CN111313988B - Authorization-free NOMA method for realizing URLLC based on halter strap transformation model - Google Patents

Authorization-free NOMA method for realizing URLLC based on halter strap transformation model Download PDF

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CN111313988B
CN111313988B CN202010109427.0A CN202010109427A CN111313988B CN 111313988 B CN111313988 B CN 111313988B CN 202010109427 A CN202010109427 A CN 202010109427A CN 111313988 B CN111313988 B CN 111313988B
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迟学芬
齐瑞哲
赵琳琳
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Jilin University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/382—Monitoring; Testing of propagation channels for resource allocation, admission control or handover
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W24/00—Supervisory, monitoring or testing arrangements
    • H04W24/02—Arrangements for optimising operational condition
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/02—Traffic management, e.g. flow control or congestion control
    • H04W28/0231—Traffic management, e.g. flow control or congestion control based on communication conditions
    • H04W28/0236—Traffic management, e.g. flow control or congestion control based on communication conditions radio quality, e.g. interference, losses or delay
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/02—Traffic management, e.g. flow control or congestion control
    • H04W28/0268—Traffic management, e.g. flow control or congestion control using specific QoS parameters for wireless networks, e.g. QoS class identifier [QCI] or guaranteed bit rate [GBR]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W74/00—Wireless channel access, e.g. scheduled or random access
    • H04W74/08—Non-scheduled or contention based access, e.g. random access, ALOHA, CSMA [Carrier Sense Multiple Access]
    • H04W74/0833—Non-scheduled or contention based access, e.g. random access, ALOHA, CSMA [Carrier Sense Multiple Access] using a random access procedure
    • H04W74/0841—Non-scheduled or contention based access, e.g. random access, ALOHA, CSMA [Carrier Sense Multiple Access] using a random access procedure with collision treatment
    • H04W74/0858—Non-scheduled or contention based access, e.g. random access, ALOHA, CSMA [Carrier Sense Multiple Access] using a random access procedure with collision treatment collision detection
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    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
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Abstract

The invention relates to an authorization-free NOMA method for realizing URLLC based on halter strap transformation model, which comprises the following steps: based on a compressed sensing theory, the number estimation of active terminals of the NOMA system is realized, and a multi-terminal superposed signal is decoded; the abstract interference diagram is used for solving the signal to interference and noise ratio of the terminal in a transmission state and solving the MAC-PHY combined reachable transmission rate according to the interrupt probability distribution; based on a service halter strap theory, solving the delay violation probability of each terminal by aiming at a delay and reliability joint analysis method for meeting high reliability and low delay of a multi-user uplink NOMA system; and solving the optimal values of the terminal transmitting power and the access probability by taking the maximum energy efficiency of the system as an optimization target, the delay reliability requirement as constraint and the terminal transmitting power and the access probability as optimization variables. The invention can relieve the problem of multi-user uplink authorization-free scheduling collision, realize strict QoS guarantee of URLLC, and improve the frequency spectrum efficiency and the system energy efficiency.

Description

Authorization-free NOMA method for realizing URLLC based on halter strap transformation model
Technical Field
The invention relates to an authorization-free non-orthogonal multiple access (NOMA) method for guaranteeing high-reliability and low-delay communication (URLLC) based on halter strap transformation model, belonging to the field of wireless network random access.
Background
High-reliability low-delay communication (URLLC) is one of three 5G core application scenes and is mainly used for bearing services such as industrial automation, automatic driving, remote medical treatment and the like. These services put higher demands on delay and reliability, and achieve at least 99.999% of highly reliable transmission within a delay bound of 1 millisecond.
In consideration of the short packet and sporadic characteristics of URLLC service, 3GPP organization proposed in the technical report "TR 38.802 V14.2.0" that a terminal carrying uplink URLLC service recommends the use of Grant-free (Grant-free) transmission. The authorization-free access has the characteristics of no message overhead such as resource application and allocation, and the time delay generated by signaling interaction can be greatly reduced. However, although the unlicensed access is beneficial to improve the characteristics of time delay and energy efficiency, it is inevitable that multiple terminals access simultaneously to cause collision. The NOMA technology can support a plurality of terminals to occupy the same frequency band resource to transmit data, and the collision problem of the authorization-free transmission is relieved. However, the existing NOMA technology cannot realize 99.999% of reliability in millisecond order, and cannot bear URLLC. In the 5G era, a new reliability-delay quality of service (QoS) analysis and guarantee theory is urgently needed, and a foundation is laid for the research and development of URLLC.
The accuracy of the unlicensed NOMA algorithm under the time delay QoS constraint has extremely high requirements on the used support theory. In the network performance analysis problem, queuing theory is a classical theoretical tool. Based on the queuing theory, the halter strap theory uses a brand-new view angle to model and analyze the delay QoS performance boundary, and provides a compact boundary for reliability and delay analysis. And modeling the communication process of the data packet into a queuing system by combining a queuing theory and an halter strap theory, and respectively solving parameters of the arrival halter strap and the service halter strap so as to construct a reliability-time delay performance function. The queuing theory and halter strap theory provide theoretical support for the design of the unlicensed NOMA algorithm under the requirement of high reliability and low delay.
Disclosure of Invention
The invention aims to solve the technical problem of providing an authorization-free NOMA method for realizing URLLC based on an halter strap transformation model, which can relieve the problem of uplink authorization-free scheduling collision of multiple users, realize strict QoS guarantee of URLLC, and improve the spectrum efficiency and the system energy efficiency.
In order to solve the technical problem, the authorization-free NOMA method for realizing URLLC based on halter strap transformation model comprises the following steps:
step 1) estimating the number g of active terminals in the NOMA system based on a compressive sensing theory, and calculating a RIP parameter lambda; if lambda is more than 0 and less than 1, adopting an MMSE-SIC multi-user signal detection algorithm based on compressed sensing, sequentially estimating a channel matrix according to the descending order of the signal-to-interference-and-noise ratio of each terminal, and solving signals transmitted by each terminal from signals superposed by the multi-terminals; otherwise, a basic SIC multi-user signal detection algorithm is adopted, and the signals transmitted by each terminal are sequentially solved from the superposed signals according to the descending order of the signal power of each terminal;
step 2) the NOMA system adopts short packet transmission with limited block length, and analyzes the reachable transmission rate of the short packet of the NOMA unauthorized access system across layers under the condition that the NOMA system jointly considers the signal-to-interference-and-noise ratio statistical characteristics of an MAC layer and a physical layer mechanism; the method comprises the following steps:
abstracting a multi-terminal NOMA system into an interference graph G ═ G(V, E) let vector σj∈{0,1}NA network transmission state j, representing an interference pattern G, (V, E), 1.. N, N is the number of terminals,
Figure BDA0002389445280000021
represents the vector σjI.e. the transmission state of terminal i in network transmission state j;
Figure BDA0002389445280000022
representing that the terminal i transmits data to the base station in a network transmission state j;
Figure BDA0002389445280000023
indicating that the terminal i does not transmit data to the base station in the network transmission state j; order to
Figure BDA0002389445280000026
Representing the signal-to-interference-and-noise ratio of a terminal i in a network transmission state j; for a given network transmission state j, solving the interruption probability of a terminal i in the network transmission state j by adopting a probability analysis method of sequence statistics
Figure BDA0002389445280000024
Combined transmission state sigmajProbability solution of occurrence jointly considers interruption probability distribution Pr { SINR { of terminal i of MAC layer and physical layer mechanismi}; for a given transport block size of l, bandwidth of B, block error rate (BLER) of ρiThen, the achievable transmission rate R of the terminal i is calculated according to the formula (3)i：
Figure BDA0002389445280000025
Wherein the SINRiSignal-to-interference-and-noise ratio of the signal transmitted for terminal i, e denotes the base of the natural logarithm, Q-1(. -) represents a Q function;
step 3), logically viewing each terminal of the multi-terminal uplink NOMA system as two queues: a terminal buffer empty queue and a terminal buffer non-empty queue; based on the halter strap theory, calculating the probability of occurrence of each terminal cache non-empty queue, the delay violation probability of each terminal cache empty queue and the data packet arriving at the terminal of the terminal cache non-empty queue, and the probability of each terminal delay exceeding the delay bound; the method comprises the following steps:
calculating the probability delta of the occurrence of the terminal cache non-empty queue according to the formula (4)i；
Figure BDA0002389445280000031
Wherein a isi(t) is the number of packets arriving at terminal i in time slot t, E [ a ]i(t)]Represents the average value of the arrival packets of the terminal i; si(t) number of packets, Es, serving terminal i in time slot ti(t)]Represents the average value of the terminal i service package;
under the condition that the terminal buffer is empty, calculating the probability p of successful transmission of the data packet of the terminal i under a given time delay boundaryki：
Figure BDA0002389445280000032
Wherein k isiThe maximum time slot number of the data packet transmitted by the terminal i needing to be successfully transmitted in the time delay boundary requirement is represented;
Figure BDA0002389445280000033
representing the probability of successful transmission of a data packet of a terminal i in a time slot t;
according to the vector sigma described in step 2)j∈{0,1}NRepresenting a network transmission state j, the probability of the occurrence of the network transmission state j is represented as:
Figure BDA0002389445280000034
the probability of successful transmission for terminal i is expressed as:
Figure BDA0002389445280000035
calculating the time delay violation probability of the data packet arriving at the terminal i of the terminal buffer empty queue according to the formula (6)
Figure BDA0002389445280000036
Figure BDA0002389445280000037
For each terminal buffer non-empty queue, order Di(t) denotes the time delay of terminal i, Ai(t) represents the number of packets that terminal i arrives from time slot 0 to time slot t, Si(t) represents the number of data packets successfully served by the terminal i from the time slot 0 to the time slot t, and the time delay D of the terminal i is calculated according to the formula (7)i(t)
Di(t)＝min{n≥0|Ai(t-n)≤Si(t)} (7)
Calculating and obtaining the time delay D of the terminal i according to the formula (8)i(t) exceeding the time delay bound
Figure BDA0002389445280000038
Probability of (2)
Figure BDA0002389445280000039
Figure BDA00023894452800000310
Wherein the content of the first and second substances,
Figure BDA0002389445280000041
is a time delay bound, ha(ai(t)) is a function of the relevant characteristics of the arrival process, E [ h ]a(ai(0))]Function h representing relevant characteristics of arrival processa(ai(t)) expected value, h, at time slot 0s(si(t)) is a function of the relevant characteristics of the service process, ehs(si(0))]Representing service procedure related characteristicsFunction hs(si(t)) at the expected value of 0 time slot,
Figure BDA0002389445280000042
is a special halter strap parameter that links the reach halter strap and service halter strap parameters together, defined as:
Figure BDA0002389445280000043
wherein theta isiIs the halter strap parameter, and is,
Figure BDA0002389445280000044
halter strap correction function representing the arrival process,
Figure BDA0002389445280000045
halter strap correction function representing service procedure;
Hiis a threshold value, and represents that the instantaneous arrival data packet is greater than the characteristic function h of the instantaneous service data packeta(ai(t)) and hs(si(t)) the minimum value of the product, defined as:
Hi:＝min{ha(ai(t))hs(si(t)):ai(t)-si(t)＞0,t≥0} (10)
obtaining the time delay violation probability under the terminal buffer non-empty queue according to the formula (11)
Figure BDA0002389445280000046
Figure BDA0002389445280000047
Merging the terminal buffer empty queue and the terminal buffer non-empty queue by utilizing a total probability formula to obtain the time delay violation probability epsilon of the terminal i under the general conditioni；
Figure BDA0002389445280000048
Step 4) constructing a multi-objective optimization problem, solving an optimal solution of the optimization problem by taking the maximum energy efficiency of the system as an optimization target, the reliability requirement of the URLLC time delay as constraint and the transmitting power and the access probability of the URLLC terminal as optimization variables to obtain a configuration scheme for controlling the access probability and the transmitting power of the URLLC terminal, wherein the method comprises the following steps:
let η (Pt, p) represent the energy efficiency function of the multi-user NOMA system, then
Figure BDA0002389445280000049
Wherein gamma isi(Pt, p) is the throughput of terminal i
Figure BDA00023894452800000410
Ωi(Pt, p) is the average energy consumption of terminal i, Ωi(Pt,p)＝E[Pti]；PtiFor the transmission power of terminal i, E [ Pt ]i]Representing the expected value of the transmission power of the terminal i; pt ═ Pt1,...,Pti,...,PtN]Transmitting power vector for terminal, p ═ p1,...,pi,...,pN]The probability vector is accessed to the terminal, and N is the number of the terminals;
order to
Figure BDA0002389445280000059
For terminal i's delay violating probability requirements, wiAnd representing the average energy consumption limit of the terminal i, the optimization problem is as follows:
Figure BDA0002389445280000051
the sum of the constraints in equation (14) is expressed as Λ (Pt, p):
Figure BDA0002389445280000052
Figure BDA0002389445280000053
Figure BDA0002389445280000054
Figure BDA0002389445280000055
Figure BDA0002389445280000056
Λ (Pt, p) ≧ 0, and all constraints in equation (14) can be satisfied if and only if Λ (Pt, p) ≧ 0;
constructing a single-target optimization problem with constraint conditions into a dual-target optimization problem without constraint conditions:
Figure BDA0002389445280000057
and (3) solving the constructed optimization problem of the formula (16) to obtain the optimal values of the terminal transmitting power vector Pt and the access probability vector p which enable the energy efficiency eta (Pt, p)) of the system to be maximum.
In the step 1), the method for estimating the number of the active terminals comprises the following steps:
assuming that the signal-to-interference-and-noise ratio of a signal transmitted by a terminal i is SINR when the number of active terminals is gi|g；
Figure BDA0002389445280000058
Wherein PtiRepresenting the transmission power, v, of terminal i2Representing gaussian noise; ziRepresenting the product of the channel matrix and the spreading code matrix of terminal i; i ismIndicating a disabilityThe signal is left to be transmitted without authorization,
Figure BDA0002389445280000061
for a given active terminal number g, solving the interruption probability Pr { SINR } of the terminal i by adopting a probability analysis method of sequence statisticsi|g< gamma }; and gamma represents a set system interrupt signal-to-interference-and-noise ratio threshold, the system interrupt probability Pr { outage | g } is represented as:
Figure BDA0002389445280000062
a is a distribution area of a terminal i;
for a given system interrupt probability value Pr { outage | g }, the number g of active terminals can be estimated according to the formula (2), wherein g is less than or equal to N.
In the step 4), the optimization problem of the formula (16) is solved by adopting a wolf pack optimization algorithm to obtain the optimal values of the terminal transmitting power vector Pt and the access probability vector p which enable the energy efficiency eta (Pt, p)) of the system to be maximum, and the method comprises the following steps:
(1) initializing wolf group X ═ { X with gray wolf number QjJ 1.. Q }, randomly distributed in the 2N-dimensional search space; initializing a position vector X of each wolfj＝[Pt,p]jCorresponding terminal transmission power vector is Ptj＝[Pt1,...,Pti,...,PtN]jTerminal access probability vector is pj＝[p1,...,pi,...,pN]j；
(2) Setting the maximum number of iterations to Zmax(ii) a In each iteration, the position vector X of each wolf of wolf group X is calculated according to formula (13)j＝[Pt,p]jCorresponding optimization objective function 1/eta (X)j) A value of (d); calculating the position vector X of each gray wolf in the wolf group X according to the formula (14)j＝[Pt,p]jCorresponding constraint function Λ (X)j) A value of (d); let QfitIndicates that lambda (X) is satisfied in the wolf group Xj) The number of gray wolfs which is 0, and the fitness weight coefficient xi which is Qfit(ii)/Q; according to the formula (1)7) Calculating fitness function values corresponding to the positions of all the gray wolves:
Figure BDA0002389445280000063
(3) calculating the fitness function value corresponding to each gray wolf in X according to a formula (17), arranging the fitness values in an ascending order, and taking the first, second and third gray wolfs as alpha, beta and kappa which represent the leaders of wolf groups; the remaining gray wolves are called omega and represent common gray wolves; the common gray wolf omega updates the position of the common gray wolf omega according to the positions of the head wolfs alpha, beta and kappa, so that the wolf group gradually approaches to the prey; combining the position vectors of three wolfs in the k-th iteration, the wolf group XjJ 1.. said, each gray wolf in Q is subjected to position update according to the following formula (18a to 19), that is, a position vector of each gray wolf at the start of the next iteration is obtained:
D1j(k)＝Xα(k)-A1(k)·|C1(k)·Xα(k)-Xj(k)| (18a)
D2j(k)＝Xβ(k)-A2(k)·|C2(k)·Xβ(k)-Xj(k)| (18b)
D3j(k)＝Xκ(k)-A3(k)·|C3(k)·Xκ(k)-Xj(k)| (18c)
Figure BDA0002389445280000071
Xα(k),Xβ(k),Xκ(k) respectively representing the position vectors, X, of the three wolfs in the k-th iterationj(k) Representing the location of each gray wolf in the kth iteration; d1j(k),D2j(k),D3j(k) Respectively representing the position relation between the gray wolf and the three wolfs in the k-th iteration; a. thel(k) And Cl(k) (l ═ 1,2,3) are parameter vectors used to control the direction of travel of the wolf pack and to control the effect of the distance between the wolf pack and the prey on the hunting process, respectively; the calculation formula is as follows:
Al(k)＝a(k)·(2r1-1),l＝1,2,3 (20)
Cl(k)＝2r2,l＝1,2,3 (21)
Figure BDA0002389445280000072
where a (k) is a vector that gradually drops from 2 to 0 as the iterative process progresses;
repeating the step (3) and iterating to the last ZmaxAnd after the last iteration is finished, the transmitting power Pt of each terminal and the access probability p of each terminal corresponding to the alpha position of the wolf are the final optimal values of the optimization variables.
The invention has the beneficial effects that:
1. the invention fully considers the accidental and short packet characteristics of the URLLC, proposes the authorization-free transmission (namely random access) according to the probability, can fully reduce the time delay and support the ultrahigh QoS requirement of the uplink URLLC. The NOMA method is adopted to relieve the collision problem of the unauthorized access, and based on the compressed sensing theory, the estimation of the number of active users and the joint detection of multi-user superposed signals are realized, so that technical support is provided for realizing the NOMA.
2. The authorization-free NOMA method fully considers the random characteristics of random access and wireless channels, and the joint influence of an abstract MAC layer mechanism and a PHY layer mechanism on the reachable transmission rate lays a foundation for reliability and time delay analysis; the method is more suitable for the actual communication scene, and is a clear theoretical support for realizing URLLC in the 5G network.
3. The invention utilizes a powerful mathematical theory tool, fully considers the influence of the burstiness of the arrival of the URLLC service on the time delay analysis, and obtains a more accurate time delay-reliability QoS performance function. Based on the halter strap theory, a universal transient analysis method for delay-reliability joint analysis of a multi-user NOMA system is established, a compact boundary is provided for reliability and delay analysis, bandwidth resources are fully saved, and a foundation is laid for reliability and delay guarantee.
4. The authorization-free NOMA method starts from theoretical innovation, explores a new reliability-delay QoS analysis/guarantee theory and method in the 5G/B5G era on the basis of an halter strap theory and a queuing theory, drives technical innovation by theoretical innovation, researches an authorization-free NOMA method with high energy efficiency, high reliability and low delay, and solves the contradiction between energy efficiency and URLLC service reliability-delay QoS requirements. The method is expected to provide theoretical support and technical reference for realizing URLLC in the 5G/B5G era.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a general flow diagram of the present invention;
FIG. 2 is an interference diagram;
FIG. 3 is a schematic diagram of the delay of packet x;
fig. 4 is a flowchart of a joint analysis formula for obtaining the reliability of the terminal delay based on the halter strap theory;
FIG. 5 is a flowchart of the wolf pack optimization (GWO) algorithm;
FIG. 6 is a diagram of an application scenario of an embodiment of a multi-user NOMA unlicensed dynamic random access method;
FIG. 7 is a diagram illustrating a process of SIC decoding a multi-user superposition signal;
FIG. 8 is a schematic illustration of an interference graph under a scenario of an embodiment.
Detailed Description
As shown in fig. 1, the authorization-free NOMA method for implementing URLLC based on halter strap transformation model includes the following steps:
step 1) estimating the number g of active terminals in the NOMA system based on a compressive sensing theory, and calculating a RIP (verified Isometry constants) parameter lambda (reference: wang, l.dai et al, "Dynamic Compressive Sensing-Based Multi-User Detection for Uplink Grant-Free NOMA", IEEE commu.lett., vol.20, No.11, pp.2320-2323, nov.2016); and if the lambda is more than 0 and less than 1, estimating a channel matrix by adopting a minimum mean square serial interference cancellation (MMSE-SIC) multi-user signal detection algorithm based on compressed sensing, and then decoding the signals superposed by the multiple terminals. Otherwise, the basic SIC multi-user detection algorithm is adopted to solve the superposed signals of the multiple terminals (namely the sum of data transmitted by all the terminals which are transmitted simultaneously);
optionally, as shown in fig. 6, in the NOMA system, one base station 1 and N URLLC terminals are included, where fig. 6 includes 3 active terminals 21, 24, 27, and 5 inactive terminals 22, 23, 25, 26, and 28; the transmission power of the active terminals 21, 24, 27 increases in sequence; all terminals are randomly distributed in the NOMA system in a Poisson Point Process (PPP), and all active terminals are accessed to the base station with a certain access probability. Aiming at the sporadic and random characteristics of URLLC service, the number of active terminals in each time slot is random, and the number of active terminals needs to be estimated before NOMA technology is adopted to perform reliable multi-terminal information detection. The method for estimating the number of active terminals is as follows:
assuming that the signal-to-interference-and-noise ratio of a signal transmitted by a terminal i is SINR when the number of active terminals is gi|g；
Figure BDA0002389445280000091
Wherein PtiRepresenting the transmission power, v, of terminal i2Representing gaussian noise; in order to ensure better sparsity and anti-interference performance, signals are spread before being sent. In this case, ZiRepresenting the product of the channel matrix and the spreading code matrix of terminal i; i ismIndicating a residual unlicensed transmission signal and,
Figure BDA0002389445280000092
for a given number of active terminals g, the set of interfering terminals is random due to the random nature of the radio channel. Solving interruption probability Pr { SINR } of terminal i by adopting probability analysis method of sequence statisticsi|g< gamma }. Gamma represents the set system interrupt signal-to-interference-and-noise ratio threshold, and gamma is set to be more than or equal to 10dB and less than or equal to 20 dB; the system outage probability Pr { outage | g } is expressed as:
Figure BDA0002389445280000093
the channel gain of the terminal includes two parts of large-scale fading and small-scale fading. Large scale fading is mainly determined by the distance of the terminal from the access point. The position distribution of the terminal in the distribution area A is abstracted by using a random point process (such as PPP), which is also the reason for the integral contained in the formula (2), and finally the system interruption probability is deduced. For a given system outage probability value (0 ≦ Pr { outage | g } < 1 in the present invention), the number of active terminals, g, can be estimated according to equation (2). Then the RIP (corrected Isometry constants) parameter λ is calculated. And if the lambda is more than 0 and less than 1, adopting an MMSE-SIC multi-user signal detection algorithm based on compressed sensing, sequentially estimating a channel matrix according to the descending order of SINR of each terminal, and solving the signal transmitted by each terminal from the signals superposed by the terminals. And on the contrary, the basic SIC multi-user signal detection algorithm is adopted, and the signals transmitted by each terminal are sequentially solved from the superposed signals according to the descending order of the signal power of each terminal.
Step 2) in order to realize high-reliability low-delay communication (URLLC), the NOMA system adopts short packet transmission with limited block length, and analyzes the short packet reachable transmission rate of a cross-layer (MAC-PHY) of the NOMA unauthorized access system under the condition that the NOMA system jointly considers the signal-to-interference-and-noise ratio statistical characteristics of an MAC layer and a Physical (PHY) layer mechanism; the method comprises the following steps:
to abstract the joint impact of the MAC and PHY layer mechanisms on the interference experienced by the terminals, the multi-terminal NOMA system is abstracted as an interference graph G ═ (V, E), as shown in fig. 2, where V ═ V (V, E)1,v2,……v4) Denotes a terminal set, E ═ E1,e2,……e4) Representing the interference relationship between the transmission links of the terminals. In the interference graph G ═ (V, E), if there is an edge between two nodes, it indicates that the transmission links of the terminals characterized by the two nodes interfere with each other. Let vector sigmaj∈{0,1}NA network transmission state j, representing an interference pattern G, (V, E), 1.. N, N is the number of terminals,
Figure BDA0002389445280000101
represents the vector σjI.e. the transmission state of terminal i in network transmission state j;
Figure BDA0002389445280000102
representing that the terminal i transmits data to the base station in a network transmission state j;
Figure BDA0002389445280000103
indicating that the terminal i does not transmit data to the base station in the network transmission state j. Order to
Figure BDA0002389445280000104
Representing the signal to interference plus noise ratio of terminal i in network transmission state j. For a given network transmission state j, solving the interruption probability of a terminal i in the network transmission state j by adopting a probability analysis method of sequence statistics
Figure BDA0002389445280000105
Combined transmission state sigmajProbability solution of occurrence interruption probability distribution Pr { SINR } of terminal i jointly considering MAC layer and PHY layer mechanismsi}. For a given transport block size of l, bandwidth of B, block error rate (BLER) of ρiThen, the achievable transmission rate R of the terminal i is calculated according to the formula (3)i：
Figure BDA0002389445280000106
Wherein e represents the base of the natural logarithm, Q-1(. cndot.) represents a Q function.
Step 3) researching a time delay and reliability combined analysis method for meeting high-reliability low-time delay requirements aiming at a multi-terminal uplink NOMA system based on the halter strap theory. Abstracting a multi-terminal uplink NOMA system into a multi-queue system, respectively solving parameters of halter strap arrival and halter strap service, and then obtaining the time delay violation probability of each terminal; the specific method comprises the following steps:
considering that URLLC traffic arrivals are sporadic, we look logically at the buffer of each terminal as two queues: a terminal buffer empty queue and a terminal buffer non-empty queue. Calculating the probability delta of the occurrence of the terminal cache non-empty queue according to the formula (4)i；
Figure BDA0002389445280000107
Wherein a isi(t) is the number of packets arriving at terminal i in time slot t, E [ a ]i(t)]Represents the average value of the arrival packets of the terminal i; si(t) number of packets, Es, serving terminal i in time slot ti(t)]Represents the average value of the terminal i service package; in the case of an empty queue in the terminal buffer, the arrival process and the service process of the data packet are not statistically independent. The probability p of successful transmission of the data packet of the terminal i under a given delay bound can be deducedki：
Figure BDA0002389445280000111
Wherein k isiIndicating the maximum number of time slots that a data packet transmitted by terminal i needs to be successfully transmitted within the delay bound requirement.
Figure BDA0002389445280000112
Representing the probability of successful transmission of a data packet of a terminal i in a time slot t;
according to the vector sigma described in step 2)j∈{0,1}NRepresenting a network transmission state j, the probability of the occurrence of the network transmission state j is represented as:
Figure BDA0002389445280000113
the probability of successful transmission for terminal i is expressed as:
Figure BDA0002389445280000114
then calculating the time delay violation probability of the data packet arriving at the terminal i of the terminal buffer empty queue
Figure BDA0002389445280000115
Figure BDA0002389445280000116
For each terminal buffer non-empty queue, the arrival process and the service process of the data packet are statistically independent. And characterizing the characteristics of the URLLC service by using the statistical characteristics of the queue arrival process, and abstracting the authorization-free transmission process of the terminal into a service process. Let Di(t) denotes the time delay of terminal i, Ai(t) represents the number of packets that terminal i arrives from time slot 0 to time slot t, Si(t) represents the number of data packets successfully served by the terminal i from the time slot 0 to the time slot t, and as shown in fig. 3, the time delay is defined as: (citation: F.Poloczek and F.Ciucu, "Service-Martingles: the Theory and Applications to the Delay Analysis of Random Access Protocols", in IEEE INFOCOM, Kowloon, Hong Kong, May 2015, pp.945-953)
Di(t)＝min{n≥0|Ai(t-n)≤Si(t)} (7)
If the data packet transmission fails due to channel noise or other terminal co-transmission interference, the data packet is retransmitted. Since the definition of the delay is given from the point of view of successful service of the data packet, the delay of the retransmission has been considered in equation (7). If the delay experienced by a packet exceeds the delay bound (which varies depending on the QoS requirements of the user for different applications), the packet will be dropped. Under the assumption that no active packet loss exists, the reliability analysis of the data packet is converted into the analysis of the violation probability of the delay bound (namely Pr { delay > delay bound }).
For the arrival process and the service process of the terminal data packet, based on the stop timing theorem of halter strap and the theory of halter strap, a joint analysis formula of the delay and the reliability of the terminal i is obtained: (citation: F.Poloczek and F.Ciucu, "Service-Martingles: the Theory and Applications to the Delay Analysis of Random Access Protocols", in IEEE INFOCOM, Kowloon, Hong Kong, May 2015, pp.945-953)
Figure BDA0002389445280000121
Wherein，
Figure BDA0002389445280000122
Time delay D for terminal ii(t) exceeding the time delay bound
Figure BDA0002389445280000123
The probability of (a) of (b) being,
Figure BDA0002389445280000124
is the delay bound, i.e. the maximum delay that can be tolerated by the terminals in the system. h isa(ai(t)) is a function of the relevant characteristics of the arrival process, E [ h ]a(ai(0))]Function h representing relevant characteristics of arrival processa(ai(t)) expected value at 0 time slot. h iss(si(t)) is a function of the relevant characteristics of the service process, ehs(si(0))]Function h representing service procedure related characteristicss(si(t)) an expected value at 0 time slot;
Figure BDA0002389445280000125
is a special halter strap parameter that links the reach halter strap and service halter strap parameters together, defined as:
Figure BDA0002389445280000126
wherein theta isiIs the halter strap parameter, and is,
Figure BDA0002389445280000127
halter strap correction function representing the arrival process,
Figure BDA0002389445280000128
halter strap correction function representing service procedure;
Hiis a threshold value, and represents that the instantaneous arrival data packet is greater than the characteristic function h of the instantaneous service data packeta(ai(t)) and hs(si(t)) the minimum value of the product, defined as:
Hi:＝min{ha(ai(t))hs(si(t)):ai(t)-si(t)＞0,t≥0} (10)
based on halter strap theory, we obtain the delay violation probability under the condition that the terminal buffer is not in an empty queue
Figure BDA0002389445280000129
Figure BDA00023894452800001210
Then, combining the terminal buffer empty queue and the terminal buffer non-empty queue into a general condition by using a total probability formula, and solving the time delay violation probability epsilon of the terminal i under the general conditioni；
Figure BDA00023894452800001211
The expected values for different arrival and service procedures are different: e.g., for Poisson arrival, constant rate service, eha(ai(0))]＝1，E[hs(si(0))]1 is ═ 1; for Markov (MMOO) arrival, ALOHA class services, E [ h ]s(si(0))]＝1，E[ha(ai(0))]＝eig1·π0+eig2·π1；
MMOO process transfer matrix
Figure BDA0002389445280000131
paIs the transition probability from state 0 to state 1, qaIs the transition probability from state 1 to state 0; the feature vector of the transfer matrix T is
Figure BDA0002389445280000132
And 4) constructing a multi-objective optimization problem, wherein the maximum energy efficiency of the system is an optimization target, the reliability requirement of the URLLC time delay is taken as a constraint, and the transmitting power and the access probability of the URLLC terminal are taken as optimization variables. Solving an optimal solution of an optimization problem by using a wolf pack optimization (GWO) algorithm to obtain an access probability and transmission power control configuration scheme of the URLLC terminal, wherein the specific method comprises the following steps:
and defining the energy efficiency function of the NOMA system as the sum of the energy efficiency functions of all the terminals, and defining the energy efficiency function of the terminal as the ratio of the throughput of the terminal to the average energy consumption of the terminal. Throughput of terminal i ΓiAverage energy consumption omega of (Pt, p) and terminal ii(Pt, p) is determined by a terminal transmit power vector Pt and a terminal access probability vector p. The expression is as follows: gamma-shapedi(Pt,p)＝pi s·Ri，Ωi(Pt,p)＝E[Pti]，PtiFor the transmission power of terminal i, E [ Pt ]i]Representing the expected value of the transmission power of the terminal i; the terminal transmitting power vector is Pt ═ Pt1,...,Pti,...,PtN]The terminal access probability vector is p ═ p1,...,pi,...,pN](ii) a g is less than or equal to N. Let η (Pt, p) represent the energy efficiency function of a multi-user NOMA system, defined as
Figure BDA0002389445280000133
Before operation, Pt is randomly assigned with an initial value, and an expected value, namely an average value, is calculated according to the initial value:
Figure BDA0002389445280000134
the maximum energy efficiency of the system is an optimization target, the time delay reliability requirement of the URLLC is a constraint, and the transmitting power and the access probability of the URLLC terminal are optimization variables. Order to
Figure BDA0002389445280000135
The time delay of the terminal i is in violation of probability requirement, and the size of the time delay is set according to the communication requirement of the user in the system (for example, URLLC communication is set to be 10)-5)，wiRepresents the power consumption limit of the terminal i, whose size is set according to the power parameter of the signal transmitter configured for a particular communication system (the setting principle is that the number of energy consumed per unit time of the terminal device, i.e. power consumption,one of the signal transmitter indicators), the optimization problem is:
Figure BDA0002389445280000141
the sum of the constraints in equation (14) is expressed as Λ (Pt, p):
Figure BDA0002389445280000142
Figure BDA0002389445280000143
Figure BDA0002389445280000144
Figure BDA0002389445280000145
Figure BDA0002389445280000146
it is clear that Λ (Pt, p) ≧ 0, and all constraints in equation (14) can be satisfied if and only if Λ (Pt, p) ≧ 0. Constructing a single-target optimization problem with constraint conditions into a dual-target optimization problem without constraint conditions:
Figure BDA0002389445280000147
next, the constructed optimization problem of the formula (16) is solved by using a wolf pack optimization algorithm to obtain the optimal values of the optimization variables (the terminal transmission power vector Pt and the access probability vector p) that maximize the optimization target (the system energy efficiency η (Pt, p)). The wild wolf colony optimization algorithm is an iterative optimization algorithm proposed based on the hierarchy system and the hunting mode of the wild wolf colony in the nature, and is applied to the invention, and the specific steps are as follows:
(1) initializing wolf group X ═ { X with gray wolf number QjJ 1.. Q }, randomly distributed in a 2N-dimensional (N is the number of terminals) search space; initializing a position vector X of each wolfj＝[Pt,pj]Corresponding terminal transmission power vector is Ptj＝[Pt1,...,Pti,...,PtN]jTerminal access probability vector is pj＝[p1,...,pi,...,pN]j。
(2) Assuming that the maximum number of iterations is Zmax. In each iteration, the position vector X of each wolf of wolf group X is calculated according to formula (13)j＝[Pt,p]jCorresponding optimization objective function 1/eta (X)j) A value of (d); calculating the position vector X of each gray wolf in the wolf group X according to the formula (14)j＝[Pt,p]jCorresponding constraint function Λ (X)j) A value of (d); let QfitIndicates that lambda (X) is satisfied in the wolf group Xj) The number of gray wolfs which is 0, and the fitness weight coefficient xi which is Qfitand/Q. The fitness function values corresponding to the positions (i.e., the optimization variable values) of all the gray wolves are calculated according to the following formula (17):
Figure BDA0002389445280000151
(3) the fitness function value corresponding to each gray wolf in X is calculated according to the formula (17), and the gray wolfs with the first, second and third fitness names alpha, beta and kappa are arranged according to the ascending order, and represent the head of the wolf group. The remaining gray wolves are called ω, representing the common gray wolves. The common gray wolf ω updates its position according to the positions of the head wolfs α, β and κ, thereby bringing the wolf group closer to the prey. Combining the position vectors of three wolfs in the k-th iteration, the wolf group XjJ 1.. said, each gray wolf in Q is subjected to position update according to the following formula (18a to 19), i.e., a position vector of each gray wolf at the start of the next iteration is obtained):
D1j(k)＝Xα(k)-A1(k)·|C1(k)·Xα(k)-Xj(k)| (18a)
D2j(k)＝Xβ(k)-A2(k)·|C2(k)·Xβ(k)-Xj(k)| (18b)
D3j(k)＝Xκ(k)-A3(k)·|C3(k)·Xκ(k)-Xj(k)| (18c)
Figure BDA0002389445280000152
Xα(k),Xβ(k),Xκ(k) respectively representing the position vectors, X, of the three wolfs in the k-th iterationj(k) The position of each gray wolf in the kth iteration is indicated. D1j(k),D2j(k),D3j(k) Respectively representing the position relation between the gray wolf and the three wolfs in the k-th iteration. A. thel(k) And Cl(k) (l ═ 1,2,3) are the parameter vectors used to control the direction of travel of the wolf pack and to control the effect of the distance between the wolf pack and the prey on the hunting process, respectively. The calculation formula is as follows:
Al(k)＝a(k)·(2r1-1),l＝1,2,3 (20)
Cl(k)＝2r2,l＝1,2,3 (21)
Figure BDA0002389445280000153
where a (k) is a vector that gradually decreases from 2 to 0 with the iteration process, and the layout of a decrease is averaged according to the set number of iterations, and if 200 iterations are performed, each decrease is 2/200 ═ 0.01; r is1And r2Is [0,1 ]]Random vector in between.
Repeating the step (3) and iterating to the last ZmaxAfter the last iteration is finished, the transmitting power Pt of each terminal corresponding to the alpha position of the wolf head and the access probability p of each terminal are the final optimal values of the optimization variables, and the optimal values are obtainedAnd substituting the optimal value of the variable into an optimization objective function eta (Pt, p) to obtain the final optimal value of the energy efficiency of the optimization objective system, and ending the algorithm.
Although the present invention has been described in detail with reference to the above embodiments, it will be understood by those skilled in the art that the present invention may be modified and equivalents may be substituted without departing from the spirit and scope of the invention.

Claims (3)

1. An authorization-free NOMA method for realizing URLLC based on halter strap transformation model is characterized by comprising the following steps:
step 1) estimating the number g of active terminals in the NOMA system based on a compressive sensing theory, and calculating a RIP parameter lambda; if lambda is more than 0 and less than 1, adopting an MMSE-SIC multi-user signal detection algorithm based on compressed sensing, sequentially estimating a channel matrix according to the descending order of the signal-to-interference-and-noise ratio of each terminal, and solving signals transmitted by each terminal from signals superposed by the multi-terminals; otherwise, a basic SIC multi-user signal detection algorithm is adopted, and the signals transmitted by each terminal are sequentially solved from the superposed signals according to the descending order of the signal power of each terminal;
step 2) the NOMA system adopts short packet transmission with limited block length, and analyzes the reachable transmission rate of the short packet of the NOMA unauthorized access system across layers under the condition that the NOMA system jointly considers the signal-to-interference-and-noise ratio statistical characteristics of an MAC layer and a physical layer mechanism; the method comprises the following steps:
the multi-terminal NOMA system is abstracted into an interference pattern G ═ (V, E), where V ═ V1,v2,……v4) Denotes a terminal set, E ═ E1,e2,……e4) Representing the interference relationship between transmission links of the terminals; let vector sigmaj∈{0,1}NA network transmission state j, representing an interference pattern G, (V, E), 1.. N, N is the number of terminals,
Figure FDA0002957598430000016
represents the vector σjI.e. the transmission state of terminal i in network transmission state j;
Figure FDA0002957598430000011
representing that the terminal i transmits data to the base station in a network transmission state j;
Figure FDA0002957598430000012
indicating that the terminal i does not transmit data to the base station in the network transmission state j; order to
Figure FDA0002957598430000013
Representing the signal-to-interference-and-noise ratio of a terminal i in a network transmission state j; for a given network transmission state j, solving the interruption probability of a terminal i in the network transmission state j by adopting a probability analysis method of sequence statistics
Figure FDA0002957598430000014
Combined transmission state sigmajProbability solution of occurrence interruption probability distribution Pr { SINR } of terminal i jointly considering MAC layer and physical layer mechanismsi}; for a given transport block size of l, bandwidth of B, block error rate of ρiThen, the achievable transmission rate R of the terminal i is calculated according to the formula (3)i：
Figure FDA0002957598430000015
Wherein the SINRiSignal-to-interference-and-noise ratio of the signal transmitted for terminal i, e denotes the base of the natural logarithm, Q-1(. -) represents a Q function;
step 3), logically viewing each terminal of the multi-terminal uplink NOMA system as two queues: a terminal buffer empty queue and a terminal buffer non-empty queue; based on the halter strap theory, calculating the probability of occurrence of each terminal cache non-empty queue, the delay violation probability of each terminal cache empty queue and the data packet arriving at the terminal of the terminal cache non-empty queue, and the probability of each terminal delay exceeding the delay bound; the method comprises the following steps:
calculating the probability delta of the occurrence of the terminal cache non-empty queue according to the formula (4)i；
Figure FDA0002957598430000021
Wherein a isi(t) is the number of packets arriving at terminal i in time slot t, E [ a ]i(t)]Represents the average value of the arrival packets of the terminal i; si(t) number of packets, Es, serving terminal i in time slot ti(t)]Represents the average value of the terminal i service package;
under the condition that the terminal buffer is empty, calculating the probability of successful transmission of the terminal i data packet under a given time delay boundary
Figure FDA0002957598430000022
Figure FDA0002957598430000023
Wherein k isiThe maximum time slot number of the data packet transmitted by the terminal i needing to be successfully transmitted in the time delay boundary requirement is represented;
Figure FDA0002957598430000024
representing the probability of successful transmission of a data packet of a terminal i in a time slot t;
according to the vector sigma described in step 2)j∈{0,1}NRepresenting a network transmission state j, the probability of the occurrence of the network transmission state j is represented as:
Figure FDA0002957598430000025
the probability of successful transmission for terminal i is expressed as:
Figure FDA0002957598430000026
calculating the time delay violation probability of the data packet arriving at the terminal i of the terminal buffer empty queue according to the formula (6)
Figure FDA0002957598430000027
Figure FDA0002957598430000028
For each terminal buffer non-empty queue, order Di(t) denotes the time delay of terminal i, Ai(t) represents the number of packets that terminal i arrives from time slot 0 to time slot t, Si(t) represents the number of data packets successfully served by the terminal i from the time slot 0 to the time slot t, and the time delay D of the terminal i is calculated according to the formula (7)i(t)
Di(t)＝min{n≥0|Ai(t-n)≤Si(t)} (7)
Calculating and obtaining the time delay D of the terminal i according to the formula (8)i(t) exceeding the time delay bound
Figure FDA0002957598430000029
Probability of (2)
Figure FDA00029575984300000210
Figure FDA00029575984300000211
Wherein the content of the first and second substances,
Figure FDA00029575984300000212
is a time delay bound, ha(ai(t)) is a function of the relevant characteristics of the arrival process, E [ h ]a(ai(0))]Function h representing relevant characteristics of arrival processa(ai(t)) expected value, h, at time slot 0s(si(t)) is a function of the relevant characteristics of the service process, ehs(si(0))]Function h representing service procedure related characteristicss(si(t)) at the expected value of 0 time slot,
Figure FDA0002957598430000031
is a special halter strap parameter that links the reach halter strap and service halter strap parameters together, defined as:
Figure FDA0002957598430000032
wherein theta isiIs the halter strap parameter, and is,
Figure FDA0002957598430000033
halter strap correction function representing the arrival process,
Figure FDA0002957598430000034
halter strap correction function representing service procedure;
Hiis a threshold value, and represents that the instantaneous arrival data packet is greater than the characteristic function h of the instantaneous service data packeta(ai(t)) and hs(si(t)) the minimum value of the product, defined as:
Hi:＝min{ha(ai(t))hs(si(t)):ai(t)-si(t)＞0,t≥0} (10)
obtaining the time delay violation probability under the terminal buffer non-empty queue according to the formula (11)
Figure FDA0002957598430000035
Figure FDA0002957598430000036
Merging the terminal buffer empty queue and the terminal buffer non-empty queue by utilizing a total probability formula to obtain the time delay violation probability epsilon of the terminal i under the general conditioni；
Figure FDA0002957598430000037
Step 4) constructing a multi-objective optimization problem, solving an optimal solution of the optimization problem by taking the maximum energy efficiency of the system as an optimization target, the reliability requirement of the URLLC time delay as constraint and the transmitting power and the access probability of the URLLC terminal as optimization variables to obtain a configuration scheme for controlling the access probability and the transmitting power of the URLLC terminal, wherein the method comprises the following steps:
let η (Pt, p) represent the energy efficiency function of the multi-user NOMA system, then
Figure FDA0002957598430000038
Wherein gamma isi(Pt, p) is the throughput of terminal i
Figure FDA0002957598430000039
Ωi(Pt, p) is the average energy consumption of terminal i, Ωi(Pt,p)＝E[Pti]；PtiFor the transmission power of terminal i, E [ Pt ]i]Representing the expected value of the transmission power of the terminal i; pt ═ Pt1,...,Pti,...,PtN]Transmitting power vector for terminal, p ═ p1,...,pi,...,pN]The probability vector is accessed to the terminal, and N is the number of the terminals;
order to
Figure FDA0002957598430000041
For terminal i's delay violating probability requirements, wiAnd representing the average energy consumption limit of the terminal i, the optimization problem is as follows:
Figure FDA0002957598430000042
the sum of the constraints in equation (14) is expressed as Λ (Pt, p):
Figure FDA0002957598430000043
Figure FDA0002957598430000044
Figure FDA0002957598430000045
Figure FDA0002957598430000046
Figure FDA0002957598430000047
Λ (Pt, p) ≧ 0, and all constraints in equation (14) can be satisfied if and only if Λ (Pt, p) ≧ 0;
constructing a single-target optimization problem with constraint conditions into a dual-target optimization problem without constraint conditions:
Figure FDA0002957598430000048
and (3) solving the constructed optimization problem of the formula (16) to obtain the optimal values of the terminal transmitting power vector Pt and the access probability vector p which enable the energy efficiency eta (Pt, p) of the system to be maximum.
2. The method of claim 1, wherein the method of estimating the number of active terminals in step 1) is as follows:
assuming that the signal-to-interference-and-noise ratio of a signal transmitted by a terminal i is SINR when the number of active terminals is gi|g；
Figure FDA0002957598430000049
Wherein PtiRepresenting the transmission power, v, of terminal i2Representing gaussian noise; ziRepresenting the product of the channel matrix and the spreading code matrix of terminal i; i ismIndicating a residual unlicensed transmission signal and,
Figure FDA0002957598430000051
for a given active terminal number g, solving the interruption probability Pr { SINR } of the terminal i by adopting a probability analysis method of sequence statisticsi|g< gamma }; and gamma represents a set system interrupt signal-to-interference-and-noise ratio threshold, the system interrupt probability Pr { outage | g } is represented as:
Figure FDA0002957598430000052
a is a distribution area of a terminal i;
for a given system interrupt probability value Pr { outage | g }, the number g of active terminals can be estimated according to the formula (2), wherein g is less than or equal to N.
3. The method of claim 1, wherein in step 4), the wolfsbane group optimization algorithm is used to solve the optimization problem of equation (16) to obtain the optimal values of the terminal transmission power vector Pt and the access probability vector p that maximize the system energy efficiency η (Pt, p)), and the method comprises:
(1) initializing wolf group X ═ { X with gray wolf number QjJ 1.. Q }, randomly distributed in the 2N-dimensional search space; initializing a position vector X of each wolfj＝[Pt,p]jCorresponding terminal transmission power vector is Ptj＝[Pt1,...,Pti,...,PtN]jTerminal access probability vector is pj＝[p1,...,pi,...,pN]j；
(2) Setting the maximum number of iterations to Zmax(ii) a In each iteration, according to the disclosureEquation (13) calculates the position vector X of each gray wolf in the wolf group Xj＝[Pt,p]jCorresponding optimization objective function 1/eta (X)j) A value of (d); calculating the position vector X of each gray wolf in the wolf group X according to the formula (14)j＝[Pt,p]jCorresponding constraint function Λ (X)j) A value of (d); let QfitIndicates that lambda (X) is satisfied in the wolf group Xj) The number of gray wolfs which is 0, and the fitness weight coefficient xi which is Qfit(ii)/Q; calculating fitness function values corresponding to the positions of all the gray wolves according to a formula (17):
Figure FDA0002957598430000053
(3) calculating the fitness function value corresponding to each gray wolf in X according to a formula (17), arranging the fitness values in an ascending order, and taking the first, second and third gray wolfs as alpha, beta and kappa which represent the leaders of wolf groups; the remaining gray wolves are called omega and represent common gray wolves; the common gray wolf omega updates the position of the common gray wolf omega according to the positions of the head wolfs alpha, beta and kappa, so that the wolf group gradually approaches to the prey; combining the position vectors of three wolfs in the k-th iteration, the wolf group XjJ 1.. said, each gray wolf in Q is subjected to position update according to the following formula (18a to 19), that is, a position vector of each gray wolf at the start of the next iteration is obtained:
D1j(k)＝Xα(k)-A1(k)·|C1(k)·Xα(k)-Xj(k)| (18a)
D2j(k)＝Xβ(k)-A2(k)·|C2(k)·Xβ(k)-Xj(k)| (18b)
D3j(k)＝Xκ(k)-A3(k)·|C3(k)·Xκ(k)-Xj(k)| (18c)
Figure FDA0002957598430000061
Xα(k),Xβ(k),Xκ(k) respectively representing the position vectors, X, of the three wolfs in the k-th iterationj(k) Representing the location of each gray wolf in the kth iteration; d1j(k),D2j(k),D3j(k) Respectively representing the position relation between the gray wolf and the three wolfs in the k-th iteration; a. thel(k) And Cl(k) (l ═ 1,2,3) are parameter vectors used to control the direction of travel of the wolf pack and to control the effect of the distance between the wolf pack and the prey on the hunting process, respectively; the calculation formula is as follows:
Al(k)＝a(k)·(2r1-1),l＝1,2,3 (20)
Cl(k)＝2r2,l＝1,2,3 (21)
Figure FDA0002957598430000062
where a (k) is a vector that gradually drops from 2 to 0 as the iterative process progresses; r is1And r2Is [0,1 ]]A random vector in between;
repeating the step (3) and iterating to the last ZmaxAnd after the last iteration is finished, the transmitting power Pt of each terminal and the access probability p of each terminal corresponding to the alpha position of the wolf are the final optimal values of the optimization variables.
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