CN115278697B - Industrial Internet of things beam optimization method for hardware damage - Google Patents
Industrial Internet of things beam optimization method for hardware damage Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
- H04W16/14—Spectrum sharing arrangements between different networks
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
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- H—ELECTRICITY
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- H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
- H04W16/24—Cell structures
- H04W16/28—Cell structures using beam steering
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- H—ELECTRICITY
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Abstract
The invention relates to a beam optimization method of an industrial Internet of things for hardware damage, and belongs to the field of Internet of things. The method comprises the following steps: s1: constructing a multi-layer heterogeneous industrial Internet of things transmission system model with multi-industrial sensor node spectrum resource sharing; s2: considering the characteristics of phase noise and distortion noise of a transceiver caused by imperfect hardware damage, meeting the constraint of maximum transmission power and the constraint of minimum transmission rate of a sensor node, and establishing the system total energy efficiency maximization problem of beam forming of a combined optimized macro base station and a femtocell base station; s3: converting the multivariable coupling and non-convex optimization problem which is difficult to solve and constructed in the step S2 into a deterministic and convex optimization problem by using a Buckel Bach method, a semi-definite relaxation method and a continuous convex approximation method; s4: and solving the convex optimization problem to obtain the optimal beamforming vector. Compared with the prior art, the invention has the advantages of saving energy of the system and protecting the main user.
Description
Technical Field
The invention belongs to the field of the Internet of things, and relates to an industrial Internet of things beam optimization method for hardware damage.
Background
With the rapid increase of the number of industrial devices and nodes, the shortage of industrial internet of things (IoT) spectrum resources and the limited quality of network transmission are caused. Therefore, the multi-layer heterogeneous industrial internet of things is a key technology for solving the problems, and the technology is used for sharing the spectrum resources of the existing main network by deploying low-power-consumption secondary internet of things nodes in the existing internet of things topological structure, so that the spectrum efficiency and the transmission quality of the whole network are greatly improved. However, the access of the new node can increase the interference to the existing sensor node of the internet of things, so how to design a better beam forming method in the environment, realize spectrum sharing and protect the transmission quality of different types of sensors at the same time, and is an entirely new challenge facing the next generation of the internet of things.
The existing industrial internet of things beam forming method is concentrated on performance optimization of a single sensing network, and ignores multi-layer heterogeneous network scenes; meanwhile, due to the influence of hardware damage caused by distortion noise and phase noise, the received signal is distorted due to beam forming under the condition of perfect hardware in the traditional case, and meanwhile, the system performance is not optimal. Therefore, the method for effectively designing the optimal beam forming of the multi-layer industrial Internet of things under the condition of imperfect hardware damage has very important engineering application value.
Disclosure of Invention
In view of the above, the present invention aims to provide an industrial internet of things beam optimization method for hardware damage, which considers the influence of residual hardware damage at a transceiver, ensures the communication quality of each internet of things node, effectively reduces the interference power to a main user node, and improves the energy efficiency of the system.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a hardware damage-oriented industrial Internet of things beam optimization method comprises the following steps:
S1: constructing a multi-layer heterogeneous industrial Internet of things transmission system model with multi-industrial sensor node spectrum resource sharing;
S2: considering the characteristics of phase noise and distortion noise of a transceiver caused by imperfect hardware damage, meeting the constraint of maximum transmission power and the constraint of minimum transmission rate of a sensor node, and establishing the system total energy efficiency maximization problem of beam forming of a combined optimized macro base station and a femtocell base station;
S3: converting the multivariable coupling and non-convex optimization problem which is difficult to solve and constructed in the step S2 into a deterministic and convex optimization problem by using a Buckel Bach method, a semi-definite relaxation method and a continuous convex approximation method;
S4: and directly solving the convex optimization problem by using a CVX tool box to obtain the optimal beamforming vector.
Further, in step S1, the constructed multi-layer heterogeneous industrial internet of things transmission system model specifically includes: assume that there are one macrocell base station and N femtocell base stations in the network, M macrocell industrial internet of things devices, N femtocell networks, and K n industrial internet of things devices in each femtocell network, where, The number of the antennas of the macro base station is N M, and the number of the antennas of each femto base station is N F; the channel vector from the macro base station to the macro cellular industrial Internet of things equipment m is h m, the channel vector from the nth femtocell base station to the macro cellular industrial Internet of things equipment m is g n,m, and the channel vector from the nth femtocell base station to the kth femtocell industrial Internet of things equipment is h n,nk; the channel vector from the p-th femtocell base station to the N-th femtocell network at the k-position of industrial Internet of things equipment is h p,nk, wherein p is more than or equal to 1 and less than or equal to N, and p is not equal to N; the channel vector from the macro base station to the n-th femtocell network at the industrial Internet of things device k is f n,k.
Further, in step S2, a system total energy efficiency maximization problem of beam forming of the joint optimization macro base station and the femto base station is established, and the expression is:
Wherein R m represents the transmission rate of the macro-cell industrial Internet of things device m, R n,k represents the data rate of the femto-cell industrial Internet of things device k in the nth femto cell, P M represents the total power consumption of the macro-cell, P F represents the total power consumption of the femto-cell, P C represents the total circuit power consumption value of the system, ζ represents the base station power amplification factor, W m represents the beam forming vector from the macro base station to the macro base station industrial Internet of things device m, Representing distortion noise of macro base station, V n,k represents beam forming vector from nth femtocell base station to kth femtocell industrial Internet of things equipment,/>Representing distortion noise of the femtocell base station n, P max represents a maximum transmit power threshold of the macrocell base station,/>Representing the maximum transmission power threshold of the nth femtocell base station, and I m represents the interference power threshold of the macrocell industrial Internet of things equipment,/>Representing a maximum cross-layer interference power threshold allowed by an mth macrocell industrial internet of things device receiver,/>Representing a minimum transmission rate threshold for a kth femtocell industrial internet of things device in an nth femtocell network; c 1 represents the maximum transmit power limit of the macrocell base station, C 2 represents the maximum power limit of the nth femtocell base station, C 3 represents the cross-layer interference power constraint of each macrocell industrial internet of things device, and C 4 represents the quality of service of each femtocell industrial internet of things device.
Further, in step S2, the calculation expression of the total network energy efficiency η E is:
Wherein R m represents the transmission rate of the macro-cell industrial Internet of things device m, and the expression is R m＝log2(1+rm), wherein R m represents the received signal-to-noise ratio of the macro-cell industrial Internet of things device m, and the expression is Wherein/>Equivalent channel vector representing industrial Internet of things device m from macro base station to macro cellular network, expressed as/>Within time slot t,/>Where θ (t) represents the phase noise of the macro base station antenna during the time slot t, and the expression is θ (t) =θ (t-1) +δ θ (t),/>Θ represents the phase noise rise variance at the macro base station, T s represents the symbol interval, c θ represents the oscillator coefficient at the macro base station, f θ represents the carrier frequency at the macro base station; mu m (t) which represents the phase noise of the macrocell base station m antenna in the time slot t, the expression is/> Mu m denotes the phase noise rise variance at the macrocell internet of things device m,Representing oscillator coefficients at a macro cellular internet of things device,/>Representing a carrier frequency at a macro cellular internet of things device; n m represents the sum of inter-cell interference and cross-layer interference, expressed as: /(I)Wherein the method comprises the steps ofEquivalent channel vector from femtocell base station n to macrocell industrial Internet of things device m is expressed asWithin time slot t,/>Wherein phi n (t) represents the phase noise of the nth femtocell base station antenna in the time slot t,/>Phi n represents the phase noise rise variance at the femtocell base station n,/>Representing the oscillator coefficient at femtocell base station n,/>Representing the carrier frequency at the femtocell base station n; d m represents distortion noise power of m-th macro-cellular industrial Internet of things equipment, and the expression isWherein/>Representing distortion noise of macro base station,/>Distortion noise representing femtocell base station n,/>Representing distortion noise variance of macro-cellular industrial internet of things device m,/>Representing a variance of amplified thermal noise at a macro cellular industrial internet of things device m;
R n,k＝log2(1+rn,k) represents the data rate of the femtocell industrial internet of things device k in the nth femtocell, wherein R n,k represents the received signal-to-noise ratio of the femtocell industrial internet of things device k in the nth femtocell, expressed as V n,k denotes the phase noise of the femtocell internet of things device k in the femtocell base station n,/>An equivalent channel vector representing the number of channels in the femtocell n from the femtocell base station n to the femtocell industrial internet of things device k is expressed asIn time slot t,/>Wherein v n,k (t) represents the phase noise of the femtocell internet of things device k in the time slot t in the femtocell base station n, and the expression is/> Representing the variance of the phase noise rise of the femtocell internet of things device k in the femtocell base station n,/>Representing the oscillator coefficient at femtocell internet of things device k in femtocell base station n,/>Representing a carrier frequency at a femtocell internet of things device k in a femtocell base station n; n n,k represents the sum of the intra-cell interference powers expressed as/>Where w m denotes the beam vector from the macro base station to the macro cellular internet of things device m,/>Equivalent channel vector representing femtocell industrial internet of things device k from macro base station to femtocell n, expressed as/>Within time slot t,/>D n,k represents distortion noise power of kth femtocell industrial Internet of things device in femtocell n,/>Representing the variance of amplified thermal noise at industrial internet of things device k in the femtocell network n.
Further, in step S3, the non-convex optimization problem is converted into a convex optimization problem by using the butcher-baz method, the semi-definite relaxation method and the continuous convex approximation method, and the converted expression is:
C9:(3),(9),(10)
Wherein, Tr (·) represents the trace of the matrix, S l represents the square of the first leading diagonal element being 1 and the remaining elements being 0, S d represents the square of the d-th leading diagonal element being 1 and the remaining elements being 0, η d (·) represents the distortion noise power of the transmit signal at the d-th antenna, η l (·) represents the distortion noise power of the transmit signal at the l-th antenna, e n,d、fl is an introduced auxiliary variable; /(I)Wherein, Wherein the method comprises the steps of Y n denotes the distortion noise covariance matrix of femtocell base station n, y p denotes the distortion noise covariance matrix of femtocell base station p, Λ denotes the distortion noise covariance matrix of macrocell base station,/>Representing a distortion noise variance of the femtocell industrial internet of things device k in the femtocell n;
wherein/> Kappa 3 represents model parameters of distortion noise;
Wherein,
A n,k、bn,k、cn,k is a relaxation variable related to femtocell internet of things device k at femtocell base station n, a m、bm、cm is a relaxation variable at macro base station,/>Last iteration of b n,k and c n,k, respectively,/> The previous iteration of b m and c m, respectively.
The invention has the beneficial effects that: the invention achieves good balance between the overall energy efficiency and the capability of overcoming the influence of hardware damage after comprehensively considering the service quality requirement of the industrial Internet of things and the maximum transmitting power of the base station. Compared with the prior art, the invention has the advantages of saving energy of the system and protecting the main user
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 objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
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For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in the following preferred detail with reference to the accompanying drawings, in which:
FIG. 1 is a model diagram of a transmission system of a multilayer heterogeneous industrial Internet of things constructed according to an embodiment of the invention;
FIG. 2 is a flow chart of the beam optimization method of the industrial Internet of things for hardware damage according to the invention;
FIG. 3 is an energy efficiency convergence diagram of the method of the present invention;
fig. 4 is a graph of the robust performance of the method of the present invention.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
Referring to fig. 1 to 4, the present invention provides an industrial internet of things beam optimization method for hardware damage in consideration of phase noise and distortion noise existing in an industrial internet of things, and for a beam forming algorithm suitable for a multi-cell downlink heterogeneous internet of things, a multi-cell downlink multi-input single-output heterogeneous industrial internet of things network is considered, and beam forming vectors of a macro base station and a femto base station are jointly optimized to achieve the purpose of maximizing femto and macro cell energy efficiency. Constructing a multi-layer heterogeneous industrial Internet of things transmission system model with multiple industrial sensor spectrum resource sharing, analyzing the characteristics of phase noise and distortion noise of a transceiver caused by imperfect hardware damage, meeting the constraint of maximum transmission power and the constraint of minimum transmission rate of sensor nodes, and establishing the system total energy efficiency maximization problem of beam forming of a combined optimized main base station and a femtocell base station; and converting the non-convex optimization problem into a deterministic convex optimization form by using a Buckel Bach method, a semi-definite relaxation method and a continuous convex approximation method, and finally obtaining the solution of the optimal beamforming vector by using a convex optimization technology. Compared with the prior art, the invention has the advantages of saving energy of the system and protecting the main user.
As shown in fig. 1, in the network of this embodiment, there are one macrocell base station and N femtocell base stations, where there are 3 macrocell internet of things devices and N femtocell internet of things devices. The macrocell base station serving a macrocell internet of things network and the nth femtocell base station serving n femtocell internet of things networks, whereinAndAssuming that in order to improve spectrum efficiency, the enterprise adopts a bottom mode of sharing spectrum resources with the femtocell internet of things equipment, and protects the service quality of each macrocell internet of things equipment by throttling the interference power of the femtocell base station to be lower than a certain threshold value, so that under perfect channel state information, the optimization problem can be expressed by jointly optimizing the total energy efficiency of a system for beamforming of the macrocell base station and the femtocell base station:
Wherein R m represents the transmission rate of the macro-cell industrial Internet of things device m, R n,k represents the data rate of the femto-cell industrial Internet of things device k in the nth femto cell, P M represents the total power consumption of the macro cell, P F represents the total power consumption of the femto cell, P C represents the total circuit power consumption value of the system, W m represents the beamforming vector from the macro base station to the macro base station industrial Internet of things device m, Representing distortion noise of macro base station, V n,k represents beam forming vector from nth femtocell base station to kth femtocell industrial Internet of things equipment,/>Representing the distortion noise of the femtocell base station n, P max represents the maximum transmit power threshold of the macrocell base station,Indicating the maximum transmit power threshold of the nth femtocell base station, I m indicating the macrocell internet of things device interference power threshold,Representing maximum interference power threshold of macro-cellular internet of things equipment,/>Representing a minimum rate threshold of k femtocell internet of things devices in the nth femtocell, C 1 represents a maximum transmit power limit of the macrocell base station, C 2 represents a maximum power limit of the nth femtocell base station, C 3 represents a cross-layer interference power constraint of each macrocell internet of things device, and C 4 represents a quality of service of each femtocell internet of things device.
Since P1 is a non-convex optimization problem, the problem is difficult to solve. Therefore, there is a need to develop a suboptimal solution to the problem. First, the problem is converted into a usable form by variable substitution:
Wherein r m represents the received signal-to-noise ratio of the macro-cell industrial Internet of things device m, r n,k represents the received signal-to-noise ratio of the femtocell industrial Internet of things device k in the nth femtocell, and the received signal-to-noise ratio is defined
Wherein,Representing an equivalent channel vector in femtocell n from femtocell base station n to femtocell industrial internet of things device k,/>Equivalent channel vector representing macro base station to industrial Internet of things device m in macro cellular network,/>Equivalent channel vector representing femtocell base station n to macrocell industrial internet of things device m,/>Representing an equivalent channel vector from the macro base station to the femtocell industrial internet of things device k in the femtocell n.
Thus, it can be derived that Wherein y n represents the distortion noise covariance matrix of femtocell base station n, y p represents the distortion noise covariance matrix of femtocell base station p, Λ represents the distortion noise covariance matrix of macrocell base station,/>Representing distortion noise variance of macro-cellular industrial internet of things device m,/>Representing the distortion noise variance of the femtocell industrial internet of things device k in the femtocell n.
Thus, R m,Rn,k,PM,PF and I m can be restated as:
according to P1 and (1), the problem can be translated into:
C6:Rank(Wm)＝Rank(Vn,k)＝1
the fractional order objective function described above can be converted into based on the Buckel Bach method:
Where η E is an energy efficiency auxiliary variable.
To treat gamma n and lambda, auxiliary variables are introducedE n,d and f l, and thus (1) can be restated as:
where κ 3 represents the model parameters of the distortion noise.
Define the variable set Σ= { B n,B,en,d,fl }, from P2, P3 and (2), we get:
Due to the sum of the objective functions The problem P4 is still non-convex and therefore requires further relaxation using variable change techniques:
Since (4) and (5) are non-convex, introducing the relaxation variables a n,k、bn,k and c n,k based on the exponential substitution method, then (4) can be converted into:
if the constraint is a convex function or less than or equal to a concave function, then the constraint is a convex constraint, so equation (6) is convex and equation (7) is non-convex. Definition of the definition And/>The previous iteration of b n,k and c n,k, respectively, based on the Taylor series expansion, equation (7) can be restated as
Formula (4) can be restated as:
Also, after the introduction of the relaxation variables a m、bm and c m, formula (5) can be restated as:
Wherein, And/>For the iterations before b m and c m, respectively, an optimization variable set is defined:
Π＝{rm,rn,k,αm,βm,am,bm,cm,αn,k,βn,k,an,k,bn,k,cn,k}
according to formulas (3) to (10), P4 can be restated as:
C9:(3),(9),(10)
Since there is a rank one constraint C 6, P5 is still non-convex, removing rank one constraint C 6 using semi-definite relaxation can transform the problem into a convex form, and then P5 can be restated as:
C9:(3),(9),(10)
since P6 is a convex optimization problem, it can be solved directly using the CVX toolbox. The iterative beam forming algorithm based on energy efficiency is shown in fig. 2, and specifically comprises the following steps:
s1: initializing system parameters including the number of macro-cellular industrial internet of things devices Number of femtocell networks/>The number of industrial internet of things devices per femtocell network/> The antenna number N M of the macro base station, the antenna number N F of each femto cell base station, the total circuit power consumption value P C of the system, the base station power amplification coefficient zeta, the channel vector h m from the macro base station to the macro cell industrial Internet of things equipment m, the channel vector g n,m from the nth femto cell base station to the macro cell industrial Internet of things equipment m, the channel vector h n,nk from the nth femto cell base station to the kth femto cell industrial Internet of things equipment, the channel vector h p,nk from the (1.ltoreq.p.ltoreq.N, p.noteq.n) th femto cell base station to the industrial Internet of things equipment k in the nth femto cell network, the channel vector f n,k from the macro base station to the industrial Internet of things equipment k in the nth femto cell network, the maximum transmitting power threshold P max of the macro base station, the maximum transmitting power threshold/>Maximum cross-layer interference power threshold/>, allowed by mth macrocell industrial internet of things device receiverMinimum transmission rate requirement threshold/>, of industrial Internet of things device k in nth femtocell network
S2: and (3) carrying out iteration initialization, wherein the iteration initialization comprises a maximum iteration number X max, an iteration algorithm convergence precision epsilon, an initial iteration number X and an initial energy efficiency coefficient eta E.
S3: judging whether the current iteration number is larger than the maximum iteration number, if so, ending. Otherwise, S4 is entered.
S4: judging whether the total energy efficiency of the network is converged, if so, ending. Otherwise, S5 is entered.
S5: and obtaining a beam forming vector W m from the macro base station to the macro cellular industrial Internet of things equipment m and a beam forming vector V n,k from the nth femtocell base station to the kth femtocell industrial Internet of things equipment, adding one to the iteration times, calculating the total energy efficiency of the network of the xth time, and entering S3.
The method comprises the following steps: according toJudging whether the obtained network total energy efficiency is converged, wherein r m (x) represents the received signal-to-noise ratio of the mth iteration of the macro-cell industrial Internet of things device m, r n,k (x) represents the received signal-to-noise ratio of the mth iteration of the femtocell industrial Internet of things device k, and eta E (x-1) represents the network total energy efficiency of the (x-1) th iteration. After the iteration number is added by one, the network total energy efficiency of the xth time is according to/>And (5) calculating.
Simulation experiment: the application effect of the present invention will be described in detail with reference to simulation.
1) Simulation conditions
It is assumed that there is one macrocell and two femtocells in the system, each macrocell having two users in the network and two users in each femtocell in the network. The radii of the macro-and femto-cells are 500 and 20 meters respectively, and the minimum distance between different femto-cells is 40 meters. The channel fading model includes large-scale fading and small-scale fading, in which the path loss index is 3. Other guideline parameters are given in table 1:
Table 1 simulation parameter table
2) Simulation results
In this example, fig. 3 shows an energy efficiency convergence diagram of the iterative method of this example. Fig. 4 shows a robustness map of the iterative method of the present example. Fig. 3 shows that the method of the present invention can converge within 8 iterations, so that it is proved that the method of the present invention has a better convergence performance, and as the number N F of femto antennas increases, the energy efficiency increases, because as the number N F of femto antennas increases, the beamforming vector can provide an additional degree of spatial freedom, and the method of the present invention reveals the phenomenon. Fig. 4 shows that as the maximum transmission power of the femtocell base station increases, the interference power I m at the macro user receiver end of all methods is larger, and other methods except the method finally exceed the interference threshold to generate interruption. The experimental results of fig. 3 and fig. 4 show that the method of the invention ensures better convergence, also ensures the service quality of the femtocell users, and has good robustness.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (1)
1. The industrial Internet of things beam optimization method for hardware damage is characterized by comprising the following steps of:
S1: constructing a multi-layer heterogeneous industrial Internet of things transmission system model with multi-industrial sensor node spectrum resource sharing;
S2: considering the characteristics of phase noise and distortion noise of a transceiver caused by imperfect hardware damage, meeting the constraint of maximum transmission power and the constraint of minimum transmission rate of a sensor node, and establishing the system total energy efficiency maximization problem of beam forming of a combined optimized macro base station and a femtocell base station;
S3: converting the non-convex optimization problem constructed in the step S2 into a convex optimization problem by using a Buckel Bach method, a semi-definite relaxation method and a continuous convex approximation method;
S4: solving a convex optimization problem to obtain an optimal beam forming vector;
In step S1, the built multi-layer heterogeneous industrial internet of things transmission system model specifically includes: assume that there are one macrocell base station and N femtocell base stations in the network, M macrocell industrial internet of things devices, N femtocell networks, and K n industrial internet of things devices in each femtocell network, where, The number of the antennas of the macro base station is N M, and the number of the antennas of each femto base station is N F; the channel vector from the macro base station to the macro cellular industrial Internet of things equipment m is h m, the channel vector from the nth femtocell base station to the macro cellular industrial Internet of things equipment m is g n,m, and the channel vector from the nth femtocell base station to the kth femtocell industrial Internet of things equipment is h n,nk; the channel vector from the p-th femtocell base station to the N-th femtocell network at the k-position of industrial Internet of things equipment is h p,nk, wherein p is more than or equal to 1 and less than or equal to N, and p is not equal to N; the channel vector from the macro base station to the n-th femtocell network at the k-position of the industrial Internet of things equipment is f n,k;
in step S2, a system total energy efficiency maximization problem of beam forming of the combined optimized macro base station and the femtocell base station is established, and the expression is:
P1：
s.t.C1:
C2:
C3:
C4:
Wherein R m represents the transmission rate of the macro-cell industrial Internet of things device m, R n,k represents the data rate of the femto-cell industrial Internet of things device k in the nth femto cell, P M represents the total power consumption of the macro-cell, P F represents the total power consumption of the femto-cell, P C represents the total circuit power consumption value of the system, ζ represents the base station power amplification factor, W m represents the beam forming vector from the macro base station to the macro base station industrial Internet of things device m, Representing distortion noise of macro base station, V n,k represents beam forming vector from nth femtocell base station to kth femtocell industrial Internet of things equipment,/>Representing distortion noise of the femtocell base station n, P max represents a maximum transmit power threshold of the macrocell base station,/>Representing the maximum transmission power threshold of the nth femtocell base station, and I m represents the interference power threshold of the macrocell industrial Internet of things equipment,/>Representing a maximum cross-layer interference power threshold allowed by an mth macrocell industrial internet of things device receiver,/>Representing a minimum transmission rate threshold for a kth femtocell industrial internet of things device in an nth femtocell network; c 1 represents the maximum transmit power limit of the macrocell base station, C 2 represents the maximum power limit of the nth femtocell base station, C 3 represents the cross-layer interference power constraint of each macrocell industrial internet of things device, and C 4 represents the quality of service of each femtocell industrial internet of things device;
In step S2, the calculation expression of the total network energy efficiency η E is:
Wherein R m represents the transmission rate of the macro-cell industrial Internet of things device m, and the expression is R m＝log2(1+rm), wherein R m represents the received signal-to-noise ratio of the macro-cell industrial Internet of things device m, and the expression is Wherein/>Equivalent channel vector representing industrial Internet of things device m from macro base station to macro cellular network, expressed as/>In the time-slot t of which the time-slot is a time-slot,Where θ (t) represents the phase noise of the macro base station antenna during the time slot t, and the expression is θ (t) =θ (t-1) +δ θ (t),/>Θ represents the phase noise rise variance at the macro base station, T s represents the symbol interval, c θ represents the oscillator coefficient at the macro base station, f θ represents the carrier frequency at the macro base station; mu m (t) which represents the phase noise of the macrocell base station m antenna in the time slot t, the expression is/> Mu m denotes the phase noise rise variance at the macrocell internet of things device m,Representing oscillator coefficients at a macro cellular internet of things device,/>Representing a carrier frequency at a macro cellular internet of things device; n m represents the sum of inter-cell interference and cross-layer interference, expressed as: /(I)Wherein the method comprises the steps ofEquivalent channel vector from femtocell base station n to macrocell industrial Internet of things device m is expressed asWithin time slot t,/>Wherein phi n (t) represents the phase noise of the nth femtocell base station antenna in the time slot t,/>Phi n represents the phase noise rise variance at the femtocell base station n,/>Representing the oscillator coefficient at femtocell base station n,/>Representing the carrier frequency at the femtocell base station n; d m represents distortion noise power of m-th macro-cellular industrial Internet of things equipment, and the expression isWherein/>Representing distortion noise of macro base station,/>Distortion noise representing femtocell base station n,/>Representing distortion noise variance of macro-cellular industrial internet of things device m,/>Representing a variance of amplified thermal noise at a macro cellular industrial internet of things device m;
R n,k＝log2(1+rn,k) represents the data rate of the femtocell industrial internet of things device k in the nth femtocell, wherein R n,k represents the received signal-to-noise ratio of the femtocell industrial internet of things device k in the nth femtocell, expressed as V n,k denotes the phase noise of the femtocell internet of things device k in the femtocell base station n,/>An equivalent channel vector representing the number of channels in the femtocell n from the femtocell base station n to the femtocell industrial internet of things device k is expressed asIn time slot t,/>Wherein v n,k (t) represents the phase noise of the femtocell internet of things device k in the time slot t in the femtocell base station n, and the expression is/> Representing the variance of the phase noise rise of the femtocell internet of things device k in the femtocell base station n,/>Representing the oscillator coefficient at femtocell internet of things device k in femtocell base station n,/>Representing a carrier frequency at a femtocell internet of things device k in a femtocell base station n; n n,k represents the sum of the intra-cell interference powers expressed as/>Where w m denotes the beam vector from the macro base station to the macro cellular internet of things device m,/>Equivalent channel vector representing femtocell industrial internet of things device k from macro base station to femtocell n, expressed as/>Within time slot t,/>D n,k represents distortion noise power of kth femtocell industrial Internet of things device in femtocell n,/>Representing a variance of amplified thermal noise at industrial internet of things device k in femtocell network n;
in step S3, the non-convex optimization problem is converted into a convex optimization problem by using the butcher-Bach method, the semi-definite relaxation method and the continuous convex approximation method, and the converted expression is:
P6:
C8:ηl(fl)≤[B]l,l,
C9:(3),(9),(10)
Wherein, Tr (·) represents the trace of the matrix, S l represents the matrix with the first leading diagonal element of 1 and the remaining elements of 0; s d represents a matrix in which the d-th leading diagonal element is 1 and the remaining elements are 0; η d (·) represents the distortion noise power of the transmit signal at the d-th antenna, η l (·) represents the distortion noise power of the transmit signal at the l-th antenna, e n,d、fl is an introduced auxiliary variable; /(I)Wherein, Wherein the method comprises the steps of Y n denotes the distortion noise covariance matrix of femtocell base station n, y p denotes the distortion noise covariance matrix of femtocell base station p, Λ denotes the distortion noise covariance matrix of macrocell base station,/>Representing a distortion noise variance of the femtocell industrial internet of things device k in the femtocell n; wherein/> Kappa 3 represents model parameters of distortion noise;
Wherein, A n,k、bn,k、cn,k is a relaxation variable related to femtocell internet of things device k at femtocell base station n, a m、bm、cm is a relaxation variable at macro base station,/>Last iteration of b n,k and c n,k, respectively,/>The previous iteration of b m and c m, respectively.
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