CN114268391A - NOMA (non-volatile memory) enhanced unmanned aerial vehicle auxiliary modeling analysis method - Google Patents

NOMA (non-volatile memory) enhanced unmanned aerial vehicle auxiliary modeling analysis method Download PDF

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CN114268391A
CN114268391A CN202111420765.7A CN202111420765A CN114268391A CN 114268391 A CN114268391 A CN 114268391A CN 202111420765 A CN202111420765 A CN 202111420765A CN 114268391 A CN114268391 A CN 114268391A
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user
base station
typical user
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CN114268391B (en
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程方
赵家进
张治中
邓炳光
孙晶晶
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Chongqing University of Post and Telecommunications
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Abstract

The invention relates to an NOMA (non-volatile memory) enhanced Unmanned Aerial Vehicle (UAV) assisted modeling analysis method, and belongs to the technical field of communication. In the method, the distribution of the unmanned aerial vehicle and the ground base station obeys the process of Poisson points, a suitable large-scale fading model and a suitable small-scale fading model of the unmanned aerial vehicle and the ground base station are selected for modeling, a typical user is set for signal-to-interference-and-noise ratio analysis, then the distance distribution between the typical user and the two layers of base stations and the probability of associating the two layers of base stations are deduced, and further the Laplace transform of interference can be deduced. And deducing to obtain an expression of the signal to interference plus noise ratio coverage rate according to the Laplace transform of the SINR and the interference. The invention analyzes the NOMA enhanced unmanned aerial vehicle auxiliary cellular network from the theoretical aspect, provides a theoretical reference for the future related scene research, and provides guidance for the design of the actual unmanned aerial vehicle auxiliary cellular network.

Description

NOMA (non-volatile memory) enhanced unmanned aerial vehicle auxiliary modeling analysis method
Technical Field
The invention belongs to the technical field of communication, and relates to a NOMA (non-volatile memory) enhanced unmanned aerial vehicle auxiliary modeling analysis method.
Background
With the development of wireless mobile communication technology, unmanned aerial vehicle communication scenes are widely researched. Due to the advantages of small structure, easiness in deployment and flexibility, the unmanned aerial vehicle can be used as an aerial base station to provide wireless service in a 5G/6G network standardization process, so that the unmanned aerial vehicle can be applied to scenes such as post-disaster communication reconstruction and task unloading of hot areas, and is expected to become a part of a future wireless network.
At present, the relevant knowledge of random geometry is a powerful tool for analyzing the unmanned aerial vehicle auxiliary cellular network, the performance of the unmanned aerial vehicle auxiliary cellular network is analyzed from the aspect of mathematics, the higher computational complexity of Monte Carlo simulation is avoided, and the relevant knowledge plays an important role in analyzing the performance of the unmanned aerial vehicle auxiliary cellular network. The NOMA technology has unique advantages in the aspects of improving the spectrum efficiency of the network, improving the user access in the cellular network and the like, and the application of the NOMA technology to the unmanned aerial vehicle-assisted cellular network is a good choice. In the existing modeling of the unmanned aerial vehicle-assisted cellular network, some defects exist, for example, in the patent application with publication number CN112672376A, the inventor utilizes the relevant knowledge of random geometry to model the unmanned aerial vehicle-assisted cellular network, but the current 5G technology such as NOMA/MIMO and the like is not applied to the scene; in the patent application with publication number CN111615200A, the inventor considers the NOMA enhanced drone assisted cellular network from the aspect of resource allocation, but lacks of theoretical analysis of the network scenario and does not obtain related performance indexes.
Therefore, a modeling method capable of accurately analyzing the drone assisted cellular network is needed.
Disclosure of Invention
In view of this, the present invention provides an NOMA enhanced unmanned aerial vehicle assisted modeling analysis method, which adopts the relevant knowledge of random geometry and combines the technical characteristics of NOMA/MIMO to model and accurately analyze an unmanned aerial vehicle assisted cellular network.
In order to achieve the purpose, the invention provides the following technical scheme:
a NOMA enhanced unmanned aerial vehicle assisted modeling analysis method comprises the following steps:
s1: modeling NOMA enhanced unmanned aerial vehicle auxiliary ground base station scene, and the distribution obeying density lambda of unmanned aerial vehicle and ground base stationUAnd λGHomogeneous poisson point process, power PUAnd PGThe height H of the unmanned aerial vehicle, the ground base station is provided with M antennas, and signals are sent to N users through the same resource block;
s2: selecting appropriate large-scale fading and small-scale fading models of the unmanned aerial vehicle and the ground base station for modeling;
s3: calculating the average received power P obtained when the user associates the unmanned aerial vehicle or the ground base station by adopting the strongest average received power association criterionr,U，Pr,G；
S4: considering a typical user, when the typical user is associated with an unmanned aerial vehicle or a ground base station, analyzing the SINR of the typical user;
s5: deriving distance distribution of typical user and two-layer base station
Figure BDA0003377271850000021
And calculating the probability of associating two layers of base stations
Figure BDA0003377271850000022
AG；
S6: derivation of laplacian transform of interference to a typical user by other base stations when the user is associated with a drone or a ground base station
Figure BDA0003377271850000023
S7: deriving an expression of SINR coverage when a typical user is associated with a drone or a terrestrial base station from the SINR analyzed in step S4 and the Laplacian transformation of the interference in step S6
Figure BDA0003377271850000024
Further, step S2 specifically includes:
the probability of an air-to-ground line of sight (LOS) link between an Unmanned Aerial Vehicle (UAV) and a User (UE) is approximately:
Figure BDA0003377271850000025
wherein
Figure BDA0003377271850000026
For its elevation angle, b, c are specific constants depending on the environment, and r is the horizontal distance between the UAV and a typical user. As can be seen from the formula, the higher the UAV altitude, the higher the LOS probability. The probability of an NLOS link between a UAV and a typical user is
Figure BDA0003377271850000027
Large scale fading, using a transmission path loss model combining line-of-sight and non-line-of-sight (NLOS), the transmission path loss of the link between the UAV and the user can be expressed as:
Figure BDA0003377271850000028
where s is the LOS, NLOS, L and N denote LOS and NLOS,
Figure BDA0003377271850000029
represents the path LOSs exponent, η, of the LOS and NLOS links between the UAV and the UEL，ηNIs an additional loss parameter. Thus, it may be expressed as h for small scale fading between the UAV and the UEL，hNWith a obedience parameter of Γ (N)L，1/NL) And Γ (N)N,1/NN) Gamma distribution of (1), NL,NNIs a Nakagami fading parameter.
In the Ground Base Station (GBS) layer, due to the transmission of signals in the sub-6GHz frequency band, the large-scale fading between the GBS and the UE can be shownShown as
Figure BDA00033772718500000210
ηG,αGThe parasitic loss parameter and the path loss exponent are shown separately. Since the GBS is equipped with multiple antennas, users connected to the GBS will obtain large-scale antenna gain G0M-N + 1. The small scale fading between a typical user and the serving base station may be denoted as hG,0The small-scale fading between a typical user and a serving base station, subject to a gamma distribution with parameter Γ (M-N +1,1), can be expressed as hG,iObey a gamma distribution with parameter Γ (N, 1).
Further, step S3 specifically includes:
the UE may communicate by employing a NOMA-enabled UAV layer or a GBS layer employing MIMO to provide optimal coverage. We use the strongest average received power association criterion, i.e. assume that a typical user is associated with the base station in each tier that provides the strongest long-term average received power.
1) The location of the UE is also not predetermined due to the stochastic spatial topology of the stochastic model. Therefore, the UE selects the UAV with the closest distance for communication, and the link between the UAV and the UE has two states of LOS and NLOS, so that the receiving power of the user is the same as that of the UAV when the user is connected to the UAV
Figure BDA0003377271850000031
Wherein, PUIs the transmission power of UAV, riDistance of the nearest base station to a typical UE in UAV layer, anA factor is collected for the power of the UE,
Figure BDA0003377271850000032
denotes path loss, i denotes the ith base station, phiUIndicating that the UAV obeys a homogeneous poisson point process.
2) And adopting the average received power of the GBS layer of the MIMO. Since the GBS is equipped with a large-scale antenna array, the antenna gain G is available to connected users0The received power of a user may be expressed as M-N +1
Figure BDA0003377271850000033
Wherein, PGIs the transmission power of GBS, riFor the base station closest to the typical UE in the GBS layer, Li,GRepresents the path loss, phiGRepresentation shows that GBS obeys the homogeneous poisson point process.
Further, step S4 specifically includes:
1) and GBS layer transmission of MIMO is supported.
When the typical UE is at a distance rG,0When GBS is connected, its SINR can be expressed as
Figure BDA0003377271850000034
Wherein,
Figure BDA0003377271850000035
representing the interference of the terrestrial base station layer,
Figure BDA0003377271850000036
representing the interference of the unmanned plane layer, epsilon ∈ { LOS, NLOS }, G0、hU,i、
Figure BDA0003377271850000037
Respectively representing effective antenna gain, small-scale fading gain and path loss h of a link between the ith base station and a typical user in the unmanned plane layerG,i、
Figure BDA0003377271850000038
Respectively, the small-scale fading gain and path loss of the link between the ith base station and the typical user in the ground base station layer, q represents the base station associated with the typical user,
Figure BDA0003377271850000039
indicating that the poisson point procedure is obeyed in UAVs for LOS/NLOS base stations,
Figure BDA00033772718500000310
is the GBS layer thermal noise power.
2) UAV layer transmissions supporting NOMA.
In the UAV layer, without loss of generality, we consider each UAV to be associated with one user in a previous round of user association process. For simplicity, it is assumed that the distance between the associated UE and the connected UAV is the same, and can be any value, denoted as rf. Compared to small-scale fading, path loss is a major component, so we apply Successive Interference Cancellation (SIC) operations at the near-user side. However, it is not predetermined whether a typical user is a near user or a far user, and we have the following near user case and far user case.
A near user scenario. When the typical user is a near user, i.e. the distance from the typical user to the BS is smaller than the distance (r) from the associated user to the BSU,0＜rf) Therefore, a typical user will decode the information of the fixed user first, and the corresponding SINR expression is
Figure BDA0003377271850000041
Wherein, am,anRespectively representing the power distribution coefficients of far users and near users, and satisfying am＞anAnd am+an＝1，
Figure BDA0003377271850000042
Is the UAV layer thermal noise power,
Figure BDA0003377271850000043
representing the interference at the level of the drone,
Figure BDA0003377271850000044
representing interference at the ground base station level.
If the information of the fixed user is successfully decoded, the interference of the fixed user can be eliminated, the typical user can decode the information, and the corresponding SINR expression is
Figure BDA0003377271850000045
For a fixed user (i.e. a far user) served by the same UAV, the NOMA technology can directly decode the information of the user, while the information of a typical user is used as interference, so the SINR of the fixed user can be expressed as
Figure BDA0003377271850000046
② remote user situation. When the typical user is a far user, i.e. the distance from the typical user to the BS is greater than the distance (r) from the associated user to the BSU,0＞rf) For a fixed user, the information of a typical user will be decoded first, and the corresponding SINR may be expressed as
Figure BDA0003377271850000047
If the information of the typical user is successfully decoded, the interference of the typical user can be eliminated, the fixed user can decode the information of the fixed user, and the corresponding SINR expression is
Figure BDA0003377271850000048
For typical users served by the same GBS (i.e. far users), their own information can be directly decoded by NOMA technique, while the information of the fixed users is regarded as interference, therefore, the SINR of the fixed users can be expressed as
Figure BDA0003377271850000051
Further, step S5 specifically includes:
the probability of at least one LOS/NLOS UAV around a typical user is:
Figure BDA0003377271850000052
wherein,
Figure BDA0003377271850000053
λUis the density of the UAV layer.
The typical user is surrounded by at least one LOS/NLOS UAV, whose distance CCDF and PDF can be expressed as:
CCDF:
Figure BDA0003377271850000054
PDF:
Figure BDA0003377271850000055
similarly, the CCDF and PDF of the distance of at least one GBS around a typical user can be expressed as:
CCDF:
Figure BDA0003377271850000056
PDF:
Figure BDA0003377271850000057
wherein λ isGIs the density of the ground base stations.
Definition of
Figure BDA0003377271850000058
The probability that a typical user is associated with a LOS/NLOS UAV is
Figure BDA0003377271850000059
Wherein s ', s ∈ { LOS, NLOS }, s' ≠ s,
Figure BDA00033772718500000510
is a compound of the formula (13),
Figure BDA00033772718500000511
Figure BDA00033772718500000512
is represented by the formula (15),
Figure BDA00033772718500000513
Figure BDA00033772718500000514
Figure BDA00033772718500000515
is represented by the formula (14).
The probability that a typical user is associated with a GBS is
Figure BDA00033772718500000516
Wherein,
Figure BDA00033772718500000517
is a compound of the formula (13),
Figure BDA00033772718500000518
Figure BDA00033772718500000519
is a compound of the formula (13),
Figure BDA00033772718500000520
Figure BDA0003377271850000061
is represented by the formula (16).
When a typical user associates with a LOS/NLOS UAV, the PDF distribution of the distance distribution is as follows
Figure BDA0003377271850000062
When a typical user associates with a GBS, the PDF distribution of the distance distribution is as follows
Figure BDA0003377271850000063
Further, step S6 specifically includes:
1) when a typical user is associated with a LOS/NLOS UAV, the Laplace transform of UAV layer interference is expressed as
Figure BDA0003377271850000064
Where s, ε ∈ { LOS, NLOS },
Figure BDA0003377271850000065
is expressed as
Figure BDA0003377271850000066
Wherein,
Figure BDA0003377271850000067
the derivation of the above equation is mainly obtained by the probability generation function of the poisson point process and the moment mother function of the gamma random variable, where μ represents an independent variable and will correspond to μ belowG，
Figure BDA0003377271850000068
2) When a typical user is associated with a GBS, the Laplace transform of UAV layer interference is expressed as
Figure BDA0003377271850000069
Figure BDA00033772718500000610
Is expressed as
Figure BDA00033772718500000611
Wherein,
Figure BDA00033772718500000612
3) when a typical user is associated with a LOS/NLOS UAV, the Laplace transform of GBS layer interference is expressed as
Figure BDA00033772718500000613
Wherein,
Figure BDA00033772718500000614
4) when a typical user is associated with GBS, the laplace transform of GBS-layer interference is expressed as
Figure BDA0003377271850000071
Wherein, ω isG(r)＝r。
Further, step S7 includes:
SINR coverage can be defined as the probability that a typical user can successfully transmit a signal under a certain SINR threshold T, and can be expressed as
Figure BDA0003377271850000072
1) When a typical user is associated with GBS, SINR coverage may be expressed as
Figure BDA0003377271850000073
Wherein,
Figure BDA0003377271850000074
the above formula is derived mainly by the Alzers's theorem.
2) When the typical user is associated with the LOS/NLOS UAV layer, according to the NOMA decoding strategy, considering that the typical user is two cases, namely a near user and a far user, SINR coverage analysis is separately performed on the typical user of the two cases.
(r) near user caseU,0＜rfThe steps for a typical user to successfully decode his own information are as follows:
a typical user first decodes information for a fixed user served by the same UAV.
Through the SIC process, a typical user decodes his own information.
Thus, in the case of near users, SINR coverage may be expressed as
Figure BDA0003377271850000075
Wherein, Tf,TtRespectively, the SINR thresholds for fixed users and typical users.
The typical user is a near user, and satisfies am-anTfWhen the SINR coverage is greater than or equal to 0, the SINR coverage may be represented as:
Figure BDA0003377271850000076
wherein
Figure BDA0003377271850000077
When a is not satisfiedm-anTfUnder the condition of not less than 0, the content of the organic solvent is,
Figure BDA0003377271850000078
② far user case, i.e. rU,0＞rfThe typical user can fix the user's letterThe information is treated as noise to successfully decode its own information. Thus, for the far user case, a is satisfiedm-anTtWhen the SINR coverage is greater than or equal to 0, the SINR coverage may be represented as:
Figure BDA0003377271850000081
wherein,
Figure BDA0003377271850000082
when a is not satisfiedm-anTtUnder the condition of not less than 0, the content of the organic solvent is,
Figure BDA0003377271850000083
when a typical user is associated with the GBS layer, the SINR coverage of the typical user can be expressed as
Figure BDA0003377271850000084
The invention has the beneficial effects that: the invention can obtain the performance of the NOMA enhanced unmanned aerial vehicle auxiliary cellular network from the aspect of mathematics, provides a theoretical reference for the research of the NOMA enhanced unmanned aerial vehicle auxiliary cellular network, and provides guidance for the design of the actual unmanned aerial vehicle auxiliary cellular network.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flow chart of the NOMA-enhanced unmanned aerial vehicle-assisted modeling analysis method of the present invention.
FIG. 2 is a schematic diagram of an embodiment of the method according to the present invention.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Referring to fig. 1 to 2, the NOMA-enhanced unmanned aerial vehicle aided modeling analysis method of the present invention specifically includes the following steps:
the method comprises the following steps: starting;
step two: modeling NOMA enhanced unmanned aerial vehicle assisted ground base station scenarios, as shown in FIG. 2, the distribution of unmanned aerial vehicles and ground base stations obeys a density λUAnd λGHomogeneous poisson point process, power PUAnd PGAnd the height H of the unmanned aerial vehicle, the ground base station is provided with M antennae, and signals are sent to N users through the same resource block.
Step three: and (4) selecting appropriate large-scale fading and small-scale fading models of the unmanned aerial vehicle and the ground base station for modeling. The probability of an air-to-ground line of sight (LOS) link between an Unmanned Aerial Vehicle (UAV) and a User (UE) is approximately:
Figure BDA0003377271850000091
wherein,
Figure BDA0003377271850000092
for its elevation angle, b, c are specific constants depending on the environment, and r is the horizontal distance between the UAV and a typical user.As can be seen from the formula, the higher the UAV altitude, the higher the LOS probability. The probability of an NLOS link between a UAV and a typical user is
Figure BDA0003377271850000093
Large scale fading, using a transmission path loss model combining line-of-sight and non-line-of-sight (NLOS), the transmission path loss of the link between the UAV and the user can be expressed as:
Figure BDA0003377271850000094
where s is the LOS, NLOS, L and N represent LOS and NLOS,
Figure BDA0003377271850000095
represents the path LOSs exponent, η, of the LOS and NLOS links between the UAV and the UEL,ηNIs an additional loss parameter. Thus, it may be expressed as h for small scale fading between the UAV and the UEL,hNWith a obedience parameter of Γ (N)L,1/NL) And Γ (N)N,1/NN) Gamma distribution of (1), NL,NNIs a Nakagami fading parameter.
In the Ground Base Station (GBS) layer, large scale fading between GBS and UE due to signal transmission in the sub-6GHz band can be expressed as
Figure BDA0003377271850000096
ηG,αGThe parasitic loss parameter and the path loss exponent are shown separately. Since the GBS is equipped with multiple antennas, users connected to the GBS will obtain large-scale antenna gain G0M-N + 1. The small scale fading between a typical user and the serving base station may be denoted as hG,0The small-scale fading between a typical user and a serving base station, subject to a gamma distribution with parameter Γ (M-N +1,1), can be expressed as hG,iObey a gamma distribution with parameter Γ (N, 1).
Step four: the UE may communicate by employing a NOMA-enabled UAV layer or a GBS layer employing MIMO to provide optimal coverage. We use the strongest average received power association criterion, i.e. assume that a typical user is associated with the base station in each tier that provides the strongest long-term average received power.
The location of the UE is also not predetermined due to the stochastic spatial topology of the stochastic model. Therefore, the UE selects the UAV with the closest distance for communication, and the link between the UAV and the UE has two states of LOS and NLOS, so that the receiving power of the user is the same as that of the UAV when the user is connected to the UAV
Figure BDA0003377271850000097
Wherein, PUIs the transmission power of UAV, riDistance of the nearest base station to a typical UE in UAV layer, anA factor is collected for the power of the UE,
Figure BDA0003377271850000101
denotes path loss, i denotes the ith base station, phiUIndicating that the UAV obeys a homogeneous poisson point process.
And adopting the average received power of the GBS layer of the MIMO. Since the GBS is equipped with a large-scale antenna array, the antenna gain G is available to connected users0The received power of a user may be expressed as M-N +1
Figure BDA0003377271850000102
Wherein, PGIs the transmission power of the GBS and,
Figure BDA0003377271850000103
for the base station closest to the typical UE in the GBS layer, Li,GRepresents the path loss, phiGRepresentation shows that GBS obeys the homogeneous poisson point process.
Step five: considering a typical user, the SINR of the typical user is analyzed when the typical user is associated with a drone or a ground base station.
And GBS layer transmission of MIMO is supported. When the typical UE is at a distance rG,0When GBS is connected, its SINR can be expressed as
Figure BDA0003377271850000104
Wherein,
Figure BDA0003377271850000105
representing the interference of the terrestrial base station layer,
Figure BDA0003377271850000106
representing the interference of the unmanned plane layer, epsilon ∈ { LOS, NLOS }, G0、hU,i、
Figure BDA0003377271850000107
Respectively representing effective antenna gain, small-scale fading gain and path loss h of a link between the ith base station and a typical user in the unmanned plane layerG,i、
Figure BDA0003377271850000108
Respectively, the small-scale fading gain and path loss of the link between the ith base station and the typical user in the ground base station layer, q represents the base station associated with the typical user,
Figure BDA0003377271850000109
indicating that the poisson point procedure is obeyed in UAVs for LOS/NLOS base stations,
Figure BDA00033772718500001010
is the GBS layer thermal noise power.
UAV layer transmissions supporting NOMA. In the UAV layer, without loss of generality, we consider each UAV to be associated with one user in a previous round of user association process. For simplicity, it is assumed that the distance between the associated UE and the connected UAV is the same, and can be any value, denoted as rf. Compared to small-scale fading, path loss is a major component, so we apply Successive Interference Cancellation (SIC) operations at the near-user side. However, typical usage is not predeterminedWhether the user is a near user or a far user, we have the following near user case and far user case.
A near user scenario. When the typical user is a near user, i.e. the distance from the typical user to the BS is smaller than the distance (r) from the associated user to the BSU,0＜rf) Therefore, a typical user will decode the information of the fixed user first, and the corresponding SINR expression is
Figure BDA00033772718500001011
Wherein, am,anRespectively representing the power distribution coefficients of far users and near users, and satisfying am＞anAnd am+an＝1。
Figure BDA0003377271850000111
Representing the interference of the UAV layer(s),
Figure BDA0003377271850000112
representing the interference of the GBS layer.
If the information of the fixed user is successfully decoded, the interference of the fixed user can be eliminated, the typical user can decode the information, and the corresponding SINR expression is
Figure BDA0003377271850000113
For a fixed user (i.e. a far user) served by the same UAV, the NOMA technology can directly decode the information of the user, while the information of a typical user is used as interference, so the SINR of the fixed user can be expressed as
Figure BDA0003377271850000114
A far user situation. When the typical user is a far user, i.e. the distance from the typical user to the BS is greater than the distance (r) from the associated user to the BSU,0＞rf) To aThe fixed user will decode the information of the typical user first, and the corresponding SINR can be expressed as
Figure BDA0003377271850000115
If the information of the typical user is successfully decoded, the interference of the typical user can be eliminated, the fixed user can decode the information of the fixed user, and the corresponding SINR expression is
Figure BDA0003377271850000116
For typical users served by the same GBS (i.e. far users), their own information can be directly decoded by NOMA technique, while the information of the fixed users is regarded as interference, therefore, the SINR of the fixed users can be expressed as
Figure BDA0003377271850000117
Step six: deriving distance distribution of typical user and two-layer base station
Figure BDA0003377271850000118
And calculating the probability of associating two layers of base stations
Figure BDA0003377271850000119
AG。
The probability of at least one LOS/NLOS UAV around a typical user is:
Figure BDA00033772718500001110
wherein,
Figure BDA00033772718500001111
λUis the density of the UAV layer.
The typical user is surrounded by at least one LOS/NLOS UAV, whose distance CCDF and PDF can be expressed as:
CCDF:
Figure BDA00033772718500001112
PDF:
Figure BDA0003377271850000121
similarly, the CCDF and PDF of the distance of at least one GBS around a typical user can be expressed as:
CCDF:
Figure BDA0003377271850000122
PDF:
Figure BDA0003377271850000123
wherein λ isGIs the density of the ground base stations.
Definition of
Figure BDA0003377271850000124
The probability that a typical user is associated with a LOS/NLOS UAV is
Figure BDA0003377271850000125
Wherein s ', s ∈ { LOS, NLOS }, s' ≠ s,
Figure BDA0003377271850000126
is a compound of the formula (13),
Figure BDA0003377271850000127
Figure BDA0003377271850000128
is represented by the formula (15),
Figure BDA0003377271850000129
Figure BDA00033772718500001210
Figure BDA00033772718500001211
is represented by the formula (14).
The probability that a typical user is associated with a GBS is
Figure BDA00033772718500001212
Wherein,
Figure BDA00033772718500001213
is a compound of the formula (13),
Figure BDA00033772718500001214
Figure BDA00033772718500001215
is a compound of the formula (13),
Figure BDA00033772718500001216
Figure BDA00033772718500001217
is represented by the formula (16).
When a typical user associates with a LOS/NLOS UAV, the PDF distribution of the distance distribution is as follows
Figure BDA00033772718500001218
When a typical user associates with a GBS, the PDF distribution of the distance distribution is as follows
Figure BDA00033772718500001219
Step seven: derivation of laplacian transform of interference to a typical user by other base stations when the user is associated with a drone or a ground base station
Figure BDA00033772718500001220
When a typical user is associated with a LOS/NLOS UAV, the Laplace transform of UAV layer interference is expressed as
Figure BDA0003377271850000131
Where s, ε ∈ { LOS, NLOS },
Figure BDA0003377271850000132
is expressed as
Figure BDA0003377271850000133
Wherein,
Figure BDA0003377271850000134
the derivation of the above equation is mainly obtained by the probability generation function of the poisson point process and the moment mother function of the gamma random variable, where μ represents an independent variable and will correspond to μ belowG,
Figure BDA0003377271850000135
When a typical user is associated with a GBS, the Laplace transform of UAV layer interference is expressed as
Figure BDA0003377271850000136
Figure BDA0003377271850000137
Is expressed as
Figure BDA0003377271850000138
Wherein,
Figure BDA0003377271850000139
when a typical user is associated with a LOS/NLOS UAV, the Laplace transform of GBS layer interference is expressed as
Figure BDA00033772718500001310
Wherein,
Figure BDA00033772718500001311
when a typical user is associated with GBS, the laplace transform of GBS-layer interference is expressed as
Figure BDA00033772718500001312
Wherein, ω isG(r)＝r。
Step eight: and deducing an expression of the SINR coverage rate when the typical user is associated with the unmanned aerial vehicle or the ground base station according to the SINR analyzed in the step five and the Laplace transform of the interference in the step seven.
SINR coverage can be defined as the probability that a typical user can successfully transmit a signal under a certain SINR threshold, and can be expressed as
Figure BDA0003377271850000141
When a typical user is associated with GBS, SINR coverage may be expressed as
Figure BDA0003377271850000142
Wherein,
Figure BDA0003377271850000143
the above formula is mainly introduced through Alzers' sAnd (6) obtaining the theory derivation.
When the typical user is associated with the LOS/NLOS UAV layer, according to the NOMA decoding strategy, considering that the typical user is two cases, namely a near user and a far user, SINR coverage analysis is separately performed on the typical user of the two cases.
Near user case, i.e. rU,0＜rfThe steps for a typical user to successfully decode his own information are as follows:
a typical user first decodes information for a fixed user served by the same UAV.
Through the SIC process, a typical user decodes his own information.
Thus, in the case of near users, SINR coverage may be expressed as
Figure BDA0003377271850000144
Wherein, Tf,TtRespectively, the SINR thresholds for fixed users and typical users.
The typical user is a near user, and satisfies am-anTfWhen the SINR coverage is greater than or equal to 0, the SINR coverage may be represented as:
Figure BDA0003377271850000145
wherein,
Figure BDA0003377271850000146
when a is not satisfiedm-anTfUnder the condition of not less than 0, the content of the organic solvent is,
Figure BDA0003377271850000147
far user case, i.e. rU,0＞rfA typical user can successfully decode its own information by treating the information of the fixed user as noise. Thus, for the far user case, a is satisfiedm-anTtWhen the SINR coverage is greater than or equal to 0, the SINR coverage may be represented as:
Figure BDA0003377271850000148
wherein,
Figure BDA0003377271850000149
when a is not satisfiedm-anTtUnder the condition of not less than 0, the content of the organic solvent is,
Figure BDA00033772718500001410
when a typical user is associated with the GBS layer, the SINR coverage of the typical user can be expressed as
Figure BDA00033772718500001411
Step nine: and (6) ending.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (10)

1. A NOMA-enhanced unmanned aerial vehicle auxiliary modeling analysis method is characterized by specifically comprising the following steps:
s1: modeling a NOMA enhanced unmanned aerial vehicle auxiliary ground base station scene;
s2: selecting appropriate large-scale fading and small-scale fading models of the unmanned aerial vehicle and the ground base station for modeling;
s3: calculating the average received power obtained when the user associates the unmanned aerial vehicle or the ground base station by adopting the strongest average received power association criterion;
s4: considering a typical user, when the typical user is associated with an unmanned aerial vehicle or a ground base station, analyzing the SINR of the typical user;
s5: deducing the distance distribution between a typical user and two layers of base stations, and calculating the probability of associating the two layers of base stations;
s6: deducing Laplace transformation of interference of other base stations to the typical user when the typical user is associated with an unmanned aerial vehicle or a ground base station;
s7: and deducing the SINR coverage rate when the typical user is associated with the unmanned aerial vehicle or the ground base station according to the SINR analyzed in the step S4 and the Laplace transform of the interference in the step S6.
2. The method for unmanned aerial vehicle assisted modeling analysis according to claim 1, wherein in step S1, modeling the NOMA enhanced unmanned aerial vehicle assisted ground base station scenario is: distribution obeying density lambda of unmanned aerial vehicle and ground base stationUAnd λGHomogeneous poisson point process, power PUAnd PGAnd the height H of the unmanned aerial vehicle, the ground base station is provided with M antennae, and signals are sent to N users through the same resource block.
3. The unmanned aerial vehicle assisted modeling analysis method according to claim 2, wherein step S2 specifically includes: the probability of an air-to-ground line of sight (LOS) link between the unmanned aerial vehicle and the user is approximated as:
Figure FDA0003377271840000011
wherein,
Figure FDA0003377271840000012
is the elevation angle, b, c are specific constants depending on the environment, r is the horizontal distance between the drone and a typical user; the probability of a non-line-of-sight (NLOS) link between a drone and a typical user is
Figure FDA0003377271840000013
Large scale fading, using a transmission path loss model combining line-of-sight and non-line-of-sight, the transmission path loss of the link between the drone and the user is expressed as:
Figure FDA0003377271840000014
where s is the LOS, NLOS, L and N represent LOS and NLOS,
Figure FDA0003377271840000015
path LOSs exponent, η, representing LOS and NLOS links between drone and userL,ηNIs an additional loss parameter; thus, it is denoted h for small scale fading between drone and userL,hNWith a obedience parameter of Γ (N)L,1/NL) And Γ (N)N,1/NN) Gamma distribution of (1), NL,NNIs a Nakagami fading parameter;
in the terrestrial base station layer, large-scale fading between the terrestrial base station and the user is expressed as
Figure FDA0003377271840000021
ηG,αGRespectively representing an additional loss parameter and a path loss index; since the GBS is equipped with multiple antennas, users connected to the ground base station will obtain large-scale antenna gain G0M-N + 1; the small scale fading between a typical user and the serving base station is denoted as hG,0The small-scale fading between a typical user and a serving base station is denoted as h, subject to a gamma distribution with parameter Γ (M-N +1,1)G,iObey a gamma distribution with parameter Γ (N, 1).
4. The unmanned aerial vehicle assisted modeling analysis method of claim 3, wherein step S3 specifically comprises: using the strongest average received power association criterion, i.e. assuming that a typical user is associated with the base station providing the strongest long-term average received power in each layer;
1) average received power P obtained by user when connecting to unmanned aerial vehicler,UIs composed of
Figure FDA0003377271840000022
Wherein, PUFor transmission power of unmanned aerial vehicle, riDistance of the nearest base station from typical user in the unmanned plane layer, anA factor is collected for the power of the user,
Figure FDA0003377271840000029
denotes path loss, i denotes the ith base station, phiURepresenting that the unmanned aerial vehicle obeys the homogeneous poisson point process;
2) average receiving power of a ground base station layer by adopting MIMO; average received power P obtained by user when connecting to ground base stationr,GIs shown as
Figure FDA0003377271840000023
Wherein, PGIs the transmission power of the ground base station, riBase station closest to typical user in ground base station layer, Li,GRepresents the path loss, phiGThe representation shows that the ground base station obeys the homogeneous poisson point process.
5. The unmanned aerial vehicle assisted modeling analysis method of claim 4, wherein step S4 specifically comprises:
1) ground base station layer transmission supporting MIMO;
when the typical user is at a distance rG,0When connected to a ground base station, its SINR is expressed as
Figure FDA0003377271840000024
Wherein,
Figure FDA0003377271840000025
representing the interference of the terrestrial base station layer,
Figure FDA0003377271840000026
representing the interference of the unmanned plane layer, epsilon ∈ { LOS, NLOS }, G0、hU,i、
Figure FDA0003377271840000027
Respectively representing effective antenna gain, small-scale fading gain and path loss h of a link between the ith base station and a typical user in the unmanned plane layerG,i、
Figure FDA0003377271840000028
Respectively, the small-scale fading gain and path loss of the link between the ith base station and the typical user in the ground base station layer, q represents the base station associated with the typical user,
Figure FDA0003377271840000031
indicating that the base station in the drone is subject to the poisson point procedure for LOS/NLOS,
Figure FDA0003377271840000032
is the ground base station layer thermal noise power;
2) supporting UAV layer transmission of NOMA;
in the unmanned plane layer, under the condition of not losing generality, each unmanned plane is considered to be associated with one user in the previous round of user association process; the distance between the associated user and the connected drone is assumed to be the same, and may be any value, denoted rf(ii) a Applying a successive interference cancellation operation at a near user side; it is determined whether the typical user is a near user or a far user, including a near user scenario and a far user scenario.
6. The unmanned aerial vehicle assisted modeling analysis method of claim 5, wherein in step S4,
(ii) a near user scenario: when the typical user is a near user, i.e. the distance from the typical user to the base station is less thanAssociating the distance of the user from the base station, i.e. rU,0＜rfTherefore, a typical user will decode the information of the fixed user first, and the corresponding SINR expression is
Figure FDA0003377271840000033
Wherein, am,anRespectively representing the power distribution coefficients of far users and near users, and satisfying am＞anAnd am+an＝1，
Figure FDA0003377271840000034
Is the thermal noise power of the unmanned plane layer,
Figure FDA0003377271840000035
representing the interference at the level of the drone,
Figure FDA0003377271840000036
representing interference of a ground base station layer;
if the information of the fixed user is successfully decoded, the interference of the fixed user can be eliminated, the typical user can decode the information of the typical user, and the corresponding SINR expression is
Figure FDA0003377271840000037
For a fixed user served by the same unmanned aerial vehicle, namely a far user, the information of the fixed user can be directly decoded by the NOMA technology, while the information of a typical user is used as interference, so that the SINR expression of the fixed user is as follows
Figure FDA0003377271840000038
Remote user scenario: when the typical user is a far user, i.e. the typical user is farther away from the BS than the associationDistance of user to BS, i.e. rU,0＞rfFor the information of the typical user to be decoded first by the fixed user, the corresponding SINR expression is
Figure FDA0003377271840000039
If the information of the typical user is successfully decoded, the interference of the typical user can be eliminated, the fixed user can decode the information of the fixed user, and the corresponding SINR expression is
Figure FDA0003377271840000041
For a typical user served by the same ground base station, namely a far user, the information of the far user can be directly decoded by the NOMA technology, and the information of a fixed user is used as interference, so the SINR expression of the fixed user is as follows
Figure FDA0003377271840000042
7. The unmanned aerial vehicle assisted modeling analysis method of claim 5, wherein step S5 specifically comprises: the probability of at least one LOS/NLOS drone around a typical user is:
Figure FDA0003377271840000043
wherein,
Figure FDA0003377271840000044
λUdensity of the unmanned aerial vehicle layer;
at least one LOS/NLOS unmanned plane around a typical user, wherein the CCDF and PDF expressions of the distance are as follows:
CCDF:
Figure FDA0003377271840000045
PDF:
Figure FDA0003377271840000046
similarly, the CCDF and PDF expressions of the distance of at least one ground base station around a typical user are:
CCDF:
Figure FDA0003377271840000047
PDF:
Figure FDA0003377271840000048
wherein λ isGIs the density of the ground base station;
definition of
Figure FDA0003377271840000049
The probability that a typical user is associated with a LOS/NLOS drone is
Figure FDA00033772718400000410
Wherein s 'and s are belonged to { LOS, NLOS }, and s' is not equal to s;
Figure FDA00033772718400000411
the probability that a typical user is associated with a terrestrial base station is
Figure FDA0003377271840000051
Wherein,
Figure FDA0003377271840000052
when a typical user associates with a LOS/NLOS drone, the PDF distribution of the distance distribution is as follows:
Figure FDA0003377271840000053
when a typical user associates with GBS, the PDF distribution of the distance distribution is as follows:
Figure FDA0003377271840000054
8. the unmanned aerial vehicle assisted modeling analysis method of claim 7, wherein step S6 specifically includes:
1) when a typical user is associated with a LOS/NLOS UAV, the Laplace transform of the drone layer interference is expressed as
Figure FDA0003377271840000055
Where s, ε ∈ { LOS, NLOS },
Figure FDA0003377271840000056
is expressed as
Figure FDA0003377271840000057
Wherein,
Figure FDA0003377271840000058
mu represents an argument, corresponding to mu belowG，
Figure FDA0003377271840000059
2) When a typical user is associated with a ground base station, the laplace transform of the UAV layer interference is expressed as
Figure FDA00033772718400000510
Figure FDA00033772718400000511
Is expressed as
Figure FDA00033772718400000512
Wherein,
Figure FDA00033772718400000513
3) when a typical user is associated with a LOS/NLOS UAV, the Laplace transform of GBS layer interference is expressed as
Figure FDA00033772718400000514
Wherein,
Figure FDA0003377271840000061
4) when a typical user is associated with GBS, the laplace transform of GBS-layer interference is expressed as
Figure FDA0003377271840000062
Wherein, ω isG(r)＝r。
9. The unmanned aerial vehicle assisted modeling analysis method of claim 8, wherein step S7 specifically includes: SINR coverage is defined as the probability that a typical user can successfully transmit a signal at a certain SINR threshold T, expressed as
Figure FDA0003377271840000063
1) When a typical user is associated with a terrestrial base station, the SINR coverage is expressed as
Figure FDA0003377271840000064
Wherein,
Figure FDA0003377271840000065
2) when the typical user is associated with the LOS/NLOS drone layer, according to the NOMA decoding strategy, considering that the typical user is two cases, namely a near user and a far user, SINR coverage analysis is separately performed on the typical user of the two cases.
10. The method for unmanned aerial vehicle assisted modeling analysis according to claim 9, wherein in step S7, SINR coverage analysis is performed for both near and far users:
(r) near user caseU,0＜rfThe steps for a typical user to successfully decode his own information are as follows:
a typical user first decodes information for fixed users served by the same UAV;
through the SIC process, a typical user decodes own information;
in the case of near users, the SINR coverage is expressed as
Figure FDA0003377271840000066
Wherein, Tf,TtSINR representing fixed and typical users, respectivelyA threshold value;
the typical user is a near user, and satisfies am-anTfWhen the condition is more than or equal to 0, the SINR coverage rate is expressed as:
Figure FDA0003377271840000067
wherein,
Figure FDA0003377271840000068
when a is not satisfiedm-anTfUnder the condition of not less than 0, the content of the organic solvent is,
Figure FDA0003377271840000069
② far user case, i.e. rU,0＞rfA typical user successfully decodes its own information by treating the information of the fixed user as noise; thus, for the far user case, a is satisfiedm-anTtWhen the condition is more than or equal to 0, the SINR coverage rate is expressed as:
Figure FDA0003377271840000071
wherein,
Figure FDA0003377271840000072
when a is not satisfiedm-anTtUnder the condition of not less than 0, the content of the organic solvent is,
Figure FDA0003377271840000073
when a typical user associates with a ground base station layer, the SINR coverage of the typical user is expressed as
Figure FDA0003377271840000074
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