CN106714293A - Resource distribution method for relay network with energy harvesting nodes based on QoS demand - Google Patents

Abstract

The invention discloses a resource distribution method for a relay network with energy harvesting nodes based on a QoS demand and belongs to the technical field of wireless communication. According to the method, a relay network system is employed. The system comprises a sending end, a receiving end and a relay node. The sending end and the relay node can harvest energy and communicate through utilization of the harvested energy. In communication at the relatively long distance, in order to improve the communication security and reliability and reduce the problems such as the communication interference, a relay technology is employed. According to the resource distribution method for the relay network researched by the invention, the energy harvesting and the relay technology are combined, system resources namely subcarriers and the power are jointly distributed, so the effective capacity is maximized in the communication process of the relay network, and the communication performance is 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 technology

With wireless communication technology continue to develop and relaying technique continuous application, the relaying of energy content collector node The research of network increasingly causes the concern of people.Wireless communication system with collection of energy node, it is possible to 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 communication below makes With.

Recently, there is the correlative study of the data is activation based on collection of energy in document, these researchs are devoted to whole more In individual data transmission procedure under energy causality constraint and limited battery capacity restraint condition, the handling capacity of whole system is improved, The present invention research transmitting terminal and via node in relayed communications network with collection of energy, and can be carried out using the energy collected Communication, realizes that network system available capacity is maximized by jointly assigning resources (subcarrier and power) in communication process. 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 networks in the case where time delay qos requirement is met, 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 Collection equipment is collected the energy for coming and enters row data communication so that throughput of system is maximized.Received using energy in relay network system Collect to be communicated, at present in it can consult reference materials, the still research without this respect.

The content of the invention

For the defect and deficiency that overcome prior art to exist, 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 is maximized, and ensures communication process energy consumption No more than the currently stored energy of battery, the invention provides a kind of junction network money based on qos requirement energy content collector node 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 radio communication Come what is realized, the system includes transmitting terminal (TX), via node (RN) and receiving terminal (RX) to junction network, and wherein transmitting terminal is with Collection of energy can be carried out after node, system uses double jump relaying technique, the wireless channel of transmitting terminal to via node to be expressed as Link 1 is link-1, and the wireless channel of via node to receiving terminal is expressed as link 2 i.e. link-2；Via node (RN) passes through Link 1 receives the data of transmitting terminal, then carries out decoding forwarding, and data are sent to receiving terminal (RX) by link 2；Relaying section Point is operated in semiduplex mode；If wireless channel obeys block decline, when a length of T of each block；The communication network has N number of sub- load Ripple, a width of WHz of each sub-carrier bin, and n-th (n ∈ { 1,2 ... N }) individual 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 ", it is contemplated that whole communication process has K Individual time slot, a length of T during each time slot₀, saved in kth (k ∈ K={ 1,2 ..., N }) individual time slot initial time transmitting terminal and relaying The energy that point is collected is expressed as E₁ ^(k)And E₂ ^(k), wherein the symbol (k) in all variable upper right corner represent the variable be when Variate-value corresponding to gap k, wireless channel link1 and link2 are represented by link-i, i ∈ { 1,2 }；

From available capacity concept, in k-th time slot sub-carrier n, wireless channel link-i, i ∈ { 1,2 } it is effective Capacity is：

Wherein E [] represents computing of averaging, and θ represents delay parameter i.e. qos parameter, I ∈ { 1,2 },Represent handling capacities of the time slot k sub-carriers n in channel link-i, γ_i,nRepresent sub-carrier n in link The transient channel power gain of link-i,Represent the transmit power in time slot k, link-i, N for subcarrier n₀Represent and receive The power spectral density of the additive white Gaussian noise (AWGN) of side, I represents inter-cell interference, and Γ represents Signal to Interference plus Noise Ratio difference, to auspicious Sharp fading channel, power gain meetsWherein β_i,nRepresent the average letter for subcarrier n, link-i Road power gain, f (γ_i,n) represent with γ_i,nIt is the function of independent variable, by the function by instantaneous channel gain γ_i,nWith it is average Channel power gain β_i,nConnect, it is considered to be in low Signal to Interference plus Noise RatioIn the case of will Substitution formula (1) process：

WithRepresent in k-th matching attribute of time slot subcarrier n, wherein Represent In k-th time slot, subcarrier n distributes to link-i；Expression is not assigned to link-i in k-th time slot subcarrier n； During to subcarrier and power distribution, obtained in k-th time slot by above-mentioned, the available capacity of link-i is：

Wherein symbol Σ represents summation operation, and in k-th time slot, the junction network is effective in the case of given qos value θ Capacity can be expressed asSymbol min is represented and askedMinimum value in both；

Distribution and the transmit power of transmitting terminal and relaying above by optimization subcarrier, in the case where certain QoS requirement is met Realize that the available capacity of the wireless communications relay network system is maximized, the resource allocation methods step is as follows：

First, problem planning

By above description, our existing plan optimizations problem (P1) are as follows：

Wherein max represents maximizing, is object function after the symbol, and s.t. represents constraint symbol, Represent that n can take arbitrary value in { 1,2 .., N }；Represent l time slots in link link-1 and link-2 respectively The transmit power of subcarrier n；E₁ ^(l)、E₂ ^(l)It is illustrated respectively in the energy that l time slot initial time transmitting terminals and via node are collected Amount, wherein l ∈ { 1,2 .., k }；Above-mentioned optimization problem is solved for convenience, relaxes the constraint of subcarrier distribution factor, even

And quote new variables(t is represented and is treated excellent to introduce new auxiliary variable t Change variable), get off to ask the maximum of t in the constraints for meeting problem (P1), then above-mentioned optimization problem can be with equivalence into asking Topic (P1-1)

By relaxing subcarrier distribution factorConstraint, optimization problem is changed into (P1-1) form from (P1) form, both It is of equal value；

2nd, problem solving

Above-mentioned optimization problem is convex optimization problem, can be solved using convex optimum theory method；The glug of problem (P1-1) is bright Day function is：

J and l represent the summation variable used in summation process, their value be respectively j ∈ { 1,2 .., K }, l ∈ 1, 2,..,j}；

Wherein, Lagrange multiplier is：α={ α₁,α₂,...,α_K,

μ={ μ₁,μ₂,...,μ_K,

λ={ λ₁,λ₂,...,λ_K,

ν={ ν₁,ν₂,...,ν_K,

η={ η_1,1,...,η_1,N；...；η_K,1,...,η_K,N}；

Subcarrier is distributed：

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：

ByCan obtain：

Whereinα is represented respectively_j、μ_jOptimal solution；

(1) optimal power allocation

Above-mentionedWithG is substituted into respectively₁(α, λ, η) and g₂(μ, ν, η), and respectively Make g₁(α, λ, η) and g₂(μ, ν, η) is rightWithDerivation：

：

：

" * " in the wherein parameter upper right corner represents the optimal solution of the parameter, [x]⁺If representing x value non-negative, [x]⁺=x；Such as Fruit x is negative, then [x]⁺=0, so far we obtained the optimal power allocation on Lagrange multiplier；

(2) optimal subcarrier distribution

In generation, returns g₁In (α, λ, η)：

K-th component extraction of time slot is out obtained：

Wherein

It can be seen that above formula onLinearly, thus

Can similarly obtain：

So can obtain on k-th dual function of time slot：

By

Then optimal subcarrier is assigned as：

So far optimal subcarrier distribution is obtained；

(3) sub- Gradient Iteration is solved

Above-mentioned dual problem convex problem, can be solved by sub- gradient iteration method, the sub- gradient point of each Lagrange multiplier Δ α is not expressed as_k、Δμ_k、Δλ_kWith Δ ν_k, expression formula is respectively such as following four formula：

Each group Lagrange multiplier is tried to achieve 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 formulaWithJust the optimal power allocation scheme of the relay network system, optimal subcarrier distribution side can be respectively obtained Case and corresponding available capacity.

The English full name of described QoS is " Quality of Service ", Chinese entitled " service quality ".QoS is net A kind of technology of the problems such as a kind of security mechanism of network is for solving network delay and obstruction.

The concept of described available capacity refers to the channel energy in the case where the certain delay parameter i.e. requirement of qos parameter (θ) is ensured The peak transfer rate of support.

Beneficial effects of the present invention are as follows：

Communicated using the energy collected in the present invention, during the Resource Allocation Formula studied in invention can not only be realized Maximized so as to strengthen the performance of wireless channel after system available capacity in network system communication process, and can guarantee that and communicated Energy constraint related request in journey；Compared to conventional wireless system, have by ring with the wireless system that can collect energy node The advantages of 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 relative distance communication farther out, 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 is maximized, and always improves communication performance.

Specific embodiment

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 radio communication Come what is realized, the system includes transmitting terminal (TX), via node (RN) and receiving terminal (RX) to junction network, and wherein transmitting terminal is with Collection of energy can be carried out after node, system uses double jump relaying technique, the wireless channel of transmitting terminal to via node to be expressed as Link 1 is link-1, and the wireless channel of via node to receiving terminal is expressed as link 2 i.e. link-2；Via node (RN) passes through Link 1 receives the data of transmitting terminal, then carries out decoding forwarding, and data are sent to receiving terminal (RX) by link 2；Relaying section Point is operated in semiduplex mode；If wireless channel obeys block decline, when a length of T of each block；The communication network has N number of sub- load Ripple, a width of WHz of each sub-carrier bin, and n-th (n ∈ { 1,2 ... N }) individual 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 ", it is contemplated that whole communication process has K Individual time slot, a length of T during each time slot₀, saved in kth (k ∈ K={ 1,2 ..., N }) individual time slot initial time transmitting terminal and relaying The energy that point is collected is expressed as E₁ ^(k)And E₂ ^(k), wherein the symbol (k) in all variable upper right corner represent the variable be when Variate-value corresponding to gap k, wireless channel link1 and link2 are represented by link-i, i ∈ { 1,2 }；

From available capacity concept, in k-th time slot sub-carrier n, wireless channel link-i, i ∈ { 1,2 } it is effective Capacity is：

Wherein E [] represents computing of averaging, and θ represents delay parameter i.e. qos parameter, I ∈ { 1,2 },Represent handling capacities of the time slot k sub-carriers n in channel link-i, γ_i,nRepresent sub-carrier n in link The transient channel power gain of link-i,Represent the transmit power in time slot k, link-i, N for subcarrier n₀Represent and receive The power spectral density of the additive white Gaussian noise (AWGN) of side, I represents inter-cell interference, and Γ represents Signal to Interference plus Noise Ratio difference, to auspicious Sharp fading channel, power gain meetsWherein β_i,nRepresent the average letter for subcarrier n, link-i Road power gain, f (γ_i,n) represent with γ_i,nIt is the function of independent variable, by the function by instantaneous channel gain γ_i,nWith it is average Channel power gain β_i,nConnect, it is considered to be in low Signal to Interference plus Noise RatioIn the case of will Substitution formula (1) process：

WithRepresent in k-th matching attribute of time slot subcarrier n, wherein Represent In k-th time slot, subcarrier n distributes to link-i；Expression is not assigned to link-i in k-th time slot subcarrier n； During to subcarrier and power distribution, obtained in k-th time slot by above-mentioned, the available capacity of link-i is：

Wherein symbol Σ represents summation operation, and in k-th time slot, the junction network is effective in the case of given qos value θ Capacity can be expressed asMin is represented and askedMinimum value in both；

Distribution and the transmit power of transmitting terminal and relaying above by optimization subcarrier, in the case where certain QoS requirement is met Realize that the available capacity of the wireless communications relay network system is maximized, the resource allocation methods step is as follows：

First, problem planning

By above description, our existing plan optimizations problem (P1) are as follows：

Wherein max represents maximizing, is object function after the symbol, and s.t. represents constraint symbol, Represent that n can take arbitrary value in { 1,2 .., N }；Represent l time slots in link link-1 and link-2 neutron respectively The transmit power of carrier wave n；E₁ ^(l)、E₂ ^(l)The energy that l time slot initial time transmitting terminals and via node are collected is illustrated respectively in, Wherein l ∈ { 1,2 .., k }；Above-mentioned optimization problem is solved for convenience, relaxes the constraint of subcarrier distribution factor, even

And quote new variables(t is represented and is treated excellent to introduce new auxiliary variable t Change variable), get off to ask the maximum of t in the constraints for meeting problem (P1), then above-mentioned optimization problem can be with equivalence into asking Topic (P1-1)

By relaxing subcarrier distribution factorConstraint, optimization problem is changed into (P1-1) form from (P1) form, both It is of equal value；

2nd, problem solving

Above-mentioned optimization problem is convex optimization problem, can be solved using convex optimum theory method；The glug of problem (P1-1) is bright Day function is：

J and l represent the summation variable used in summation process, their value be respectively j ∈ { 1,2 .., K }, l ∈ 1, 2,..,j}；

Wherein, Lagrange multiplier is：α={ α₁,α₂,...,α_K,

μ={ μ₁,μ₂,...,μ_K}

λ={ λ₁,λ₂,...,λ_K,

ν={ ν₁,ν₂,...,ν_K,

η={ η_1,1,...,η_1,N；...；η_K,1,...,η_K,N,

Subcarrier is distributed：

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：

ByCan obtain：

Whereinα is represented respectively_j、μ_jOptimal solution；

(1) optimal power allocation

Above-mentionedWithG is substituted into respectively₁(α, λ, η) and g₂(μ, ν, η), and respectively Order

g₁(α, λ, η) and g₂(μ, ν, η) is rightWithDerivation：

：

：

" * " in the wherein parameter upper right corner represents the optimal solution of the parameter, [x]⁺If representing x value non-negative, [x]⁺=x；Such as Fruit x is negative, then [x]⁺=0, so far we obtained the optimal power allocation on Lagrange multiplier；

(2) optimal subcarrier distribution

In generation, returns g₁In (α, λ, η)：

K-th component extraction of time slot is out obtained：

Wherein

It can be seen that above formula onLinearly, thus

Can similarly obtain：

So can obtain on k-th dual function of time slot：

By

Then optimal subcarrier is assigned as：

So far optimal subcarrier distribution is obtained；

(3) sub- Gradient Iteration is solved

Above-mentioned dual problem convex problem, can be solved by sub- gradient iteration method, the sub- gradient point of each Lagrange multiplier Δ α is not expressed as_k、Δμ_k、Δλ_kWith Δ ν_k, expression formula is respectively such as following four formula：

Each group Lagrange multiplier is tried to achieve 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 formulaWithJust the 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. a kind of junction network resource allocation methods based on qos requirement energy content collector node, in radio communication Realized after network, the system includes transmitting terminal, via node and receiving terminal, wherein transmitting terminal and via node can be carried out Collection of energy, system uses double jump relaying technique, the wireless channel of transmitting terminal to via node to be expressed as link 1 i.e. link-1, Via node is expressed as link 2 i.e. link-2 to the wireless channel of receiving terminal；Via node receives transmitting terminal by link 1 Data, then carry out decoding forwarding, and data are sent to receiving terminal by link 2；Via node is operated in semiduplex mode；If nothing Line channel obeys block decline, when a length of T of each block；The communication network has N number of subcarrier, a width of WHz of each sub-carrier bin, And n-th (n ∈ { 1,2 ... N }) individual subcarrier can only be assigned uniquely to link 1 and link 2 one of them；Adjacent twice can Measure the time interval collected to be defined as one " time slot ", it is considered to which whole communication process has K time slot, a length of T during each time slot₀, The energy collected in kth (k ∈ { 1,2 ... K }) individual time slot initial time transmitting terminal and via node is expressed as E₁ ^(k)And E₂ ^(k), wherein the symbol (k) in all variable upper right corner represents that the variable is in the variate-value corresponding to time slot k, Radio Link Link-1 and link-2 are represented by link-i, i ∈ { 1,2 }；

From available capacity concept, in k-th time slot sub-carrier n, the available capacity of wireless channel link-i, i ∈ { 1,2 } For：

$C_{i,n}^{\left(k\right)}(\mathrm{\θ},p_{i,n}^{\left(k\right)},{\mathrm{\β}}_{i,n})=-\frac{1}{\mathrm{\θ}T}\log E\[e^{-{\mathrm{\θr}}_{i,n}^{\left(k\right)}}\]---\left(1\right)$

Wherein E [] represents computing of averaging, and θ represents delay parameter i.e. qos parameter,i∈ { 1,2 },Represent time slot k sub-carrier n, the handling capacity of channel link-i, γ i_,nRepresent sub-carrier n in link link-i Transient channel power gain,Represent the transmit power in time slot k, link-i, N for subcarrier n₀Represent recipient's The power spectral density of additive white Gaussian noise (AWGN), I represents inter-cell interference, and Γ represents Signal to Interference plus Noise Ratio difference, Rayleigh is declined Fall channel, and power gain meetsWherein β_i,nRepresent the average channel work(for subcarrier n, link-i Rate gain, f (γ i_,n) represent with γ i_,nIt is the function of independent variable, by the function by instantaneous channel gain γ i_,nWith average letter Road power gain β_i,nConnect, it is considered to be in low Signal to Interference plus Noise RatioIn the case of willGeneration Entering formula (1) process：

WithRepresent in k-th matching attribute of time slot subcarrier n, whereinRepresent the K time slot, subcarrier n distributes to link-i；Expression is not assigned to link-i in k-th time slot subcarrier n；It is given When subcarrier and power distribution, obtained in k-th time slot by above-mentioned, the available capacity of link-i is：

Wherein symbol Σ represents summation operation, in k-th time slot, the available capacity of the junction network in the case of given qos value θ Can be expressed asSymbol min is represented and askedMinimum value in both；

Distribution and the transmit power of transmitting terminal and relaying above by optimization subcarrier, realize in the case where certain QoS requirement is met The available capacity of the wireless communications relay network system is maximized, and the resource allocation methods step is as follows：

First, problem planning

By above description, our existing plan optimizations problem (P1) are as follows：

$\begin{array}{ccc}\left(P1\right)& \max & \min \{C_1^{\left(k\right)}\left(\mathrm{\θ}\right),C_2^{\left(k\right)}\left(\mathrm{\θ}\right)\},k=1,...,K\\ & s.t.& 0\≤\underset{l=1}{\overset{k}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\σ}}_{1,n}^{\left(k\right)}{T}_0{p_{1,n}}^{\left(l\right)}\≤\underset{l=1}{\overset{k}{\mathrm{\Σ}}}{E_1}^{\left(l\right)},k=1,...,K\\ & & 0\≤\underset{l=1}{\overset{k}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\σ}}_{2,n}^{\left(k\right)}{T}_0{p_{2,n}}^{\left(l\right)}\≤\underset{l=1}{\overset{k}{\mathrm{\Σ}}}{E_2}^{\left(l\right)},k=1,...,K\\ & & {\mathrm{\σ}}_{1,n}^{\left(k\right)}+{\mathrm{\σ}}_{2,n}^{\left(k\right)}=1,{\mathrm{\σ}}_{i,n}^{\left(k\right)}\∈\{0,1\},i\∈\{1,2\},\∀n\∈\{1,2,...,N\},k=1,...,K\end{array}---\left(4\right)$

Wherein max represents maximizing, is object function after the symbol, and s.t. represents constraint symbol,Represent n Arbitrary value in { 1,2 .., N } can be taken；Represent l time slots in link link-1 and link-2 sub-carriers n respectively Transmit power；E₁ ^(l)、E₂ ^(l)It is illustrated respectively in the energy that l time slot initial time transmitting terminals and via node are collected, wherein l ∈{1,2,..,k}；Above-mentioned optimization problem is solved for convenience, relaxes the constraint of subcarrier distribution factor, even

And quote new variablesNew auxiliary variable t is introduced, problem is being met (P1) constraints gets off to ask the maximum of t, and then above-mentioned optimization problem can be a problem (P1-1) with equivalence

(P1-1)max t

By relaxing subcarrier distribution factorConstraint, optimization problem is changed into (P1-1) form from (P1) form, and both are Valency；

2nd, problem solving

Above-mentioned optimization problem is convex optimization problem, can be solved using convex optimum theory method；The Lagrangian letter of problem (P1-1) Number is：

$\begin{array}{c}L(t,\mathrm{\σ},\tilde{p},\mathrm{\α},\mathrm{\μ},\mathrm{\λ},v,\mathrm{\η})=t+\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\α}}_i\[\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\σ}}_{1,n}^{\left(j\right)}{C}_{1,n}^{\left(j\right)}({\mathrm{\θ}}_0,p_{1,n}^{\left(j\right)},{\mathrm{\β}}_{1,n})-t\]+\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\μ}}_i\[\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\σ}}_{2,n}^{\left(j\right)}{C}_{2,n}^{\left(j\right)}({\mathrm{\θ}}_0,p_{2,n}^{\left(j\right)},{\mathrm{\β}}_{2,n})-t\]+\\ \underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_j\[\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{E}_1^{\left(l\right)}-\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{T}_0{\tilde{p}}_{1,n}^{\left(l\right)}\]+\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{v}_j\[\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{E}_2^{\left(l\right)}-\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{T}_0{\tilde{p}}_{2,n}^{\left(l\right)}\]+\underset{j=1}{\overset{K}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_{j,n}(1-{\mathrm{\σ}}_{1,n}^{\left(j\right)}-{\mathrm{\σ}}_{2,n}^{\left(j\right)})\end{array}---\left(6\right)$

J and l represent the summation variable used in summation process, their value be respectively j ∈ { 1,2 .., K }, l ∈ 1, 2,..,j}；

Wherein, Lagrange multiplier is：α={ α₁,α₂,...,α_K,

μ={ μ₁,μ₂,...,μ_K,

λ={ λ₁,λ₂,...,λ_K,

ν={ ν₁,ν₂,...,ν_K,

η={ η_1,1,...,η_1,N；...；η_K,1,...,η_K,N,

Subcarrier is distributed：

Power distribution:

Then dual problem can be obtained:

$\begin{array}{ccc}\left(P2\right)& min& g(\mathrm{\α},\mathrm{\μ},\mathrm{\λ},v,\mathrm{\η})\\ & s.t.& \mathrm{\α}\≥0,\mathrm{\μ}\≥0,\mathrm{\λ}\≥0,v\≥0\end{array}---\left(7\right)$

WhereinG (α, μ, λ, ν, η) is handled as follows：

$\begin{array}{c}g(\mathrm{\α},\mathrm{\μ},\mathrm{\λ},v,\mathrm{\η})=g_0\left(\mathrm{\μ}\right)+\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{g}_1(\mathrm{\α},\mathrm{\λ},\mathrm{\η})+\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{g}_2(\mathrm{\μ},v,\mathrm{\η})\\ +\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_j\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{E}_1^{\left(l\right)}+\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{v}_j\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{E}_2^{\left(l\right)}+\underset{j=1}{\overset{K}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_n\end{array}---\left(8\right)$

Wherein：

$g_1(\mathrm{\α},\mathrm{\λ},\mathrm{\η})=\underset{\{{\mathrm{\σ}}_{1,n},{\tilde{p}}_{1,n}\}}{\max }\[\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\α}}_j{\mathrm{\σ}}_{1,n}^{\left(j\right)}{C}_{1,n}^{\left(j\right)}({\mathrm{\θ}}_0,p_{1,n}^{\left(j\right)},{\mathrm{\β}}_{1,n})-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_j\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{T}_0{\tilde{p}}_{1,n}^{\left(l\right)}-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_{j,n}{\mathrm{\σ}}_{1,n}^{\left(j\right)}\]---\left(10\right)$

$g_2(\mathrm{\μ},v,\mathrm{\η})=\underset{\{{\mathrm{\σ}}_{2,n},{\tilde{p}}_{2,n}\}}{\max }\[\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\α}}_j{\mathrm{\σ}}_{2,n}^{\left(j\right)}{C}_{2,n}^{\left(j\right)}({\mathrm{\θ}}_0,p_{2,n}^{\left(j\right)},{\mathrm{\β}}_{2,n})-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{v}_j\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{T}_0{\tilde{p}}_{2,n}^{\left(l\right)}-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_{j,n}{\mathrm{\σ}}_{2,n}^{\left(j\right)}\]---\left(11\right)$

ByCan obtain：

$\underset{j=1}{\overset{K}{\Σ}}{\mathrm{\α}}_j^{*}+\underset{j=1}{\overset{K}{\Σ}}{\mathrm{\μ}}_j^{*}=1---\left(12\right)$

Whereinα is represented respectively_j、μ_jOptimal solution；

(1) optimal power allocation

Above-mentionedWithG is substituted into respectively₁(α, λ, η) and g₂(μ, ν, η), and make respectively

g₁(α, λ, η) and g₂(μ, ν, η) is rightWithDerivation：

：

：

" * " in the wherein parameter upper right corner represents the optimal solution of the parameter, [x]⁺If representing x value non-negative, [x]⁺=x；If x It is negative, then [x]⁺=0, so far we obtained the optimal power allocation on Lagrange multiplier；

(2) optimal subcarrier distribution

In generation, returns g₁In (α, λ, η)：

$g_1(\mathrm{\α},\mathrm{\λ},\mathrm{\η})=\underset{\{{\tilde{p}}_{1,n}^{\left(k\right)},{\mathrm{\σ}}_{1,n}^{\left(k\right)}\}}{\max }\[\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\α}}_j{\mathrm{\σ}}_{1,n}^{\left(j\right)}{C}_{1,n}^{\left(j\right)}({\mathrm{\θ}}_0,p_{1,n}^{\left(j\right)},{\mathrm{\β}}_{1,n})-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_j\underset{l=1}{\overset{j}{\mathrm{\Σ}}}{T}_o{\tilde{p}}_{1,n}^{\left(l\right)}-\underset{j=1}{\overset{K}{\mathrm{\Σ}}}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_{j,n}{\mathrm{\σ}}_{1,n}^{\left(j\right)}\]---(15-1)$

K-th component extraction of time slot is out obtained：

$\begin{array}{c}{g}_1^{\left(k\right)}(\mathrm{\α},\mathrm{\λ},\mathrm{\η})={\mathrm{\α}}_k{\mathrm{\σ}}_{1,n}^{\left(k\right)}{C}_{1,n}^{\left(k\right)}-T_0{\mathrm{\σ}}_{1,n}^{\left(k\right)}{p}_{1,n}^{\left(k\right)}\underset{j=k}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_j-\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_{k,n}{\mathrm{\σ}}_{1,n}^{\left(k\right)}\\ ={\mathrm{\σ}}_{1,n}^{\left(k\right)}\[{\mathrm{\α}}_k{C}_{1,n}^{\left(k\right)}-T_0{p}_{1,n}^{\left(k\right)}\underset{j=k}{\overset{K}{\mathrm{\Σ}}}{\mathrm{\λ}}_j-\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_{k,n}\]\\ ={\mathrm{\σ}}_{1,n}^{\left(k\right)}\[h_{1,n}^{\left(k\right)}-\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\η}}_{k,n}\]\end{array}---(15-2)$

Wherein

It can be seen that above formula onLinearly, thus

${{\mathrm{\&sigma;}}^{*}}_{1,n}^{\left(k\right)}=\left\{\begin{array}{cc}1,& h_{1,n}^{\left(k\right)}>\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&eta;}}_{k,n}\\ \&lsqb;0,1\&rsqb;,& h_{1,n}^{\left(k\right)}=\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&eta;}}_{k,n}\\ 0,& h_{1,n}^{\left(k\right)}<\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&eta;}}_{k,n}\end{array}\right.---(16-1)$

Can similarly obtain：

${{\mathrm{\&sigma;}}^{*}}_{2,n}^{\left(k\right)}=\left\{\begin{array}{cc}1,& h_{2,n}^{\left(k\right)}>\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&eta;}}_{k,n}\\ \&lsqb;0,1\&rsqb;,& h_{2,n}^{\left(k\right)}=\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&eta;}}_{k,n}\\ 0,& h_{2,n}^{\left(k\right)}<\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&eta;}}_{k,n}\end{array}\right.---(16-2)$

So can obtain on k-th dual function of time slot：

$g^{\left(k\right)}(\mathrm{\&alpha;},\mathrm{\&lambda;},\mathrm{\&mu;},v,\mathrm{\&eta;})=g_1^{\left(k\right)}(\mathrm{\&alpha;},\mathrm{\&lambda;},\mathrm{\&eta;})+g_2^{\left(k\right)}(\mathrm{\&mu;},v,\mathrm{\&eta;})=\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}\{{\&lsqb;h_{1,n}^{\left(k\right)}-\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_{k,n}\&rsqb;}^{+}+{\&lsqb;h_{2,n}^{\left(k\right)}-\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_{k,n}\&rsqb;}^{+}+\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&eta;}}_{k,n}\}---\left(17\right)$

By

$\underset{n=1}{\overset{N}{\&Sigma;}}{\mathrm{\&eta;}}_{k,n}=max\{h_{1,n}^{\left(k\right)},h_{2,n}^{\left(k\right)}\}---\left(18\right)$

Then optimal subcarrier is assigned as：

$\begin{array}{cc}{h}_{1,n}^{\left(k\right)}\&GreaterEqual;h_{2,n}^{\left(k\right)}& h_{1,n}^{\left(k\right)}<h_{2,n}^{\left(k\right)}\\ \left\{\begin{array}{c}{{\mathrm{\&sigma;}}^{*}}_{1,n}^{\left(k\right)}=1\\ {{\mathrm{\&sigma;}}^{*}}_{2,n}^{\left(k\right)}=1\end{array}\right.& \left\{\begin{array}{c}{{\mathrm{\&sigma;}}^{*}}_{1,n}^{\left(k\right)}=0\\ {{\mathrm{\&sigma;}}^{*}}_{2,n}^{\left(k\right)}=1\end{array}\right.\end{array}---\left(19\right)$

So far optimal subcarrier distribution is obtained；

(3) sub- Gradient Iteration is solved

Above-mentioned dual problem convex problem, can be solved by sub- gradient iteration method, the sub- gradient difference table of each Lagrange multiplier It is shown as Δ α_k、Δμ_k、Δλ_kWith Δ ν_k, expression formula is respectively such as following four formula：

Each group Lagrange multiplier is tried to achieve 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 formula WithJust can respectively obtain the optimal power allocation scheme of the relay network system, optimal subcarrier distribution scheme and Corresponding available capacity.