CN114501480B - User association and beam forming combined multi-objective optimization method in millimeter wave distributed network - Google Patents

User association and beam forming combined multi-objective optimization method in millimeter wave distributed network Download PDF

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CN114501480B
CN114501480B CN202210313790.3A CN202210313790A CN114501480B CN 114501480 B CN114501480 B CN 114501480B CN 202210313790 A CN202210313790 A CN 202210313790A CN 114501480 B CN114501480 B CN 114501480B
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CN114501480A (en
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朱鹏程
张震
钱宇
李佳珉
尤肖虎
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Southeast University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W16/00Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/22Traffic simulation tools or models
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W16/00Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/24Cell structures
    • H04W16/28Cell structures using beam steering
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W24/00Supervisory, monitoring or testing arrangements
    • H04W24/02Arrangements for optimising operational condition
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W28/00Network traffic management; Network resource management
    • H04W28/16Central resource management; Negotiation of resources or communication parameters, e.g. negotiating bandwidth or QoS [Quality of Service]
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W28/00Network traffic management; Network resource management
    • H04W28/16Central resource management; Negotiation of resources or communication parameters, e.g. negotiating bandwidth or QoS [Quality of Service]
    • H04W28/18Negotiating wireless communication parameters
    • H04W28/20Negotiating bandwidth
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00Reducing energy consumption in communication networks
    • Y02D30/70Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a user association and beam forming combined multi-objective optimization method in a millimeter wave distributed network, which comprises the following steps: step S1: establishing a mathematical model based on a distributed antenna network technology in a millimeter wave frequency band; step S2: determining a plurality of optimization targets and determining weights of the optimization targets through fuzzy logic; step S3: establishing a mathematical model of the joint optimization problem, and determining an objective function and constraint conditions of the mathematical model; step S4: and (3) solving the optimization problem proposed in the step (S3) by adopting a fuzzy logic guided gene extension genetic algorithm. The invention can effectively balance and optimize the throughput, the end-to-end delay and the load balance of the communication system through effectively adjusting the user association and the beam forming.

Description

User association and beam forming combined multi-objective optimization method in millimeter wave distributed network
Technical Field
The invention relates to the technical field of wireless communication, in particular to a user association and beam forming combined multi-objective optimization method in a millimeter wave distributed network.
Background
In recent years, with the development of the age, the demand for wireless communication is increasing, and this demand is embodied in various aspects of network throughput, network delay, reliability, mass connection, and the like. In order to meet new requirements of the era on wireless communication technology, millimeter wave transmission technology is attracting attention in the wireless communication field. The use of millimeter waves for wireless communication can effectively increase bandwidth and improve transmission reliability. However, millimeter waves have the problems of large free space loss and poor penetrating power, so that the problems are solved by using the technologies of beam forming, massive MIMO, distributed antennas and the like. The distributed antenna technology can enlarge the coverage of a wireless network and enhance the service quality of the network. The access network is distributed and deployed in a master-slave base station mode, so that various index performances of the network can be effectively improved, and some practical problems of millimeter wave transmission can be solved. In the distributed network, the user association is a popular research direction, and a group of reasonable user association can effectively improve the overall performance of the distributed network and reduce unnecessary resource consumption in the distributed network.
The existing optimization scheme in the millimeter wave distributed network generally only aims at optimizing network throughput or total power or total delay of the network, and the joint optimization of a plurality of optimization variables is ignored for a plurality of targets, so that important network indexes cannot be well considered, and the overall performance of the network is reduced.
Disclosure of Invention
The invention aims to provide a user association and beam forming combined multi-objective optimization method in a millimeter wave distributed network, which can effectively balance and optimize throughput, end-to-end delay and load balance of a communication system by effectively adjusting the user association and the beam forming.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a user association and beam forming combined multi-objective optimization method in a millimeter wave distributed network comprises the following steps:
step S1: establishing a mathematical model based on a distributed antenna network technology in a millimeter wave frequency band;
step S2: determining a plurality of optimization targets and determining weights of the optimization targets through fuzzy logic;
step S3: establishing a mathematical model of the joint optimization problem, and determining an objective function and constraint conditions of the mathematical model;
step S4: solving the optimization problem proposed in the step S3 by adopting a fuzzy logic guided gene extension genetic algorithm;
said step SIn 1, in a millimeter wave distributed network with a single cell, there are K single antenna users, L remote wireless units (Remote Radio Unit, RRU), the first remote wireless unit is equipped with Q antennas l . The baseband signal received by user k may be represented by the following equation:
wherein Sigma represents the sum operation, [. Cndot.] H Represents the operation of conjugate transposition,representing the channel gain vector from the first remote radio unit to the kth user,/->Representing a beamforming vector, s, designed by the first remote wireless unit for transmitting signals to the kth user k CN (0, 1) is a complex scalar representing the data symbols transmitted to user k, X-CN (μ, σ) 2 ) The random variable X satisfies the mean value of mu and the variance of sigma in the complex domain 2 Is used for the normal distribution of the (c),representing noise->Representing the power of gaussian white noise.
Thus, the signal-to-interference-and-noise ratio of the received signal of user k can be expressed by:
wherein |·| represents absolute value operations, (·) 2 Representing a squaring operation. The reception rate of user k can be expressed by the following equation:
R k =B log 2 (1+SINR k )
where B represents the channel bandwidth, log 2 (. Cndot.) represents a logarithmic operation based on 2.
In the step S2, the multiple optimization targets are the total throughput of the downlink millimeter wave network, the total delay of the downlink millimeter wave network and the network load balance degree respectively.
The total throughput of the downlink millimeter wave network is defined as the sum of all user receiving rates, and can be expressed by the following formula:
the total delay of the downlink millimeter wave network is defined as the sum of the delays of all the effective transmission links in the network, and can be expressed by the following formula:
wherein d lk Representing the transmission delay, z, from the remote radio unit, i, to user, k lk Representing a user association between remote wireless unit l and user k, there is z when information is transferred between remote wireless unit l and user k lk =1, otherwise z lk =0, and it is assumed that each user can only have user associations with one remote radio unit.
Network load balancing is defined as the variance of the number of users served by each remote wireless unit, and can be expressed by the following equation:
wherein the method comprises the steps ofRepresenting an open square operation, < >>Indicating the number of users served by the remote wireless unit,representing an average of the number of users served by the remote wireless unit.
In the step S2, the specific implementation steps of the fuzzy logic method are as follows:
step S21: the selection of the trigonometric function as the membership function of the fuzzy inference system can be represented by the following formula:
thus, we can use a triplet (alpha 123 ) To represent a membership function.
Step S22: defining fuzzy terminology sets and corresponding membership function triplets as:
step S23: defining 9 rules of fuzzy inference, thereby determining a fuzzy inference rule table:
step S24: operating a fuzzy inference system according to the quality of service (QoS, quality of Service) requirement of the user and the price (Cost) requirement of the user, fuzzifying the information and inputting the information into the fuzzy inference system, and determining a weight parameter omega according to fuzzy rule reasoning 1 ,ω 2 ,ω 3
In the step S3, the specific implementation steps of the establishment of the optimization model are as follows:
step S31, determining an objective function of the optimization problem, wherein the objective function of the joint optimization problem is defined as a sum of weighted addition after each optimization objective is normalized to the interval [0,1], and the sum can be expressed by the following formula:
wherein omega 123 Weights respectively representing three optimization targets of total throughput of the downlink millimeter wave network, total delay of the downlink millimeter wave network and network load balance degree are respectively obtained by pushing the logic simulation method in the step S2, and T' =T max T is a linear transformation of the throughput T, with the aim of converting the problem of finding the maximum of the throughput T into the problem of finding the minimum of T' (. Cndot.) A. C. max Representing operations taking the maximum value (.) min Representing a minimum value operation.
Step S32, determining constraint conditions of an optimization problem, where two constraint conditions of the optimization problem are respectively that each user can only be associated with one remote wireless unit, and the constraint conditions can be represented by the following formula:
and the range of beamforming vectors, because there are too many alternatives for beamforming vectors, a codebook is needed to select, which can be represented by the set W, and thus the constraint can be represented by the following equation:
w l,k ∈W
step S33, determining a mathematical model of the final joint multi-objective optimization problem, which can be expressed by the following formula:
w l,k ∈W
wherein,representing a jointly optimized beamforming vector w l,k User-associated variable z lk The subsequent function value is minimized, and s.t. means that the condition to be described later is satisfied.
The step S4 specifically includes:
step S41, a basic model of a gene extension genetic algorithm is established, and basic elements of the genetic algorithm such as chromosomes, genes, population sizes, maximum evolution times, crossover probability, mutation probability, fitness function and the like are defined;
step S42, randomly initializing a population, and setting the evolution times t=0;
step S43, calculating the fitness of each individual in the population;
step S44, selecting, crossing, mutating, and setting the evolution times t=t+1;
step S45, if the number of evolutions t does not reach the maximum number of evolutions, jumping to step S43; otherwise, ending the step and outputting a final beam forming vector w l,k Associating variable z with user lk
The step S41 specifically includes:
step S411, defining a chromosome and a gene: the chromosome represents a binary sequence of solutions to the optimization problem, also known as an individual. Each chromosome has two parts of genes, the first part of genes represents user association, and binary sequences formed by arranging the user association of the l multiplied by k groups according to a certain sequence are formed, wherein a gene expansion method is used for improving the effectiveness of evolution; the second part of genes represent beam forming vectors, which are binary sequences formed by arranging l x k groups of beam forming vectors according to the arrangement sequence of user association, and the binary sequence of each group of beam forming vectors is a binary form of a beam forming vector codebook index;
step S412, defining population size N pop Maximum number of evolutions G max Crossover probability p c Probability of variation p m And sets these constants;
step S413, defining a fitness function as an optimization objective function;
the step S44 specifically includes:
step S441, selecting individuals in the population according to the fitness, and using a classical proportional disk random selection scheme, individuals a i The probability of being selected may be represented by the following equation:
wherein f (a) i ) Representing individual a i The adaptability of the system can simulate the process of survival of the right in the nature, and the selection operation is completed;
step S442, performing cross operation, adopting a discrete cross operator method, and performing cross operation based on the cross probability. Assuming that the crossover sequence is 1100001, two segments of protogenes are subjected to binary code exchange at a position of 0 of the crossover sequence, and if the two segments of protogenes are 0101110, 1110011, the two segments of protogenes are subjected to gene 0110010, 1101111 according to the crossover rule;
step S443, performing mutation operation, adopting a single-point mutation operator method, and performing mutation operation based on mutation probability. The single-point mutation operator method changes the value of a binary number on a gene so as to finish mutation operation.
The beneficial effects are that: the invention can effectively balance and optimize the throughput, the end-to-end delay and the load balance of the communication system by effectively adjusting the user association and the beam forming, can effectively improve the overall performance of the millimeter wave distributed network, balances various indexes, and gives consideration to various demands of the wireless network, thereby having wide application prospect.
Drawings
Fig. 1 is a flowchart of a method for optimizing user association and beam forming in a millimeter wave distributed network;
FIG. 2 is a flowchart of a gene expansion genetic algorithm employed in the present invention;
FIG. 3 is a graph comparing normalized function values of throughput, time delay, and load balance using a fuzzy logic guided genetic algorithm (FLGA, fuzzy Logic guided Genetic Algorithm) and a fuzzy logic guided gene extension genetic algorithm (FLGEGA, fuzzy Logic guided Gene Extended Genetic Algorithm) in accordance with an embodiment of the present invention;
fig. 4 is a graph comparing normalized function values of throughput, time delay, and load balance using a gene extension genetic algorithm (GEGA, gene Extended Genetic Algorithm) and a fuzzy logic guided gene extension genetic algorithm (FLGEGA, fuzzy Logic guided Gene Extended Genetic Algorithm) in an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
As shown in fig. 1, the method for optimizing the user association and beam forming combination multi-objective in the millimeter wave distributed network provided by the invention comprises the following steps:
step S1: establishing a mathematical model based on a distributed antenna network technology in a millimeter wave frequency band; the method comprises the following steps:
in a millimeter wave distributed network with a single cell, K single antenna users exist, L remote wireless units (Remote Radio Unit, RRU) are arranged, and the number of antennas of the first remote wireless unit is Q l . The baseband signal received by user k may be represented by the following equation:
wherein Sigma represents the sum operation, [. Cndot.] H Represents the operation of conjugate transposition,representing the channel gain vector from the first remote radio unit to the kth user,/->Representing a beamforming vector, s, designed by the first remote wireless unit for transmitting signals to the kth user k CN (0, 1) is a complex scalar representing the data symbols transmitted to user k, X-CN (μ, σ) 2 ) Watch (watch)The random variable X satisfies the mean value of mu and the variance of sigma in the complex domain 2 Is used for the normal distribution of the (c),representing noise->Representing the power of gaussian white noise.
Thus, the signal-to-interference-and-noise ratio of the received signal of user k can be expressed by:
wherein |·| represents absolute value operations, (·) 2 Representing a squaring operation. The reception rate of user k can be expressed by the following equation:
R k =B log 2 (1+SINR k )
where B represents the channel bandwidth, log 2 (. Cndot.) represents a logarithmic operation based on 2.
Step S2: determining a plurality of optimization targets and determining weights of the optimization targets through fuzzy logic; the method comprises the following steps:
the plurality of optimization targets are the total throughput of the downlink millimeter wave network, the total delay of the downlink millimeter wave network and the network load balance degree respectively.
The total throughput of the downlink millimeter wave network is defined as the sum of all user receiving rates, and can be expressed by the following formula:
the total delay of the downlink millimeter wave network is defined as the sum of the delays of all the effective transmission links in the network, and can be expressed by the following formula:
wherein d lk Representing the transmission delay, z, from the remote radio unit, i, to user, k lk Representing a user association between remote wireless unit l and user k, there is z when information is transferred between remote wireless unit l and user k lk =1, otherwise z lk =0, and it is assumed that each user can only have user associations with one remote radio unit.
Network load balancing is defined as the variance of the number of users served by each remote wireless unit, and can be expressed by the following equation:
wherein the method comprises the steps ofRepresenting an open square operation, < >>Indicating the number of users served by the remote wireless unit,representing an average of the number of users served by the remote wireless unit.
Step S3: establishing a mathematical model of the joint optimization problem, and determining an objective function and constraint conditions of the mathematical model; the method comprises the following specific steps:
step S31, determining an objective function of the optimization problem, wherein the objective function of the joint optimization problem is defined as a sum of weighted addition after each optimization objective is normalized to the interval [0,1], and the sum can be expressed by the following formula:
wherein omega 123 The weights of the three optimization targets, namely the total throughput of the downlink millimeter wave network, the total delay of the downlink millimeter wave network and the network load balance degree, are respectively represented, and are fuzzy in the step S2The logical method pushes that T' =t max T is a linear transformation of the throughput T, with the aim of converting the problem of finding the maximum of the throughput T into the problem of finding the minimum of T' (. Cndot.) A. C. max Representing operations taking the maximum value (.) min Representing a minimum value operation.
Step S32, determining constraint conditions of an optimization problem, where two constraint conditions of the optimization problem are respectively that each user can only be associated with one remote wireless unit, and the constraint conditions can be represented by the following formula:
and the range of beamforming vectors, because there are too many alternatives for beamforming vectors, a codebook is needed to select, which can be represented by the set W, and thus the constraint can be represented by the following equation:
w l,k ∈W
the selected codebook S of beamforming vectors, derived from a discrete Fourier transform (Discrete Fourier Transform, DFT) matrix, constructs Q l ×Q l Discrete fourier transform matrix:
wherein the method comprises the steps ofSince the set of rows and columns of this matrix is identical, the set W can be determined. Such a design of a beamforming selection codebook is not necessarily an optimal design, but is a design with references.
Step S33, determining a mathematical model of the final joint multi-objective optimization problem, which can be expressed by the following formula:
w l,k ∈W
wherein,representing a jointly optimized beamforming vector w l,k User-associated variable z lk The subsequent function value is minimized, and s.t. means that the condition to be described later is satisfied.
Step S4: solving the optimization problem proposed in the step S3 by adopting a fuzzy logic guided gene extension genetic algorithm; the method comprises the following specific steps:
step S41, a basic model of a gene extension genetic algorithm is established, and basic elements of the genetic algorithm such as chromosomes, genes, population sizes, maximum evolution times, crossover probability, mutation probability, fitness function and the like are defined; the method comprises the following specific steps:
step S411, defining a chromosome and a gene: the chromosome represents a binary sequence of solutions to the optimization problem, also known as an individual. Each chromosome has two parts of genes, the first part of genes represents user association, and binary sequences formed by arranging the user association of the l multiplied by k groups according to a certain sequence are formed, wherein a gene expansion method is used for improving the effectiveness of evolution; the second part of genes represent beam forming vectors, which are binary sequences formed by arranging l x k groups of beam forming vectors according to the arrangement sequence of user association, and the binary sequence of each group of beam forming vectors is a binary form of a beam forming vector codebook index;
the method of gene extension is to use a set of binary sequences of length m to represent a set of user associations, since the binary sequences of length m total 2 m The seed case, therefore, is defined only by 2 m-1 The case indicates that there is a user association, another 2 m-1 A situation indicates no user association. Compared with the traditional method of using a binary number to represent user association, the gene expansion method can be used forAnd searching the optimal evolution direction of the population is expanded, and enough optimization space is provided for the population, so that a better optimization effect is achieved.
Step S412, defining population size N pop Maximum number of evolutions G max Crossover probability p c Probability of variation p m And sets these constants;
step S413, defining a fitness function as an optimization objective function;
step S42, randomly initializing a population, and setting the evolution times t=0;
step S43, calculating the fitness of each individual in the population;
step S44, selecting, crossing, mutating, and setting the evolution times t=t+1; the method comprises the following specific steps:
step S441, selecting individuals in the population according to the fitness, and using a classical proportional disk random selection scheme, individuals a i The probability of being selected may be represented by the following equation:
wherein f (a) i ) Representing individual a i The adaptability of the system can simulate the process of survival of the right in the nature, and the selection operation is completed;
step S442, performing cross operation, adopting a discrete cross operator method, and performing cross operation based on the cross probability. Assuming a crossover sequence of 1100001, two protogenes are binary-coded at "0" of the crossover sequence, and if the two protogenes are 0101110, 1110011, the two protogenes are subjected to 0110010, 1101111 according to the crossover rule.
Step S443, performing mutation operation, adopting a single-point mutation operator method, and performing mutation operation based on mutation probability. The single-point mutation operator method changes the value of a binary number on a gene so as to finish mutation operation.
Step S45, if the number of evolutions t does not reach the maximum number of evolutions, jumping to step S43; otherwise, ending the step and outputting the finalBeamforming vector w l,k Associating variable z with user lk
According to the above steps, the parameters qos=0.5, cost=0.5, g are set max =500,N pop =100,p c =0.7,p m =0.4,Q l The computer simulation is performed by using 1-bit binary code for user association and 8-bit binary code for user association for FLGEGA, and the simulation result is shown in fig. 3, and the method using gene extension can make various indexes of the communication system better.
According to the above steps, setting the parameter G max =600,N pop =100,p c =0.7,p m =0.4,Q l =8, set the parameter ω in GEGA 1 =0.5,ω 2 =0.5,ω 3 The parameters qos=1 and cost=0.1 are set in FLGEGA to perform computer simulation, and the simulation result is shown in fig. 4, so that various indexes of the communication system can be better by using the fuzzy logic method.
The invention can effectively balance and optimize the throughput, the end-to-end delay and the load balance of the communication system by effectively adjusting the user association and the beam forming, can effectively improve the overall performance of the millimeter wave distributed network, balances various indexes, and gives consideration to various demands of the wireless network, thereby having wide application prospect.
The foregoing is only a preferred embodiment of the invention, it being noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the invention.

Claims (3)

1. A user association and beam forming combined multi-objective optimization method in a millimeter wave distributed network is characterized in that: the method comprises the following steps:
step S1: establishing a mathematical model based on a distributed antenna network technology in a millimeter wave frequency band;
step S2: determining a plurality of optimization targets and determining weights of the optimization targets through fuzzy logic;
step S3: establishing a mathematical model of the joint optimization problem, and determining an objective function and constraint conditions of the mathematical model;
step S4: solving the optimization problem proposed in the step S3 by adopting a fuzzy logic guided gene extension genetic algorithm;
in the step S1, in a single-cell millimeter wave distributed network, K single-antenna users exist, L remote wireless units are provided, and the number of antennas provided by the first remote wireless unit is Q l The baseband signal received by user k may be represented by:
wherein Sigma represents the sum operation, [. Cndot.] H Represents the operation of conjugate transposition,representing the channel gain vector from the first remote radio unit to the kth user,/->Representing a beamforming vector, s, designed by the first remote wireless unit for transmitting signals to the kth user k CN (0, 1) is a complex scalar representing the data symbols transmitted to user k, X-CN (μ, σ) 2 ) The random variable X satisfies the mean value of mu and the variance of sigma in the complex domain 2 Is used for the normal distribution of the (c),representing noise->Power representing gaussian white noise;
thus, the signal-to-interference-and-noise ratio of the received signal of user k is represented by:
wherein |·| represents absolute value operations, (·) 2 Representing the squaring operation, the reception rate of user k is represented by:
R k =Blog 2 (1+SINR k )
where B represents the channel bandwidth, log 2 (. Cndot.) represents a base 2 logarithmic operation;
in the step S2, the plurality of optimization targets are the total throughput of the downlink millimeter wave network, the total delay of the downlink millimeter wave network and the network load balance degree respectively;
the total throughput of the downlink millimeter wave network is defined as the sum of all user receiving rates, and is expressed by the following formula:
the total delay of the downlink millimeter wave network is defined as the sum of the delays of all the effective transmission links in the network, and is expressed by the following formula:
wherein d lk Representing the transmission delay, z, from the remote radio unit, i, to user, k lk Representing a user association between remote wireless unit l and user k, there is z when information is transferred between remote wireless unit l and user k lk =1, otherwise z lk =0, and each user is set to have a user association with only one remote wireless unit;
network load balancing is defined as the variance of the number of users served by each remote wireless unit, expressed by the following equation:
wherein the method comprises the steps ofRepresenting an open square operation, < >>Indicating the number of subscribers of the remote radio unit/service,/->An average value representing the number of users served by the remote wireless unit;
in the step S3, the specific implementation steps of the establishment of the optimization model are as follows:
step S31, determining an objective function of the optimization problem, wherein the objective function of the joint optimization problem is defined as the sum of weighted addition after each optimization target is normalized to the interval [0,1], and the sum is expressed by the following formula:
wherein omega 123 Weights respectively representing three optimization targets of total throughput of the downlink millimeter wave network, total delay of the downlink millimeter wave network and network load balance degree are respectively obtained by pushing the logic simulation method in the step S2, and T' =T max T is a linear transformation of the throughput T, with the aim of converting the problem of finding the maximum of the throughput T into the problem of finding the minimum of T' (. Cndot.) A. C. max Representing operations taking the maximum value (.) min Representing minimum value operation;
step S32, determining constraint conditions of an optimization problem, where two constraint conditions of the optimization problem are respectively that each user can only be associated with one remote wireless unit, and the constraint conditions are represented by the following formula:
and the range of beamforming vectors, represented by set W, the constraint can be expressed by:
w l,k ∈W
step S33, determining a mathematical model of the final joint multi-objective optimization problem, expressed by the following formula:
w l,k ∈W
wherein,representing a jointly optimized beamforming vector w l,k User-associated variable z lk Minimizing the subsequent function value, s.t. means making it meet the conditions described later;
the step S4 specifically includes:
step S41, a basic model of a gene extension genetic algorithm is established, and basic elements of the genetic algorithm are defined: chromosome, gene, population size, maximum evolution number, crossover probability, mutation probability, fitness function;
step S42, randomly initializing a population, and setting the evolution times t=0;
step S43, calculating the fitness of each individual in the population;
step S44, selecting, crossing, mutating, and setting the evolution times t=t+1;
step S45, if the number of evolutions t does not reach the maximum number of evolutions, jumping to step S43; otherwise, ending the step and outputting a final beam forming vector w l,k Associating variable z with user lk
The step S41 specifically includes:
step S411, defining a chromosome and a gene: binary sequences of solutions to chromosome expression optimization problems, also known as individuals; each chromosome has two parts of genes, the first part of genes represents user association, and binary sequences formed by arranging the user association of the l multiplied by k groups according to a certain sequence are formed, wherein a gene expansion method is used for improving the effectiveness of evolution; the second part of genes represent beam forming vectors, which are binary sequences formed by arranging l x k groups of beam forming vectors according to the arrangement sequence of user association, and the binary sequence of each group of beam forming vectors is a binary form of a beam forming vector codebook index;
step S412, defining population size N pop Maximum number of evolutions G max Crossover probability p c Probability of variation p m And sets these constants;
step S413, defining a fitness function as an optimization objective function;
the method of gene extension in step S411 is to use a set of binary sequences of length m to represent a set of user associations, since the binary sequences of length m total 2 m The seed case, therefore, is defined only by 2 m-1 The case indicates that there is a user association, another 2 m-1 A situation indicates no user association.
2. The method for combined multi-objective optimization of user association and beamforming in millimeter wave distributed network according to claim 1, wherein: in the step S32, a codebook S for selecting a beamforming vector is derived from a discrete fourier transform matrix, and Q is constructed l ×Q l Discrete fourier transform matrix:
wherein the method comprises the steps ofSince the set of rows and columns of this matrix is phaseAlso, the set W can be determined thereby.
3. The method for combined multi-objective optimization of user association and beamforming in millimeter wave distributed network according to claim 1, wherein: the step S44 specifically includes:
step S441, selecting individuals in the population according to the fitness, and using a classical proportional disk random selection scheme, individuals a i The probability of being selected may be represented by the following equation:
wherein f (a) i ) Representing individual a i The adaptability of the system can simulate the process of survival of the right in the nature, and the selection operation is completed;
step S442, performing cross operation, adopting a discrete cross operator method, and performing cross operation based on cross probability;
step S443, performing mutation operation, namely performing mutation operation based on mutation probability by adopting a single-point mutation operator method, wherein the single-point mutation operator method changes the value of a binary number on a gene so as to finish mutation operation.
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