 As shown, the spectral efficiency of the network area within the affected region decreases with increasing base station failure probability and signal-to-interference-to-noise ratio threshold. Figure 7 It can be seen that when the base station failure probability is 50%, the network area spectrum efficiency in the affected area decreases by approximately 0.24 bit / s / Hz / km^. 2 .

[0103] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for analyzing the performance of cellular networks under strong electromagnetic pulse attacks, characterized in that, include: Construct a downlink system model of a cellular network under a strong electromagnetic pulse attack based on stochastic geometry; Based on the downlink system model of cellular networks under strong electromagnetic pulse attack, the cumulative distribution function of the shortest distance between a typical user and a surviving base station is calculated, and the probability density function of the shortest distance between a typical user and a surviving base station is calculated based on the cumulative distribution function. Based on the downlink system model of a cellular network under a strong electromagnetic pulse attack, the signal-to-interference-to-noise ratio of a typical user is calculated. Using the probability density function of the closest distance between a typical user and a surviving base station and the signal-to-interference-to-noise ratio of a typical user, the influence radius of a strong electromagnetic pulse attack is defined to describe the affected area. Based on the signal-to-noise ratio and influence radius of a typical user in a cellular network under a strong electromagnetic pulse attack, calculate the probability of a typical user being covered and the probability of cellular network coverage within the affected area under a strong electromagnetic pulse attack. Based on the signal-to-noise ratio, probability of being covered, and radius of influence of typical users in a cellular network under a strong electromagnetic pulse attack, calculate the average reachable rate of users within the coverage area and the regional spectral efficiency of the cellular network within the affected area under a strong electromagnetic pulse attack. The high electromagnetic pulse (HEP) attack is an omnidirectional HEP attack, emitted from the attack origin point O, with an attack radius of [missing information]. The attack range is Base stations within the attack range experience random damage, with a damage probability of . ,in, Let O be the Euclidean distance between the base station and the attack origin. It is a two-dimensional plane; The cellular network is a single-antenna isomorphic cellular network. The initial base stations in the cellular network are distributed in a two-dimensional plane using independent homogeneous Poisson point processes. The initial base station distribution density... The initial distribution of base stations is denoted as Mobile users are distributed in a two-dimensional plane using a homogeneous Poisson point process independent of the initial base station distribution; user distribution density. The distribution of users is denoted as The association strategy between users and base stations is the nearest base station association strategy; the base station transmits at a constant power. Transmit signal, The reciprocal of the transmit power; the serving base station and users experience Rayleigh fading and standard path loss, the path loss index. The interference power follows a statistical distribution g. A model of a cellular network downlink system under a strong electromagnetic pulse attack includes: (1) Distribution density of surviving base stations in cellular networks under strong electromagnetic pulse attacks : ； in, The distribution density of surviving base stations, For indicator functions, The initial base station distribution density, The attack radius of a strong electromagnetic pulse. For the distribution density of surviving base stations about The function; (2) Location of surviving service base stations The set of surviving base station locations, at a distance of o from the attack origin. Typical users from the location Power received by the serving base station at the location and the total interference received from all other surviving base stations in the cellular network. for: ； ； in, Indicates the distance from the attack origin o Typical users from the location Maintain a constant transmission power The useful signal received by the serving base station after the transmitting signal has undergone Rayleigh fading with a mean of 1. Indicates that it is located at The distance between the service base station and a typical user; and They respectively represent the locations The distance between the interfering base station and a typical user, and the interference channel coefficient; Useful signal The location of the surviving jamming base station. The mean is The exponential distribution.

2. The method for analyzing the performance of cellular networks under a strong electromagnetic pulse attack according to claim 1, characterized in that, The formula for calculating the signal-to-interference-to-noise ratio (SNR) for a typical user is as follows: ； in, Indicates the distance from the attack origin o The signal-to-interference-to-noise ratio for typical users, This represents the power of additive white Gaussian noise; The numerator in the formula for calculating the signal-to-interference-plus-noise ratio (SNR) for a typical user is the power received by the typical user from the serving base station, while the denominator is the aggregated interference from all other surviving base stations in the network, excluding the serving base station.

3. The method for analyzing the performance of cellular networks under strong electromagnetic pulse attacks according to claim 2, characterized in that, Cumulative distribution function of the shortest distance between a typical user and a surviving base station and probability density function for: ； ； Where r is the shortest distance between a typical user and a surviving base station, and R is a random variable representing the shortest distance between a typical user and a surviving base station. The distance between a typical user and the attack origin o. The distribution density of surviving base stations; This represents the distance between the base station and the attack origin point o. , This represents the distance between a typical user and the serving base station. This represents the angle between the line drawn from a typical user to the attack origin o and the line drawn from a typical user to the serving base station. This represents the complementary cumulative distribution function.

4. The method for analyzing the performance of cellular networks under a strong electromagnetic pulse attack according to claim 3, characterized in that, Strong electromagnetic pulse attack radius The radius of influence is defined as follows: ； in, This represents the radius by which a strong electromagnetic pulse affects network performance. This indicates the attack radius of a strong electromagnetic pulse. To represent the minimum value of precision, This represents the expected closest distance between a typical user and a surviving base station. This represents the initial base station distribution density. Indicates the infimum.

5. The method for analyzing the performance of cellular networks under a strong electromagnetic pulse attack according to claim 4, characterized in that, Distance from the attack origin o under a strong electromagnetic pulse attack The probability that a typical user will be covered is: ； in, The typical distance between a user and the serving base station is The expectation of the function under the given conditions This indicates the distance between a typical user and the serving base station. The probability that the signal-to-interference-to-noise ratio (SINR) is greater than T under certain conditions. This is the threshold for the signal-to-interference-to-noise ratio. The typical distance between a user and the serving base station is The probability density function, where e is the natural base. This represents the probability that a typical user will be covered. For typical users The Laplace transform of the aggregated interference received from other surviving base stations in the cellular network after the base station has provided service is expressed as: ； in, To the expectation of a function that disturbs the statistical distribution g, The distribution density of surviving base stations is a function of the distribution density of the base stations. The distance between the base station and the attack origin o. , This indicates the distance between a typical user and an interfering base station. This represents the angle between the straight line formed by the typical user and the attack origin o and the straight line formed by the typical user and the interfering base station. Coverage probability of cellular networks under strong electromagnetic pulse attacks The calculation formula is: ； in, Distance from the attack origin o The probability that a typical user is covered.

6. The method for analyzing the performance of cellular networks under a strong electromagnetic pulse attack according to claim 5, characterized in that, Distance from the attack origin o under a strong electromagnetic pulse attack Average reachability when users are covered for: ； in, This indicates that a typical user is covered, and y represents the possible threshold under the condition that the signal-to-interference-to-noise ratio is greater than a given threshold T. To the distance from the attack origin The probability that the SINR of a typical user is greater than y. Represents the expectation of the function; Regional spectral efficiency of cellular networks under strong electromagnetic pulse attacks The estimation formula is: ； in, This represents the distribution angle of the base stations in a polar coordinate system with the attack origin o as the origin. Distance from the attack origin o The average reachability rate when users are covered.

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