CN106714293B - Junction network resource allocation methods based on qos requirement energy content collector node - Google Patents

Junction network resource allocation methods based on qos requirement energy content collector node Download PDF

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CN106714293B
CN106714293B CN201611255936.4A CN201611255936A CN106714293B CN 106714293 B CN106714293 B CN 106714293B CN 201611255936 A CN201611255936 A CN 201611255936A CN 106714293 B CN106714293 B CN 106714293B
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subcarrier
time slot
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CN106714293A (en
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马丕明
崔敏玉
马艳波
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Shandong University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W52/00Power management, e.g. Transmission Power Control [TPC] or power classes
    • H04W52/04Transmission power control [TPC]
    • H04W52/18TPC being performed according to specific parameters
    • H04W52/26TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service]
    • H04W52/265TPC being performed according to specific parameters using transmission rate or quality of service QoS [Quality of Service] taking into account the quality of service QoS
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W52/00Power management, e.g. Transmission Power Control [TPC] or power classes
    • H04W52/04Transmission power control [TPC]
    • H04W52/30Transmission power control [TPC] using constraints in the total amount of available transmission power
    • H04W52/34TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading
    • H04W52/346TPC management, i.e. sharing limited amount of power among users or channels or data types, e.g. cell loading distributing total power among users or channels
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W52/00Power management, e.g. Transmission Power Control [TPC] or power classes
    • H04W52/04Transmission power control [TPC]
    • H04W52/38TPC being performed in particular situations
    • H04W52/46TPC being performed in particular situations in multi-hop networks, e.g. wireless relay networks
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W72/00Local resource management
    • H04W72/04Wireless resource allocation
    • H04W72/044Wireless resource allocation based on the type of the allocated resource
    • H04W72/0453Resources in frequency domain, e.g. a carrier in FDMA
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W72/00Local resource management
    • H04W72/04Wireless resource allocation
    • H04W72/044Wireless resource allocation based on the type of the allocated resource
    • H04W72/0473Wireless resource allocation based on the type of the allocated resource the resource being transmission power
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W72/00Local resource management
    • H04W72/50Allocation or scheduling criteria for wireless resources
    • H04W72/54Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/542Allocation or scheduling criteria for wireless resources based on quality criteria using measured or perceived quality
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W72/00Local resource management
    • H04W72/50Allocation or scheduling criteria for wireless resources
    • H04W72/54Allocation or scheduling criteria for wireless resources based on quality criteria
    • H04W72/543Allocation or scheduling criteria for wireless resources based on quality criteria based on requested quality, e.g. QoS

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Quality & Reliability (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

Based on the junction network resource allocation methods of qos requirement energy content collector node, belong to wireless communication technology field.Relay network system is used in the present invention, includes within the system transmitting terminal, receiving end and relay node, wherein transmitting terminal and relay node can carry out collection of energy, and be communicated using the energy of collection.In the farther away communication of relative distance, for enhancing communication security reliability and reduce Communication Jamming the problems such as, we use relaying technique.In the junction network resource allocation methods that the present invention studies, in conjunction with collection of energy and relaying technique by co-allocation system resource, that is, subcarrier and its power, so that available capacity maximizes during the relay network, communication performance is always improved.

Description

Junction network resource allocation methods based on qos requirement energy content collector node
Technical field
The present invention relates to a kind of junction network resource allocation methods based on qos requirement energy content collector node, belong to nothing Line communication technology field.
Background technique
With the continuous development of wireless communication technology and the continuous application of relaying technique, the relaying of energy content collector node The research of network has attracted more and more attention from people.Wireless communication system with collection of energy node, can use such as the sun Energy battery, absorption of vibrations equipment, microbiological fuel cell etc. collect energy from nature, so that wireless communication system work makes With.In such systems, energy can be collected while being communicated, and is stored in the battery so that subsequent communication makes With.
Recently, the correlative study that the data having based on collection of energy are sent more in document, these researchs are devoted to whole In a data transmission procedure under energy causality constraint and limited battery capacity restraint condition, the handling capacity of whole system is improved, Transmitting terminal and relay node can be with collection of energy in relayed communications network for present invention research, and are carried out using the energy collected Communication is maximized in communication process by jointly assigning resources (subcarrier and power) Lai Shixian network system available capacity. Such as " Resource Allocation for Delay-Sensitive Traffic over LTE-Advanced Relay Networks”[IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS,VOL.14,NO.8,AUGUST 2015] discussed in LTE-A junction network in the case where meeting time delay qos requirement, by co-allocation subcarrier and power come Maximize the available capacity of system.In " Transmission with Energy Harvesting Nodes in Fading Wireless Channels:Optimal Policies " [IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL.29, NO.8, SEPTEMBER 2011] in have studied in a wireless communication system using energy receive Collect equipment and collects the energy progress data communication come so that throughput of system maximizes.It is received in relay network system using energy Collection is to be communicated, at present in it can consult reference materials, the still not research of this respect.
Summary of the invention
In order to overcome defect and deficiency of the existing technology, the energy content collector node based on qos requirement is being considered The resource allocation of junction network to realize that relay network system available capacity maximizes, and guarantees communication process energy consumption No more than the currently stored energy of battery, the junction network money based on qos requirement energy content collector node that the present invention provides a kind of Source distribution method.
Technical scheme is as follows:
A kind of junction network resource allocation methods based on qos requirement energy content collector node are by wireless communication Junction network realizes, which includes transmitting terminal (TX), relay node (RN) and receiving end (RX), wherein transmitting terminal and in Collection of energy can be carried out after node, system uses double jump relaying technique, and the wireless channel of transmitting terminal to relay node is expressed as Link 1 is link-1, and the wireless channel of relay node to receiving end is expressed as link 2 i.e. link-2;Relay node (RN) passes through Link 1 receives the data of transmitting terminal, is then decoded forwarding, sends data to receiving end (RX) by link 2;Relaying section Point work is in semiduplex mode;If wireless channel obeys block decline, each piece of when a length of T;The communication network shares N number of sub- load Wave, each subcarrier bandwidth is WHz, and n-th (n ∈ { 1,2 ... N }) a subcarrier can only be assigned uniquely to link 1 and chain One of road 2;The time interval of adjacent collection of energy twice is defined as one " time slot ", considers that entire communication process has K A time slot, when each time slot a length of T0, in kth (k ∈ K={ 1,2 ..., N }) a time slot initial time transmitting terminal and relaying section The energy that point is collected is expressed as E1 (k)And E2 (k), wherein the symbol (k) in all variable upper right corner indicate the variable be when Variate-value corresponding to gap k, wireless channel link1 and link2 are represented by link-i, i ∈ { 1,2 };
By available capacity concept it is found that in k-th of time slot sub-carrier n, wireless channel link-i, i ∈'s { 1,2 } is effective Capacity are as follows:
Wherein E [] indicates operation of averaging, and θ indicates delay parameter, that is, qos parameter, I ∈ { 1,2 },Indicate handling capacity of the time slot k sub-carrier n in channel link-i, γi,nIndicate sub-carrier n in link The transient channel power gain of link-i,Indicate the transmission power for subcarrier n in time slot k, link-i, N0Expression connects The power spectral density of the additive white Gaussian noise (AWGN) of debit, I indicate inter-cell interference, and Γ indicates Signal to Interference plus Noise Ratio difference, right Rayleigh fading channel, power gain meetWherein βi,nIndicate being averaged for subcarrier n, link-i Channel power gain, f (γi,n) indicate with γi,nFor the function of independent variable, by the function by instantaneous channel gain γi,nPeace Equal channel power gain βi,nIt connects, consideration is in low Signal to Interference plus Noise RatioIn the case where willSubstitution formula (1) handle:
WithIndicate the matching attribute in k-th of time slot subcarrier n, wherein It indicates In k-th of time slot, subcarrier n distributes to link-i;It indicates to be not assigned to link-i in k-th of time slot subcarrier n; When to subcarrier and power distribution, by above-mentioned in k-th of time slot, the available capacity of link-i are as follows:
Wherein symbol Σ indicates summation operation, and in k-th of time slot, in given qos value θ, the junction network is effective Capacity can be expressed asSymbol min expression is askedMinimum value in the two;
Above by the distribution of optimization subcarrier and the transmission power of transmitting terminal and relaying, in the case where meeting certain QoS and requiring Realize that the available capacity of the wireless communications relay network system maximizes, steps are as follows for the resource allocation methods:
One, problem is planned
By above description, our existing plan optimization problem (P1) is as follows:
Wherein max indicates maximizing, is objective function after the symbol, and s.t. indicates constraint symbol, Indicate that n can take arbitrary value in { 1,2 .., N };L time slot is respectively indicated in link link-1 and link-2 The transmission power of subcarrier n;E1 (l)、E2 (l)It is illustrated respectively in the energy that l time slot initial time transmitting terminal and relay node are collected It measures, wherein l ∈ { 1,2 .., k };In order to facilitate above-mentioned optimization problem is solved, relax the constraint of subcarrier distribution factor, even
And quote new variablesIntroducing new auxiliary variable t, (t is indicated to excellent Change variable), get off to ask the maximum value of t in the constraint condition for meeting problem (P1), then above-mentioned optimization problem can be of equal value at asking It inscribes (P1-1)
By relaxing subcarrier distribution factorConstraint, optimization problem becomes (P1-1) form from (P1) form, two Person is of equal value;
Two, problem solving
Above-mentioned optimization problem is convex optimization problem, and convex optimum theory method can be used and solve;The glug of problem (P1-1) is bright Day function is:
J and l indicate the summation variable used in summation process, their value be respectively j ∈ { 1,2 .., K }, l ∈ 1, 2,..,j};
Wherein, Lagrange multiplier are as follows: α={ α12,...,αK,
μ={ μ12,...,μK,
λ={ λ12,...,λK,
ν={ ν12,...,νK,
η={ η1,1,...,η1,N;...;ηK,1,...,ηK,N};
Subcarrier distribution:
Power distribution:
Then dual problem can be obtained:
(P2)min g(α,μ,λ,ν,η)
s.t.α≥0,μ≥0,λ≥0,ν≥0 (7)
WhereinG (α, μ, λ, ν, η) is handled as follows:
Wherein:
ByIt can obtain:
WhereinRespectively indicate αj、μjOptimal solution;
(1) optimal power allocation
Above-mentionedWithG is substituted into respectively1(α, λ, η) and g2(μ, ν, η), and respectively Enable g1(α, λ, η) and g2(μ, ν, η) is rightWithDerivation:
:
:
Wherein " * " in the parameter upper right corner indicates the optimal solution of the parameter, [x]+It indicates if x value is non-negative, [x]+=x;Such as Fruit x is negative, then [x]+=0, so far we have obtained the optimal power allocation about Lagrange multiplier;
(2) optimal subcarrier distribution
?In generation, returns g1In (α, λ, η):
The component extraction of k-th of time slot is come out:
Wherein
It can be seen that above formula aboutLinearly, it therefore obtains
It can similarly obtain:
So the dual function about k-th of time slot can be obtained:
By?
Then optimal subcarrier distribution are as follows:
So far optimal subcarrier distribution is obtained;
(3) sub- Gradient Iteration solves
Above-mentioned dual problem convex problem can be solved by sub- gradient iteration method, the sub- gradient point of each Lagrange multiplier It is not expressed as Δ αk、Δμk、ΔλkWith Δ νk, expression formula is respectively such as following four formula:
Each group Lagrange multiplier is acquired by sub- gradient iteration method using the sub- gradient of above-mentioned each Lagrange multiplier, then In generation, returns optimal power allocation formulaWithOptimal subcarrier distribution power formulaWithAvailable capacity formulaWithThe optimal power allocation scheme of the relay network system, optimal subcarrier distribution side can be respectively obtained Case and corresponding available capacity.
The full name in English of the QoS is " Quality of Service ", Chinese entitled " service quality ".QoS is net A kind of technology for the problems such as a kind of security mechanism of network is for solving network delay and obstruction.
The concept of the available capacity refers in the case where guaranteeing the certain delay parameter i.e. requirement of qos parameter (θ), channel energy The peak transfer rate of support.
Beneficial effects of the present invention are as follows:
It is communicated in the present invention using the energy of collection, during the Resource Allocation Formula studied in invention is not only able to achieve It maximizes to enhance the performance of wireless channel after system available capacity in network system communication process, and can guarantee and communicated Energy constraint related request in journey;Compared to conventional wireless system, the wireless system with collectable energy node has by ring The advantages that border restraining force is small, persistence is high, service life is significantly longer is improved greatly to the one of performance in wireless communication systems.? In the farther away communication of relative distance, for enhancing communication security reliability and reduce Communication Jamming the problems such as, we using relaying Technology.Collection of energy and relaying technique are combined in the present invention, co-allocation system resource in system communication processes so as to effectively hold Amount maximizes, and always improves communication performance.
Specific embodiment
Below with reference to embodiment, the invention will be further described, but not limited to this.
Embodiment:
A kind of junction network resource allocation methods based on qos requirement energy content collector node are by wireless communication Junction network realizes, which includes transmitting terminal (TX), relay node (RN) and receiving end (RX), wherein transmitting terminal and in Collection of energy can be carried out after node, system uses double jump relaying technique, and the wireless channel of transmitting terminal to relay node is expressed as Link 1 is link-1, and the wireless channel of relay node to receiving end is expressed as link 2 i.e. link-2;Relay node (RN) passes through Link 1 receives the data of transmitting terminal, is then decoded forwarding, sends data to receiving end (RX) by link 2;Relaying section Point work is in semiduplex mode;If wireless channel obeys block decline, each piece of when a length of T;The communication network shares N number of sub- load Wave, each subcarrier bandwidth is WHz, and n-th (n ∈ { 1,2 ... N }) a subcarrier can only be assigned uniquely to link 1 and chain One of road 2;The time interval of adjacent collection of energy twice is defined as one " time slot ", considers that entire communication process has K A time slot, when each time slot a length of T0, in kth (k ∈ K={ 1,2 ..., N }) a time slot initial time transmitting terminal and relaying section The energy that point is collected is expressed as E1 (k)And E2 (k), wherein the symbol (k) in all variable upper right corner indicate the variable be when Variate-value corresponding to gap k, wireless channel link1 and link2 are represented by link-i, i ∈ { 1,2 };
By available capacity concept it is found that in k-th of time slot sub-carrier n, wireless channel link-i, i ∈'s { 1,2 } is effective Capacity are as follows:
Wherein E [] indicates operation of averaging, and θ indicates delay parameter, that is, qos parameter, I ∈ { 1,2 },Indicate handling capacity of the time slot k sub-carrier n in channel link-i, γi,nIndicate sub-carrier n in link The transient channel power gain of link-i,Indicate the transmission power for subcarrier n in time slot k, link-i, N0Expression connects The power spectral density of the additive white Gaussian noise (AWGN) of debit, I indicate inter-cell interference, and Γ indicates Signal to Interference plus Noise Ratio difference, right Rayleigh fading channel, power gain meetWherein βi,nIndicate being averaged for subcarrier n, link-i Channel power gain, f (γi,n) indicate with γi,nFor the function of independent variable, by the function by instantaneous channel gain γi,nPeace Equal channel power gain βi,nIt connects, consideration is in low Signal to Interference plus Noise RatioIn the case where willSubstitution formula (1) handle:
WithIndicate the matching attribute in k-th of time slot subcarrier n, wherein It indicates In k-th of time slot, subcarrier n distributes to link-i;It indicates to be not assigned to link-i in k-th of time slot subcarrier n; When to subcarrier and power distribution, by above-mentioned in k-th of time slot, the available capacity of link-i are as follows:
Wherein symbol Σ indicates summation operation, and in k-th of time slot, in given qos value θ, the junction network is effective Capacity can be expressed asMin expression is askedMinimum value in the two;
Above by the distribution of optimization subcarrier and the transmission power of transmitting terminal and relaying, in the case where meeting certain QoS and requiring Realize that the available capacity of the wireless communications relay network system maximizes, steps are as follows for the resource allocation methods:
One, problem is planned
By above description, our existing plan optimization problem (P1) is as follows:
Wherein max indicates maximizing, is objective function after the symbol, and s.t. indicates constraint symbol, Indicate that n can take arbitrary value in { 1,2 .., N };L time slot is respectively indicated in link link-1 and link-2 The transmission power of subcarrier n;E1 (l)、E2 (l)It is illustrated respectively in the energy that l time slot initial time transmitting terminal and relay node are collected It measures, wherein l ∈ { 1,2 .., k };In order to facilitate above-mentioned optimization problem is solved, relax the constraint of subcarrier distribution factor, even
And quote new variablesIntroducing new auxiliary variable t, (t is indicated to excellent Change variable), get off to ask the maximum value of t in the constraint condition for meeting problem (P1), then above-mentioned optimization problem can be of equal value at asking It inscribes (P1-1)
By relaxing subcarrier distribution factorConstraint, optimization problem becomes (P1-1) form, the two from (P1) form It is of equal value;
Two, problem solving
Above-mentioned optimization problem is convex optimization problem, and convex optimum theory method can be used and solve;The glug of problem (P1-1) is bright Day function is:
J and l indicate the summation variable used in summation process, their value be respectively j ∈ { 1,2 .., K }, l ∈ 1, 2,..,j};
Wherein, Lagrange multiplier are as follows: α={ α12,...,αK,
μ={ μ12,...,μK}
λ={ λ12,...,λK,
ν={ ν12,...,νK,
η={ η1,1,...,η1,N;...;ηK,1,...,ηK,N,
Subcarrier distribution:
Power distribution:
Then dual problem can be obtained:
(P2)min g(α,μ,λ,ν,η)
s.t.α≥0,μ≥0,λ≥0,ν≥0 (7)
WhereinG (α, μ, λ, ν, η) is handled as follows:
Wherein:
ByIt can obtain:
WhereinRespectively indicate αj、μjOptimal solution;
(1) optimal power allocation
Above-mentionedWithG is substituted into respectively1(α, λ, η) and g2(μ, ν, η), and respectively It enables
g1(α, λ, η) and g2(μ, ν, η) is rightWithDerivation:
:
:
Wherein " * " in the parameter upper right corner indicates the optimal solution of the parameter, [x]+It indicates if x value is non-negative, [x]+=x;Such as Fruit x is negative, then [x]+=0, so far we have obtained the optimal power allocation about Lagrange multiplier;
(2) optimal subcarrier distribution
?In generation, returns g1In (α, λ, η):
The component extraction of k-th of time slot is come out:
Wherein
It can be seen that above formula aboutLinearly, it therefore obtains
It can similarly obtain:
So the dual function about k-th of time slot can be obtained:
By?
Then optimal subcarrier distribution are as follows:
So far optimal subcarrier distribution is obtained;
(3) sub- Gradient Iteration solves
Above-mentioned dual problem convex problem can be solved by sub- gradient iteration method, the sub- gradient point of each Lagrange multiplier It is not expressed as Δ αk、Δμk、ΔλkWith Δ νk, expression formula is respectively such as following four formula:
Each group Lagrange multiplier is acquired by sub- gradient iteration method using the sub- gradient of above-mentioned each Lagrange multiplier, then In generation, returns optimal power allocation formulaWithOptimal subcarrier distribution power formulaWithAvailable capacity formulaWithThe optimal power allocation scheme of the relay network system, optimal subcarrier distribution side can be respectively obtained Case and corresponding available capacity.

Claims (1)

  1. It is by in wireless communication 1. a kind of junction network resource allocation methods based on qos requirement energy content collector node It is realized after network, which includes transmitting terminal, relay node and receiving end, wherein transmitting terminal and relay node Collection of energy is carried out, system uses double jump relaying technique, and the wireless channel of transmitting terminal to relay node is expressed as link 1 i.e. Link-1, the wireless channel of relay node to receiving end are expressed as link 2 i.e. link-2;Relay node is received by link 1 Then the data of transmitting terminal are decoded forwarding, send data to receiving end by link 2;Relay node works in half-duplex Mode;If wireless channel obeys block decline, each piece of when a length of T;The communication network shares N number of subcarrier, each subcarrier Bandwidth is WHz, and n-th (n ∈ { 1,2 ... N }) a subcarrier can only be assigned uniquely to link 1 and link 2 one of them;Phase The time interval of adjacent collection of energy twice is defined as one " time slot ", considers that entire communication process has K time slot, each time slot Shi Changwei T0, respectively indicated in the energy that a time slot initial time transmitting terminal of kth (k ∈ { 1,2 ... K }) and relay node are collected For E1 (k)And E2 (k), wherein the symbol (k) in all variable upper right corner indicates that the variable is the variate-value corresponding to time slot k, nothing Wired link link-1 and link-2 are represented by link-i, i ∈ { 1,2 };
    By available capacity concept it is found that in k-th of time slot sub-carrier n, the available capacity of wireless channel link-i, i ∈ { 1,2 } Are as follows:
    Wherein E [] indicates operation of averaging, and θ indicates delay parameter, that is, qos parameter, Indicate time slot k sub-carrier n, the handling capacity of channel link-i, γi,nIndicate sub-carrier n in the instantaneous of link link-i Channel power gain,Indicate the transmission power for subcarrier n in time slot k, link-i, N0Indicate that the additivity of recipient is high The power spectral density of this white noise (AWGN), I indicate inter-cell interference, and Γ indicates Signal to Interference plus Noise Ratio difference, to rayleigh fading channel, Power gain meetsWherein βi,nIndicate the average channel power gain for subcarrier n, link-i, f (γi,n) indicate with γi,nFor the function of independent variable, by the function by instantaneous channel gain γi,nAnd average channel power gain βi,nIt connects, consideration is in low Signal to Interference plus Noise RatioIn the case where willSubstitution formula (1) carries out It handles:
    WithIndicate the matching attribute in k-th of time slot subcarrier n, wherein It indicates the K time slot, subcarrier n distribute to link-i;It indicates to be not assigned to link-i in k-th of time slot subcarrier n;It is given When subcarrier and power distribution, it can obtain in k-th of time slot, the available capacity of link-i are as follows:
    Wherein symbol Σ indicates summation operation, in k-th of time slot, the available capacity of the junction network in given qos value θ It can be expressed asSymbol min expression is askedMinimum value in the two;
    Above by the distribution of optimization subcarrier and the transmission power of transmitting terminal and relaying, realized in the case where meeting certain QoS and requiring The available capacity of the wireless communications relay network system maximizes, and steps are as follows for the resource allocation methods:
    One, problem is planned
    By above description, our existing plan optimization problem (P1) is as follows:
    Wherein max indicates maximizing, is objective function after the symbol, and s.t. indicates constraint symbol,It indicates N can take arbitrary value in { 1,2 .., N };L time slot is respectively indicated to carry in link link-1 and link-2 neutron The transmission power of wave n;E1 (l)、E2 (l)It is illustrated respectively in the energy that l time slot initial time transmitting terminal and relay node are collected, Middle l ∈ { 1,2 .., k };In order to facilitate above-mentioned optimization problem is solved, relax the constraint of subcarrier distribution factor, evenAnd quote new variablesNew auxiliary variable t is introduced, problem (P1) is being met Constraint condition gets off to ask the maximum value of t, and then above-mentioned optimization problem can equivalence problematic (P1-1)
    By relaxing subcarrier distribution factorConstraint, optimization problem becomes (P1-1) form from (P1) form, and the two is Valence;
    Two, problem solving
    Above-mentioned optimization problem is convex optimization problem, and convex optimum theory method can be used and solve;The Lagrangian letter of problem (P1-1) Number is:
    J and l indicate the summation variable used in summation process, their value be respectively j ∈ { 1,2 .., K }, l ∈ 1, 2,..,j};
    Wherein, Lagrange multiplier are as follows: α={ α12,...,αK,
    μ={ μ12,...,μK,
    λ={ λ12,...,λK,
    ν={ ν12,...,νK,
    η={ η1,1,...,η1,N;...;ηK,1,...,ηK,N,
    Subcarrier distribution:
    Power distribution:
    Then dual problem can be obtained:
    (P2)min g(α,μ,λ,ν,η)
    s.t.α≥0,μ≥0,λ≥0,ν≥0 (7)
    WhereinG (α, μ, λ, ν, η) is handled as follows:
    Wherein:
    ByIt can obtain:
    WhereinRespectively indicate αj、μjOptimal solution;
    (1) optimal power allocation
    Above-mentionedWithG is substituted into respectively1(α, λ, η) and g2(μ, ν, η), and g is enabled respectively1 (α, λ, η) and g2(μ, ν, η) is rightWithDerivation:
    :
    :
    Wherein " * " in the parameter upper right corner indicates the optimal solution of the parameter, [x]+It indicates if x value is non-negative, [x]+=x;If x It is negative, then [x]+=0, so far we have obtained the optimal power allocation about Lagrange multiplier;
    (2) optimal subcarrier distribution
    ?In generation, returns g1In (α, λ, η):
    The component extraction of k-th of time slot is come out:
    Wherein
    It can be seen that above formula aboutLinearly, it therefore obtains
    It can similarly obtain:
    So the dual function about k-th of time slot can be obtained:
    By?
    Then optimal subcarrier distribution are as follows:
    So far optimal subcarrier distribution is obtained;
    (3) sub- Gradient Iteration solves
    Above-mentioned dual problem convex problem can be solved by sub- gradient iteration method, and the sub- gradient of each Lagrange multiplier distinguishes table It is shown as Δ αk、Δμk、ΔλkWith Δ νk, expression formula is respectively such as following four formula:
    Each group Lagrange multiplier is acquired by sub- gradient iteration method using the sub- gradient of above-mentioned each Lagrange multiplier, then generation returns Optimal power allocation formulaWithOptimal subcarrier distribution power formulaWithAvailable capacity formula WithCan respectively obtain the optimal power allocation scheme of the relay network system, optimal subcarrier distribution scheme and Corresponding available capacity.
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