MIMO heterogeneous network performance analysis method under strong electromagnetic pulse influence

Abstract

The invention discloses a method for analyzing the performance of an MIMO (Multiple Input Multiple Output) heterogeneous network under the influence of a strong electromagnetic pulse, and relates to the technical field of wireless communication network performance analysis. Considering the base station degradation condition of damaged partial antennas in partial base stations under the influence of strong electromagnetic pulses; based on stochastic geometry, constructing a spatial distribution model of MIMO heterogeneous network surviving base stations and degraded base stations under the strong electromagnetic pulse influence; deriving a coverage probability and lowest area spectrum efficiency estimation formula of the network, and calculating the coverage probability and the lowest area spectrum efficiency of the MIMO heterogeneous network under different base station degradation probabilities and antenna damage probabilities; the specific influence of the base station degradation probability and the antenna damage probability on the coverage performance of the MIMO heterogeneous network and the lowest area spectrum efficiency can be determined, and a thought is provided for researching the comprehensive action effect of the strong electromagnetic pulse on the information network and pre-disaster deployment or post-disaster recovery.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication network performance analysis, and in particular to a method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse. Background Art

[0002] Heterogeneous networks and multi-antenna technology are two key methods to improve the performance of 5G networks and meet the exponential growth of mobile data traffic and high-quality service requirements. Therefore, MIMO heterogeneous networks are widely used in actual 4G and 5G communications. However, due to the inherent sensitivity of communication systems to strong electromagnetic pulses, strong electromagnetic pulses are becoming a major threat to cellular networks and smart grid infrastructure. Therefore, studying the effects of strong electromagnetic pulses on cellular network performance is of great significance for pre-disaster deployment and post-disaster recovery.

[0003] In the past few decades, random geometry has become one of the most effective mathematical tools for modeling and analyzing the performance of communication networks. At present, there have been many studies on model construction and performance analysis of pre-disaster or post-disaster cellular networks based on random geometry, but most post-disaster networks only consider the impact of natural disasters. In cellular networks affected by natural disasters, the status of base stations is assumed to be that some base stations are completely damaged and have no communication capabilities, and the remaining base stations survive and maintain the original communication functions. For cellular networks affected by strong electromagnetic pulses, the base station may be partially damaged, that is, some antennas of the base station are damaged, resulting in a decrease in communication capabilities. The present invention proposes a MIMO heterogeneous network performance analysis method under the influence of strong electromagnetic pulses based on random geometry for MIMO heterogeneous networks with partial base station damage, without considering the impact range of disasters or strong electromagnetic pulses, so as to clarify the impact of antenna damage probability on network coverage performance and minimum regional spectrum efficiency. Summary of the invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for analyzing the performance of MIMO heterogeneous networks under the influence of strong electromagnetic pulses, so as to solve the technical problem that the existing post-disaster network performance analysis based on random geometry mostly assumes that the infrastructure is completely damaged by natural disasters, and ignores the network performance analysis caused by partial damage to the infrastructure due to the strong electromagnetic pulse; the specific influence of the base station degradation probability and the antenna damage probability on the coverage performance and the minimum regional spectrum efficiency of the MIMO heterogeneous network can be clarified, providing ideas for studying the comprehensive effects of strong electromagnetic pulses on information networks as well as pre-disaster deployment or post-disaster recovery.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse proposed by the present invention includes:

[0007] Construct a downlink system model of MIMO heterogeneous networks under the influence of strong electromagnetic pulses based on random geometry;

[0008] The signal-to-interference-to-noise ratio of a typical user is calculated based on the downlink system model of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse;

[0009] Using the signal-to-interference-to-noise ratio of typical users, the coverage probability of each layer of the MIMO heterogeneous network under the influence of strong electromagnetic pulses is calculated;

[0010] According to the downlink system model of the MIMO heterogeneous network under the influence of strong electromagnetic pulses and the coverage probability of each layer of the MIMO heterogeneous network, the coverage probability and the minimum regional spectrum efficiency of the MIMO heterogeneous network under the influence of strong electromagnetic pulses are calculated.

[0011] As a further optimization scheme of the MIMO heterogeneous network performance analysis method under the influence of a strong electromagnetic pulse described in the present invention, the MIMO heterogeneous network is a K-layer network, each layer of the network has multiple base stations, each layer of base stations is distributed in a two-dimensional plane as an independent homogeneous Poisson point process, and the distribution density of the k-th layer base station is λ k , the distribution of the k-th layer base stations is denoted as Φ k ; Mobile users are distributed in a two-dimensional plane in a homogeneous Poisson point process independent of the base station distribution, and the user distribution density is λ u ,λ u >>λ k , the user distribution is denoted as Φ u , 1≤k≤K; the transmission power, number of antennas, bias factor, signal interference noise ratio threshold and number of users served simultaneously in each time slot of each base station are different, among which, P k 、M k , B k , γ k , U k are the transmission power, number of antennas, bias factor, signal-to-interference-noise ratio threshold, and number of users served simultaneously per time slot of the base station at the kth layer;

[0012] The probability of downgrading the k-th base station is p dk , the probability of antenna damage of the degraded base station is p Mk , antenna damage probability p Mk The remaining number of antennas M′ must be guaranteed k is an integer, M′ k =(1-p Mk )×M k , then the total power of the base station is degraded k ' is reduced to P k ′=(1-p Mk )×P k ; if M′ k >Uk , the downgraded base station service strategy remains unchanged, and the number of users served by the k-th layer downgraded base station at the same time per time slot is U' k =U k ; if M' k <U k , the number of users U' served by the k-th layer downgraded base station at the same time per time slot k Reduced to U' k =M' k .

[0013] As a further optimization scheme of the MIMO heterogeneous network performance analysis method under the influence of a strong electromagnetic pulse described in the present invention, a downlink system model of the MIMO heterogeneous network under the influence of a strong electromagnetic pulse includes:

[0014] (1) Distribution of downgraded base stations at the kth layer and the distribution of surviving base stations

[0015]

[0016] Where x is the base station location, Φ k is the k-th layer base station distribution of MIMO heterogeneous network, 1(x) is a Bernoulli random variable, 1(x) = 1 means the base station at x is downgraded; p dk is the probability of downgrading the k-th layer base station, Degrade the base station distribution density of the kth layer, is the distribution density of surviving base stations in the kth layer;

[0017] (2) A typical user starts from x0∈φ k The power received by the serving base station BS and the interference received from the entire network:

[0018]

[0019]

[0020] Among them, from typical users to locations The channel gain distribution of the surviving serving base station follows the gamma distribution D k =M k -U k +1; to position The channel gain distribution of the degraded service base station follows the gamma distribution D′ k =M′ k -U′ k +1, Represents approximation; from typical user to location The channel gain distribution of the surviving interfering base station follows the gamma distribution To location The channel gain distribution of the degraded interfering base station follows the gamma distribution P(x) is a typical user from x0∈Φ k The power received by the serving BS at k is the transmission power of the surviving base station in the kth layer, P k ′ is the transmission power of the downgraded base station at the kth layer; is the channel gain distribution when the typical user x0 is served by the k-th layer surviving base station, is the channel gain distribution when the typical user x0 is served by the k-th layer downgraded base station, D k and D′ k is the shape parameter of the Gamma distribution, M′ k is the number of antennas of the k-th layer downgraded base station, α is the path loss index, I is the interference received by a typical user from the entire network, is the distribution of surviving base stations in the jth layer, P j is the transmission power of the surviving base station in the jth layer, U j is the number of users served simultaneously by the surviving base station in the jth layer per time slot, g x,j is the channel gain distribution when a typical user is interfered by the j-th layer surviving base station, is the j-th layer downgraded base station distribution, P j ′ is the j-th layer downgraded base station transmission power, U′ j is the number of users served simultaneously by the j-th layer downgraded base station per time slot, g′ x,j is the channel gain distribution of a typical user interfered by the j-th layer downgraded base station, {x0} is the serving base station\ is removed;

[0021] (3) The probability that a typical user is associated with a surviving base station or a degraded base station in the kth layer:

[0022]

[0023] in, represents the transmission power of the surviving or degraded base station in the jth layer, B j is the j-th layer bias factor, r j is the distance from a typical user to the nearest base station on the jth layer, and α is the path loss exponent; is the probability that a typical user is associated with a surviving base station in the kth layer, is the distribution density of surviving base stations in the kth layer, P k is the transmission power of the surviving base station in the kth layer, B k is the bias factor of the kth layer; is the probability that a typical user is associated with a downgraded base station at the kth layer, is the distribution density of downgraded base stations in the kth layer, P k′ is the transmission power of the k-th layer downgraded base station, is the distribution density of surviving base stations in the jth layer, is the distribution density of downgraded base stations in the jth layer, P j is the transmission power of the surviving base station in the jth layer, P j ′ is the j-th layer downgraded base station transmission power.

[0024] As a further optimization scheme of the MIMO heterogeneous network performance analysis method under the influence of a strong electromagnetic pulse described in the present invention, the calculation formula of the signal interference noise ratio of a typical user is as follows:

[0025]

[0026] Among them, SINR k represents the signal interference plus noise ratio of a typical user served by the base station at x0 on the kth layer. The numerator in the calculation formula of the signal interference plus noise ratio of the typical user is the power received by the typical user from the serving base station, and the denominator in the calculation formula of the signal interference plus noise ratio of the typical user is the aggregate interference from all other base stations in the network except the serving base station.

[0027] As a further optimization scheme of the MIMO heterogeneous network performance analysis method under the influence of strong electromagnetic pulses described in the present invention, the k-th layer coverage probability P of the MIMO heterogeneous network under the influence of strong electromagnetic pulses c The calculation formula of (k) is:

[0028]

[0029] in, The probability of *, γ k is the SINR threshold of the kth layer, is the channel gain distribution when a typical user at x0 is served by the k-th surviving base station, is the channel gain distribution when a typical user at x0 is served by the k-th layer downgraded base station; D k =M k -U k +1, D′ k =M′ k -U′ k +1, ||·|| is the L1 induced matrix norm, Yes D k ×D k The lower triangular Toeplitz matrix, It is D′ k ×D′ k The lower triangular Toeplitz matrix is ​​represented as:

[0030]

[0031] Among them, q m for The matrix elements on the mth diagonal parallel to the main diagonal, m = 0, 1, ... D k -1,q′ n for The matrix elements on the nth diagonal parallel to the main diagonal, n = 0, 1, ..., D ′ k -1, Γ(*) is the Gamma function, 2F1(*) is the Gaussian hypergeometric function;

[0032] Coverage probability P of MIMO heterogeneous networks under the influence of strong electromagnetic pulses c The calculation formula is:

[0033]

[0034] As a further optimization scheme of the MIMO heterogeneous network performance analysis method under the influence of a strong electromagnetic pulse described in the present invention, the calculation formula of the minimum regional spectrum efficiency ASE of the MIMO heterogeneous network is:

[0035]

[0036] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0037] The present invention proposes an analysis method for the coverage performance and minimum regional spectrum efficiency of MIMO heterogeneous networks under the influence of strong electromagnetic pulses. Compared with the prior art, the method takes into account the degradation of base stations with damaged antennas in some base stations under the influence of strong electromagnetic pulses; constructs a spatial distribution model of surviving base stations and degraded base stations in the MIMO heterogeneous network under the influence of strong electromagnetic pulses based on random geometry; derives an estimation formula for network coverage probability and minimum regional spectrum efficiency, and calculates the coverage probability and minimum regional spectrum efficiency of the MIMO heterogeneous network under different base station degradation probabilities and antenna damage probabilities; based on this analysis method, the specific influence of the base station degradation probability and antenna damage probability on the coverage performance and minimum regional spectrum efficiency of the MIMO heterogeneous network can be clarified, providing ideas for studying the comprehensive effects of strong electromagnetic pulses on information networks as well as pre-disaster deployment or post-disaster recovery. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 A schematic diagram of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse according to the present invention;

[0039] Figure 2 It is a schematic diagram of network coverage performance comparison under different macro base station damage probabilities in an example of the present invention;

[0040] Figure 3A schematic diagram showing a comparison of network coverage performance under different damage probabilities of small base stations in an example of the present invention;

[0041] Figure 4 It is a schematic diagram of comparing the minimum regional spectrum efficiency under different macro base station damage probabilities in an example of the present invention;

[0042] Figure 5 It is a schematic diagram of comparing the minimum regional spectrum efficiency under different damage probabilities of small base stations in an example of the present invention. DETAILED DESCRIPTION

[0043] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings:

[0044] The technical solution adopted by the present invention is: a method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse, the steps of which are as follows:

[0045] Step 1: According to Figure 1 The schematic diagram of MIMO heterogeneous network under the influence of strong electromagnetic pulse is shown, and the downlink system model is constructed.

[0046] The MIMO heterogeneous network is a K-layer network. There are multiple base stations in each layer of the network. The base stations in each layer are distributed in a two-dimensional plane as an independent homogeneous Poisson point process. The distribution density of the base stations in the kth layer is λ k , the distribution of the k-th layer base stations is denoted as Φ k ; Mobile users are distributed in a two-dimensional plane in a homogeneous Poisson point process independent of the base station distribution, and the user distribution density is λ u , the user distribution is denoted as Φ u , 1≤k≤K; the transmission power, number of antennas, bias factor, signal interference noise ratio threshold and number of users served simultaneously in each time slot of each base station are different, among which, P k 、M k , B k , γ k , U k are the transmission power, number of antennas, bias factor, signal-to-interference-noise ratio threshold, and number of users served simultaneously per time slot of the base station at the kth layer;

[0047] The network is fully loaded, that is, the user distribution density λ u Much larger than the base station distribution density λ k ,When spatial division multiple access is adopted in a cell, the total power of the base stations in the network is evenly distributed to the users being served simultaneously in each time slot;

[0048] The signal sent by any base station in the network experiences a standard path loss, and the path loss exponent is α (α>2); the multi-antenna technology adopts zero-forcing precoding, and any base station has perfect channel state information and the channel follows Rayleigh fading;

[0049] The network adopts universal frequency reuse and open access, that is, a typical user at the origin can receive not only the signal from the serving base station, but also the interference from all other base stations; the typical user adopts the maximum average bias receiving power association strategy;

[0050] The probability of downgrading the k-th base station is p dk , the probability of antenna damage of the degraded base station is p Mk , antenna damage probability p Mk The remaining number of antennas M′ must be guaranteed k is an integer, M′ k =(1-p Mk )×M k , then the total power of the base station is degraded k ' is reduced to P k ′=(1-p Mk )×P k ; if M′ k >U k , the downgraded base station service strategy remains unchanged, and the number of users served by the k-th layer downgraded base station at the same time per time slot is U′ k =U k ; if M′ k <U k , the number of users U′ served by the k-th layer downgraded base station at the same time per time slot k Reduced to U′ k =M′ k .

[0051] (1) Distribution of downgraded base stations at the kth layer and the distribution of surviving base stations

[0052]

[0053] Where x is the base station location, Φ k is the k-th layer base station distribution of the MIMO heterogeneous network, 1(x) is a Bernoulli random variable, 1(x) = 1 means the base station at x is downgraded; p dk is the probability of downgrading the k-th layer base station, Degrade the base station distribution density of the kth layer, is the distribution density of surviving base stations in the kth layer;

[0054] (2) A typical user starts from x0∈Φ k The power received by the serving base station BS and the interference received from the entire network:

[0055]

[0056] Among them, from typical users to locations The channel gain distribution of the surviving serving base station follows the gamma distribution D k =M k -U k +1; to position The channel gain distribution of the degraded service base station follows the gamma distribution D′ k =M′ k -U′ k +1,h x,k From typical users to locations The channel gain distribution of the surviving serving base station at h x ' ,k From typical users to locations Channel gain distribution of downgraded service base stations at locations; from typical users to locations The channel gain distribution of the surviving interfering base station follows the gamma distribution To location The channel gain distribution of the degraded interfering base station follows the gamma distribution g x,k From typical users to locations The channel gain distribution of the surviving interfering base station at g′ x,k From typical users to locations The channel gain distribution of the degraded interfering base station at x0∈Φ, where P(x) is the channel gain distribution of the typical user from the base station at x0∈Φ k The power received by the serving BS at k is the transmission power of the surviving base station in the kth layer, P k ′ is the transmission power of the downgraded base station at the kth layer; is the channel gain distribution when the typical user x0 is served by the k-th layer surviving base station, is the channel gain distribution when the typical user x0 is served by the k-th layer downgraded base station, D k and D′ k is the shape parameter of the Gamma distribution, M′ k is the number of antennas of the k-th layer downgraded base station, α is the path loss index, I is the interference received by a typical user from the entire network, is the distribution of surviving base stations in the jth layer, P j is the transmission power of the surviving base station in the jth layer, U j is the number of users served simultaneously by the surviving base station in the jth layer per time slot, g x,j is the channel gain distribution when a typical user is interfered by the j-th layer surviving base station, is the j-th layer downgraded base station distribution, P j ′ is the j-th layer downgraded base station transmission power, U′ j is the number of users served simultaneously by the j-th layer downgraded base station per time slot, g′ x,jis the channel gain distribution of a typical user interfered by the j-th layer downgraded base station, {x0} is the serving base station \ To remove;

[0057] (3) The probability that a typical user is associated with a surviving base station or a degraded base station in the kth layer:

[0058]

[0059] in, represents the transmission power of the surviving or degraded base station in the jth layer, B j is the j-th layer bias factor, r j is the distance from a typical user to the nearest base station on the jth layer, and α is the path loss exponent; is the probability that a typical user is associated with a surviving base station in the kth layer, is the distribution density of surviving base stations in the kth layer, P k is the transmission power of the surviving base station in the kth layer, B k is the bias factor of the kth layer; is the probability that a typical user is associated with a downgraded base station at the kth layer, is the distribution density of downgraded base stations in the kth layer, P k ′ is the transmission power of the k-th layer downgraded base station, is the distribution density of surviving base stations in the jth layer, is the distribution density of downgraded base stations in the jth layer, P j is the transmission power of the surviving base station in the jth layer, P j ′ is the j-th layer downgraded base station transmission power.

[0060] Step 2: Calculate the signal interference noise ratio of a typical user based on the MIMO heterogeneous network system model under the influence of strong electromagnetic pulses.

[0061] The signal-to-interference-to-noise ratio calculation formula for a typical user is:

[0062]

[0063] Among them, SINR k represents the signal interference plus noise ratio of a typical user served by the base station at x0 on the kth layer. The numerator in the calculation formula of the signal interference plus noise ratio of the typical user is the power received by the typical user from the serving base station, and the denominator in the calculation formula of the signal interference plus noise ratio of the typical user is the aggregate interference from all other base stations in the network except the serving base station.

[0064] Step 3: Calculate the coverage probability of the MIMO heterogeneous network under the influence of a strong electromagnetic pulse using a typical user signal interference noise ratio, where the coverage probability is the coverage performance of the network.

[0065] The coverage probability P of the kth layer network in MIMO heterogeneous networks under the influence of strong electromagnetic pulses c The calculation formula of (k) is:

[0066]

[0067] in, The probability of *, γ k is the SINR threshold of the kth layer, is the channel gain distribution when a typical user at x0 is served by the k-th surviving base station, is the channel gain distribution when a typical user at x0 is served by the k-th layer downgraded base station; D k =M k -U k +1, D′ k =M′ k -U′ k +1, ||·|| is the L1 induced matrix norm, Yes D k ×D k The lower triangular Toeplitz matrix, It is D′ k ×D′ k The lower triangular Toeplitz matrix is ​​represented as:

[0068]

[0069]

[0070] Among them, q m for The matrix elements on the mth diagonal parallel to the main diagonal, m = 0, 1, ... D k -1,q′ n for The matrix elements on the nth diagonal parallel to the main diagonal, n = 0, 1, ..., D ′ k -1, Γ(*) is the Gamma function, 2F1(*) is the Gaussian hypergeometric function;

[0071] Coverage probability P of MIMO heterogeneous networks under the influence of strong electromagnetic pulses c The calculation formula is:

[0072]

[0073] Step 4: Calculate the minimum regional spectrum efficiency of the network based on the MIMO heterogeneous network system model under the influence of strong electromagnetic pulses and the typical user signal interference noise ratio.

[0074] The calculation formula for the minimum regional spectrum efficiency of MIMO heterogeneous networks under the influence of strong electromagnetic pulses is:

[0075]

[0076] Example 1

[0077] A performance analysis method for MIMO heterogeneous networks under the influence of strong electromagnetic pulses, using a two-layer network and base station degradation probability Base station distribution density λ2=4λ1, transmission power P2=0.01P1, number of antennas [M1,M2]=[16,8], number of users served simultaneously per time slot [U1,U2]=[4,2], bias factor B k =1 / U k , path loss index α=4.

[0078] According to the above-mentioned random geometry-based MIMO heterogeneous network performance analysis method under the influence of strong electromagnetic pulses, the relationship between the macro base station antenna damage probability and the coverage probability is as follows: Figure 2 As shown in the figure, the relationship between the small base station antenna damage probability and coverage probability is as follows Figure 3 As shown. Figure 2 , 3 It can be seen that the coverage probability decreases with the increase of the probability of antenna damage at each layer, and the impact of the probability of antenna damage at each layer on the coverage probability decreases with the increase of its SINR threshold; when the SINR threshold of the macro base station layer is low, the impact of the damage of a single antenna of the macro base station on the coverage probability is greater than that of a single antenna of the small base station; when the SINR threshold of the macro base station is high, the impact of the damage of a single antenna of the macro base station on the coverage probability is less than that of a single antenna of the small base station; in addition, when the number of remaining antennas of each base station layer is less than the number of users served simultaneously per time slot, the impact of the damage of a single antenna of the small base station on the coverage probability is much greater than that of the damage of a single antenna of the macro base station.

[0079] The relationship between the probability of macro base station antenna damage and the minimum regional spectrum efficiency is as follows: Figure 4 As shown in the figure, the relationship between the small base station antenna damage probability and the minimum regional spectrum efficiency is as follows Figure 5 As shown. Figure 4 , 5 As shown in the figure, the lowest regional spectral efficiency decreases with the increase of the probability of antenna damage at each layer, and the impact of the probability of antenna damage at each layer on the lowest regional spectral efficiency increases with the increase of its SINR threshold; when the SINR threshold of the macro base station layer is low, the impact of the damage of a single antenna of the macro base station on the lowest regional spectral efficiency is smaller than that of a single antenna of the small base station; when the SINR threshold of the macro base station is high, the impact of the damage of a single antenna of the macro base station on the lowest regional spectral efficiency is greater than that of a single antenna of the small base station; when the number of remaining antennas of each base station layer is less than the number of users served simultaneously per time slot, the difference in distribution density makes the lowest regional spectral efficiency more sensitive to the probability of antenna damage of the small base station.

[0080] The above description is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a technician familiar with the technical field within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for analyzing the performance of MIMO heterogeneous networks under the influence of strong electromagnetic pulses, characterized in that: include: Construct a downlink system model of MIMO heterogeneous networks under the influence of strong electromagnetic pulses based on random geometry; The signal-to-interference-to-noise ratio of a typical user is calculated based on the downlink system model of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse; Using the signal-to-interference-to-noise ratio of typical users, the coverage probability of each layer of the MIMO heterogeneous network under the influence of strong electromagnetic pulses is calculated; According to the downlink system model of the MIMO heterogeneous network under the influence of strong electromagnetic pulses and the coverage probability of each layer of the MIMO heterogeneous network, the coverage probability and the minimum regional spectrum efficiency of the MIMO heterogeneous network under the influence of strong electromagnetic pulses are calculated.

2. The method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse according to claim 1, characterized in that: The MIMO heterogeneous network is a K-layer network. There are multiple base stations in each layer of the network. The base stations in each layer are distributed in a two-dimensional plane as an independent homogeneous Poisson point process. The distribution density of the base stations in the kth layer is λ k , the distribution of the k-th layer base stations is denoted as Φ k ; Mobile users are distributed in a two-dimensional plane in a homogeneous Poisson point process independent of the base station distribution, and the user distribution density is λ u ,λ u >>λ k , the user distribution is denoted as Φ u , 1≤k≤K; the transmission power, number of antennas, bias factor, signal interference noise ratio threshold and number of users served simultaneously in each time slot of each base station are different, among which, P k 、M k , B k , γ k , U k are the transmission power, number of antennas, bias factor, signal-to-interference-noise ratio threshold, and number of users served simultaneously per time slot of the base station at the kth layer; The probability of downgrading the k-th base station is p dk , the probability of antenna damage of the degraded base station is p Mk , antenna damage probability p Mk The remaining number of antennas M′ must be guaranteed k is an integer, M′ k =(1-p Mk )×M k , then the total power of the base station is degraded k ' is reduced to P k ′=(1-p Mk )×P k ; if M′ k >U k , the downgraded base station service strategy remains unchanged, and the number of users served by the k-th layer downgraded base station at the same time per time slot is Uπ k =U k ; if M′ k <U k , the number of users U′ served by the k-th layer downgraded base station at the same time per time slot k Reduced to U′ k =M′ k .

3. The method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse according to claim 2, characterized in that: The downlink system model of MIMO heterogeneous network under the influence of strong electromagnetic pulse includes: (1) Distribution of downgraded base stations at the kth layer and the distribution of surviving base stations Where x is the base station location, Φ k is the k-th layer base station distribution of the MIMO heterogeneous network, 1(x) is a Bernoulli random variable, 1(x) = 1 means the base station at x is downgraded; p dk is the probability of downgrading the k-th layer base station, is the k-th layer downgraded base station distribution density, is the distribution density of surviving base stations in the kth layer; (2) A typical user starts from x0∈Φ k The power received by the serving base station BS and the interference received from the entire network: Among them, from typical users to locations The channel gain distribution of the surviving serving base station follows the gamma distribution To location The channel gain distribution of the degraded service base station follows the gamma distribution Represents approximation; from typical user to location The channel gain distribution of the surviving interfering base station follows the gamma distribution To location The channel gain distribution of the degraded interfering base station follows the gamma distribution For a typical user from x0∈φ k The power received by the serving BS at k is the transmission power of the surviving base station in the kth layer, P k ′ is the transmission power of the downgraded base station at the kth layer; is the channel gain distribution when the typical user x0 is served by the k-th layer surviving base station, is the channel gain distribution when the typical user x0 is served by the k-th layer downgraded base station, D k and D′ k is the shape parameter of the Gamma distribution, M′ k is the number of antennas of the k-th layer downgraded base station, α is the path loss index, I is the interference received by a typical user from the entire network, is the distribution of surviving base stations in the jth layer, P j is the transmission power of the surviving base station in the jth layer, U j is the number of users served simultaneously by the surviving base station in the jth layer per time slot, g x,j is the channel gain distribution when a typical user is interfered by the j-th layer surviving base station, is the j-th layer downgraded base station distribution, P j ′ is the j-th layer downgraded base station transmission power, U′ j is the number of users served simultaneously by the j-th layer downgraded base station per time slot, g′ x,j is the channel gain distribution of a typical user when interfered by the j-th layer downgraded base station, {x0} For service base station\for removal; (3) The probability that a typical user is associated with a surviving base station or a degraded base station in the kth layer: in, represents the transmission power of the surviving or degraded base station in the jth layer, B j is the j-th layer bias factor, r j is the distance from a typical user to the nearest base station on the jth layer, and α is the path loss exponent; is the probability that a typical user is associated with a surviving base station in the kth layer, is the distribution density of surviving base stations in the kth layer, P k is the transmission power of the surviving base station in the kth layer, B k is the bias factor of the kth layer; is the probability that a typical user is associated with a downgraded base station at the kth layer, is the k-th layer downgrade base station distribution density, P k ′ is the transmission power of the k-th layer downgraded base station, is the distribution density of surviving base stations in the jth layer, is the distribution density of downgraded base stations in the jth layer, P j is the transmission power of the surviving base station in the jth layer, P j ′ is the j-th layer downgraded base station transmission power.

4. The method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse according to claim 3 is characterized in that: The calculation formula for the signal-to-interference-to-noise ratio of a typical user is as follows: Among them, SINR k represents the signal interference plus noise ratio of a typical user served by the base station at x0 on the kth layer. The numerator in the calculation formula of the signal interference plus noise ratio of the typical user is the power received by the typical user from the serving base station, and the denominator in the calculation formula of the signal interference plus noise ratio of the typical user is the aggregate interference from all other base stations in the network except the serving base station.

5. The method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse according to claim 4, characterized in that: The k-th layer coverage probability P of MIMO heterogeneous networks under the influence of strong electromagnetic pulses c The calculation formula of (k) is: in, The probability of *, γ k is the SINR threshold of the kth layer, is the channel gain distribution when a typical user at x0 is served by the k-th layer surviving base station, is the channel gain distribution when a typical user at x0 is served by the k-th layer downgraded base station; D k =M k -U k +1, D′ k =M' k -U' k +1, ||·|| is the L1 induced matrix norm, Yes D k ×D k The lower triangular Toeplitz matrix, It's D' k ×D' k The lower triangular Toeplitz matrix is ​​represented as: Among them, q m for The matrix elements on the mth diagonal parallel to the main diagonal, m = 0, 1, ... D k -1,q' n for The matrix elements on the nth diagonal parallel to the main diagonal, n = 0, 1, ..., D' k -1, Γ(*) is the Gamma function, 2F1(*) is the Gaussian hypergeometric function; Coverage probability P of MIMO heterogeneous networks under the influence of strong electromagnetic pulses c The calculation formula is:

6. The method for analyzing the performance of a MIMO heterogeneous network under the influence of a strong electromagnetic pulse according to claim 5, characterized in that: The calculation formula for the minimum regional spectrum efficiency ASE of MIMO heterogeneous networks is:

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