CN106937295A - Heterogeneous network high energy efficiency power distribution method based on game theory - Google Patents

Abstract

The present invention provides the heterogeneous network high energy efficiency power distribution method based on game theory, comprises the following steps：Step 1：Heterogeneous network topology is set up；Step 2：Power distribution efficiency function is set up；Step 3：Maximize efficiency function；Step 4：Set up two-stage Stackelberg betting models；Step 4.1：The foundation of microcellulor network efficiency function model；Step 4.2：The foundation of macrocellular network benefit function model；Step 5：The efficiency optimization of macrocellular network；Step 6：The efficiency optimization of microcellulor network n；Step 7：The optimization of interference price y.The present invention introduces jamming power constraints in the power distribution problems for pursuing high energy efficiency, propose the non-convex problem of maximization efficiency function, and the problem is decomposed by setting up two-stage Stackelberg betting models, different efficiency majorized functions are set up from microcellulor network for macrocellular network respectively, the optimization solution of high energy efficiency power distribution problems is eventually found.

Description

Heterogeneous network high energy efficiency power distribution method based on game theory

Technical field

The invention belongs to computer communication field, and in particular to heterogeneous network is based on the high energy efficiency of Stackelberg games Power distribution method.

Background technology：

According to statistics, 2010 to 2015 years, global traffic increased 66 times altogether with 131% annual growth.However, 3G skills Art to the annual growth of the peak rate of 4G technologies be only 55%.With the development in the world of 4G communication systems, 5G movements The communication technology also begins to appear in research field.It is clear that new wireless access technology and RFDC amount demand Between be exist very big distance.Because radio link efficiency almost reaches its original very limited, following wireless access capability Improve largely will by infrastructure technique improvement, for example, increase node density, cooperation and the radio frequency skill that cooperates Art etc..So, the sharp increase of amount of communication data and for the infrastructure quantity that mobile subscriber provides service is persistently climbed The energy ezpenditure that will inevitably increase in wireless network is risen, causes substantial amounts of greenhouse gas emission, so as to be protected to environment The sustainable development of shield and network causes crisis.Thus the communication equipment for bringing allows the Expenditure Levels of the energy is neglected originally Depending on communications industry power saving be increasingly subject to people pay attention to.From the point of view of the energy, environment and economic dispatch multiple angle, energy-conservation drop That consumes indeed turns into communications industry problem demanding prompt solution.

In addition, in heterogeneous network, interference control is also an important field of research, especially when microcellulor network with In identical frequency range, effective interference control seems more important to macrocellular network.Reason is that this frequency spectrum share can cause Cross-layer interference is produced between microcellulor network and macrocellular network.Meanwhile, identical radio frequency can also be shared between microcellulor network Resource improves spectrum efficiency, and this again can cause to produce same layer to disturb between microcellulor network.Cross-layer is disturbed and with layer interference Coexist, can significantly reduce network performance.If without effective interference management, power resource will be wasted greatly, and net The overall energy utilization efficiency of network is likely to or even can be more even worse than without the situation in the presence of microcellulor network.It is existing for different The interference control strategy of network forming network can be divided into two major classes：Interference mitigation/dispelling tactics and come from the dry of cognitive radio networks Disturb power constraint strategy.In jamming power constraints policy, microcellulor network should be protected to the interference summation that macrocellular network is produced Hold in an acceptable level.

Resource allocation all plays very important effect in interference management and in improving energy efficiency.However, most of existing The work of some resource allocations, its target is usually the simple energy efficiency for improving user or whole network, few to consider simultaneously Disturb the influence to energy efficiency.Also there are some research work and the dry of the network based on OFDMA is solved using resource allocation Disturb control problem.Therefore, existing method is using resource allocation target or improves energy efficiency, or reduces interference, will It is also more rare that both are combined the research for considering simultaneously.

The content of the invention：

The present invention provides the high energy efficiency power distribution method that a kind of heterogeneous network is based on Stackelberg games, is come with this Solve present in prior art because of the sharp increase of amount of communication data and for mobile subscriber provides the infrastructure quantity for servicing The energy ezpenditure inevitably increased in wireless network that persistently rises caused by greenhouse effects, and then to environmental protection and The problems such as crisis that the sustainable development of network is caused.The present invention is achieved through the following technical solutions：

The present invention introduces jamming power constraints in the power distribution problems for pursuing high energy efficiency, proposes to maximize efficiency The non-convex problem of function, and the problem is decomposed by setting up two-stage Stackelberg betting models, respectively for grand honeybee Nest network (Macrocell) sets up different efficiency majorized functions from microcellulor network (Picocell)；To macrocellular network with The efficiency majorized function of microcellulor network proposes that Lagrange duality decomposes (LDDM) method and optimizes, and interference price is entered Row optimization, eventually finds the optimization solution of high energy efficiency power distribution problems；Comprise the following steps that：

Step 1：Heterogeneous network topology is set up

A two-layer heterogeneous network, a center macrocellular network and N number of microcellulor network are set up, whole frequency band is divided into K subcarrier, all of microcellulor network and macrocellular network share identical frequency spectrum together, and interference includes that cross-layer is disturbed and same Layer interference, because the transmission power of microcellular network basestation will be far smaller than the transmission power of macrocellular network base station, you can suddenly Slightly disregard, the present invention only considers to be disturbed from macrocellular network to the cross-layer of microcellulor network.

Step 2：Power distribution efficiency function is set up

Macrocellular network and n-th microcellulor network energy ezpenditure use P respectively_mAnd P_nRepresent, such as shown in formula (1)：Grand honeybee Nest network and n-th microcellulor network energy ezpenditure formula can also be expressed as income：

Wherein, k_mAnd k_nMacrocellular network and n-th efficiency of the power amplifier of microcellulor network are represented respectively；P_kWithThe power that macrocellular network and n-th microcellulor network are distributed on k-th subcarrier is represented respectively；P_cmAnd P_cnDifference table Show macrocellular network and n-th circuit power of microcellulor network and be separate with transmission power between being；

Therefore, efficiency function η is set up for η (y, P_n,P_m), wherein y represents interference price.

Step 3：Maximize efficiency function

Pursuing the problem of high energy efficiency can be converted into maximization efficiency function η (y, P_n,P_m), such as shown in formula (2)：

Wherein, β_RIIt is the compromise and β of data transfer rate and interference income_RI>0；β_PIBe the compromise of energy ezpenditure and interference cost and β_PI>0；Introduce β_RI、β_PIThe purpose of the two weight factors be by the unit-normalization of efficiency function be bit/joule；Y is represented Interference price and y>0, the unit of price is disturbed for the price of per unit jamming power；Be on k-th subcarrier n-th it is micro- Total interference that cellular network is received in macrocellular network；P_maxWithIt is respectively the total of macrocellular network and n-th microcellulor network Maximum transmission power,It is the jamming power upper limit that n-th microcellulor network can be tolerated,R_kTable Show the data transfer rate of macrocellular network, wherein σ²Represent additive white Gaussian noise of the macrocellular network in each subcarrier, h_kIt is grand honeybee Nest network arrives the channel gain of macrocell user on k-th subcarrier, N-th data transfer rate of microcellulor network is represented, whereinIt is macrocellular network to n-th microcellulor network channel gain, Represent on sub-carrierk, microcellulor network j (j ≠ n) to n-th channel gain of microcellulor network,It is microcellulor network n In the bandwidth that the additive white Gaussian noise of each subcarrier, W are distributed to each subcarrier,Represent the n-th microcellulor network n To the channel gain of microcellulor user on k subcarrier)；Represent that j-th microcellulor network is distributed on k-th subcarrier Power；

Then, maximizing the optimization problem of efficiency can then be write as the maximization constrained with jamming power and transmission power The problem of function η.

Step 4：Set up two-stage Stackelberg betting models

Drawn by the definition of η, optimization problem is a non-convex problem, it is difficult to solved with efficient algorithm, can be by this Fractional order function is converted into the equivalent subtraction of fractional programming, and this is that one kind that efficiency optimization problem is solved in heterogeneous network has efficacious prescriptions Method, however, will have very many parameters needs to optimize, can increase computing cost, therefore this fractional programming problems is entered One step is decomposed into two subproblems, by the method for game obtain suboptimal solution using the macrocellular network in efficiency optimization problem as Follower, microcellulor network forms a two-stage Stackelberg betting model as leader, it is noted that although this Optimization problem is divided into two benches, but they are by disturbing Costco Wholesale close-coupled together.

Step 4.1：The foundation of microcellulor network efficiency function model

Microcellulor network will suppress cross-layer and disturb as leader by asking for interference price to macrocellular network, from And the income of its own is improved to greatest extent, n-th benefit function of microcellulor networkAs shown in formula (8)：

Wherein,It is power allocation vector of n-th microcellulor network in subcarrier K, therefore, for microcellulor network n Efficiency function optimization, such as shown in formula (9)：

(3), s.t. (5), 7) represent meet formula (3), (5), the condition of (7).

Step 4.2：The foundation of macrocellular network benefit function model

Macrocellular network maximizes it according to microcellulor network as follower according to the provided interference of interference quotation Effectiveness, the benefit function U of macrocellular network_m(P_k), such as shown in formula (10)：

Therefore, the EE for macrocellular network optimizes as shown in formula (11)：

(6), (4), s.t. (7) represent and meet formula (3), (5), the condition of (7).

Step 5：The efficiency optimization of macrocellular network

Because macrocellular network benefit function model is one on P_kConvex function, its all of constraints is all line Property, formula (11) is a convex optimization problem, introduces Lagrange duality decomposition algorithm (LDDM) to solve, Lagrangian letter Shown in number, such as formula (12)：

Wherein λ and v_nIt is non-negative dual variable corresponding with constraints (3) and (6), dual function g (λ, ν_n) as public Shown in the upper bound of the optimal value of formula (11), such as formula (13)：

So, dual problem can be just defined as shown in formula (14)：

When the quantity of subcarrier is sufficiently large, the duality gap between primal problem and dual problem is almost zero, Dual problem just can on each subcarrier be broken down into K independent subproblem, and independent subproblem just corresponds to subcarrier, there is K Individual subcarrier, so have K subproblem, such as shown in formula (15)：

Wherein,By KKT conditionsMacrocellular net can be drawn The optimization power distribution strategies of networkAs shown in formula (16)：

Wherein, (A)⁺=max (0, A)；

Order

Be can be observed how by formula (16), if jamming power price y>B_k, macrocellular can be stopped on k-th subcarrier Transmission.

Step 6：The efficiency optimization of microcellulor network n

In order to obtain maximization benefit, microcellulor network n can be according to the appropriate tune of the power allocation case of macrocellular network Whole interference price y, introduces Lagrange duality decomposition algorithm (LDDM) to solve, such as shown in formula (17)：

Wherein ρ andIt is non-negative dual variable corresponding with constraints (5) and (7),

By KKT conditions, the optimization power distribution problems of microcellulor network nCan be written as shown in formula (18)：

It is the j-th optimization power of microcellulor network.

Step 7：The optimization of interference price y

Understood according to step 5,It is a piecewise function, and in B_kThere is breakpoint, forDirectly interference price y differentiations can not be solved to disturb the optimization problem of price y, discussed first optimal Interference price y values whether there is, and formula (17) is divided into two parts on each subcarrier on interference price y, be respectivelyWithUnderstood according to formula (18),It is the convex letter for disturbing price y Number, therefore, we only need to study L_PThe property of (y).

Step 7.1：By B_k(k=1,2 ..., K) is arranged by ascending order, without loss of generality, makes B₁≤B₂≤…≤B_K, so that shape Into K interval (0, B₁)(B₁,B₂),…(B_K-1,B_K)；With (0, B₁) as a example by, when y → 0, can be with derived expression (19):

Step 7.2：Draw L_PShown in the second dervative of (y) on y, such as formula (20)：

Except non-point B that can be micro-₁, L_PY () is a convex function, and haveOr

Step 7.3：Analysis can draw more than, except point B_k, L (P_k,λ,ν_n) it is the convex function on y.With existing skill Art compares, and beneficial aspects of the invention are：

(1) problem for being difficult to solve for non-convex problem of resource allocation etc., sets up two-stage Stackelberg betting models, Make macrocellular network and microcellulor network that respective income is maximized under the conditions of in a balanced way.

(2) for macrocellular network and the different characteristics of microcellulor network, different optimization problem solution party are proposed respectively Case.LDDM algorithms are used for macrocellular network, optimal distributing scheme is then obtained using LDDM algorithms for microcellulor network.

(3) jamming power is incorporated into the optimization problem of high energy efficiency resource allocation in the way of price, as problem Constraints, realizes while network data rate is improved, to take cost of energy and interference cost into account, realizes high The resource allocation policy of the low interference of efficiency.

(4) present invention introduces jamming power constraints in the power distribution problems for pursuing high energy efficiency, proposes to maximize The non-convex problem of efficiency function, and the problem is decomposed by setting up two-stage Stackelberg betting models, it is directed to respectively Macrocellular network (Macrocell) sets up different efficiency majorized functions from microcellulor network (Picocell)；To macrocellular net Network proposes that Lagrange duality decomposes (LDDM) method and optimizes with the efficiency majorized function of microcellulor network, and to interference valency Lattice are optimized, and eventually find the optimization solution of high energy efficiency power distribution problems.

Specific embodiment

With reference to embodiment, the present invention is further illustrated.

The present invention introduces jamming power constraints in the power distribution problems for pursuing high energy efficiency, proposes to maximize efficiency The non-convex problem of function, and the problem is decomposed by setting up two-stage Stackelberg betting models, respectively for grand honeybee Nest network (Macrocell) sets up different efficiency majorized functions from microcellulor network (Picocell)；To macrocellular network with The efficiency majorized function of microcellulor network proposes that Lagrange duality decomposes (LDDM) method and optimizes, and interference price is entered Row optimization, eventually finds the optimization solution of high energy efficiency power distribution problems；Comprise the following steps that：

Step 1：Heterogeneous network topology is set up

A two-layer heterogeneous network, a center macrocellular network and N number of microcellulor network are set up, whole frequency band is divided into K subcarrier, all of microcellulor network and macrocellular network share identical frequency spectrum together, and interference includes that cross-layer is disturbed and same Layer interference, because the transmission power of microcellular network basestation will be far smaller than the transmission power of macrocellular network base station, you can suddenly Slightly disregard, the present invention only considers to be disturbed from macrocellular network to the cross-layer of microcellulor network.

Step 2：Power distribution efficiency function is set up

Macrocellular network and n-th microcellulor network energy ezpenditure use P respectively_mAnd P_nRepresent, such as shown in formula (1)：Grand honeybee Nest network and n-th microcellulor network energy ezpenditure formula can also be expressed as income：

Wherein, k_mAnd k_nMacrocellular network and n-th efficiency of the power amplifier of microcellulor network are represented respectively；P_kWithThe power that macrocellular network and n-th microcellulor network are distributed on k-th subcarrier is represented respectively；P_cmAnd P_cnDifference table Show macrocellular network and n-th circuit power of microcellulor network and be separate with transmission power between being；

Therefore, efficiency function η is set up for η (y, P_n,P_m), wherein y represents interference price.

Step 3：Maximize efficiency function

Pursuing the problem of high energy efficiency can be converted into maximization efficiency function η (y, P_n,P_m), such as shown in formula (2)：

Wherein, β_RIIt is the compromise and β of data transfer rate and interference income_RI>0；β_PIIt is the compromise and β of energy ezpenditure and interference cost_PI >0；Introduce β_RI、β_PIThe purpose of the two weight factors be by the unit-normalization of efficiency function be bit/joule；Y represents interference Price and y>0, the unit of price is disturbed for the price of per unit jamming power；It is n-th microcellulor on k-th subcarrier Total interference that network is received in macrocellular network；P_maxWithIt is respectively the total of macrocellular network and n-th microcellulor network Maximum transmission power,It is the jamming power upper limit that n-th microcellulor network can be tolerated,R_kTable Show the data transfer rate of macrocellular network, wherein σ²Represent additive white Gaussian noise of the macrocellular network in each subcarrier, h_kIt is grand honeybee Nest network arrives the channel gain of macrocell user on k-th subcarrier, N-th data transfer rate of microcellulor network is represented, whereinIt is macrocellular network to n-th microcellulor network channel gain, Represent on sub-carrierk, microcellulor network j (j ≠ n) to n-th channel gain of microcellulor network,It is microcellulor network n In the bandwidth that the additive white Gaussian noise of each subcarrier, W are distributed to each subcarrier,Represent the n-th microcellulor network n To the channel gain of microcellulor user on k subcarrier)；Represent that j-th microcellulor network is distributed on k-th subcarrier Power；

Then, maximizing the optimization problem of efficiency can then be write as the maximization constrained with jamming power and transmission power The problem of function η.

Step 4：Set up two-stage Stackelberg betting models

Drawn by the definition of η, optimization problem is a non-convex problem, it is difficult to solved with efficient algorithm, can be by this Fractional order function is converted into the equivalent subtraction of fractional programming, and this is that one kind that efficiency optimization problem is solved in heterogeneous network has efficacious prescriptions Method, however, will have very many parameters needs to optimize, can increase computing cost, therefore this fractional programming problems is entered One step is decomposed into two subproblems, by the method for game obtain suboptimal solution using the macrocellular network in efficiency optimization problem as Follower, microcellulor network forms a two-stage Stackelberg betting model as leader, it is noted that although this Optimization problem is divided into two benches, but they are by disturbing Costco Wholesale close-coupled together.

Step 4.1：The foundation of microcellulor network efficiency function model

Microcellulor network will suppress cross-layer and disturb as leader by asking for interference price to macrocellular network, from And the income of its own is improved to greatest extent, n-th benefit function of microcellulor networkAs shown in formula (8)：

Wherein,It is power allocation vector of n-th microcellulor network in subcarrier K, therefore, for microcellulor network n Efficiency function optimization, such as shown in formula (9)：

(3), s.t. (5), 7) represent meet formula (3), (5), the condition of (7).

Step 4.2：The foundation of macrocellular network benefit function model

Macrocellular network maximizes it according to microcellulor network as follower according to the provided interference of interference quotation Effectiveness, the benefit function U of macrocellular network_m(P_k), such as shown in formula (10)：

Therefore, the EE for macrocellular network optimizes as shown in formula (11)：

(6), (4), s.t. (7) represent and meet formula (3), (5), the condition of (7).

Step 5：The efficiency optimization of macrocellular network

Because macrocellular network benefit function model is one on P_kConvex function, its all of constraints is all line Property, formula (11) is a convex optimization problem, introduces Lagrange duality decomposition algorithm (LDDM) to solve, Lagrangian letter Shown in number, such as formula (12)：

Wherein λ and v_nIt is non-negative dual variable corresponding with constraints (3) and (6), dual function g (λ, ν_n) as public Shown in the upper bound of the optimal value of formula (11), such as formula (13)：

So, dual problem can be just defined as shown in formula (14)：

When the quantity of subcarrier is sufficiently large, the duality gap between primal problem and dual problem is almost zero, Dual problem just can on each subcarrier be broken down into K independent subproblem, and independent subproblem just corresponds to subcarrier, there is K Individual subcarrier, so have K subproblem, such as shown in formula (15)：

Wherein,By KKT conditionsMacrocellular net can be drawn The optimization power distribution strategies of networkAs shown in formula (16)：

Wherein, (A)⁺=max (0, A)；

Order

Be can be observed how by formula (16), if jamming power price y>B_k, macrocellular can be stopped on k-th subcarrier Transmission.

Step 6：The efficiency optimization of microcellulor network n

In order to obtain maximization benefit, microcellulor network n can be according to the appropriate tune of the power allocation case of macrocellular network Whole interference price y, introduces Lagrange duality decomposition algorithm (LDDM) to solve, such as shown in formula (17)：

Wherein ρ andIt is non-negative dual variable corresponding with constraints (5) and (7),

By KKT conditions, the optimization power distribution problems of microcellulor network nCan be written as shown in formula (18)：

It is the j-th optimization power of microcellulor network.

Step 7：The optimization of interference price y

Understood according to step 5,It is a piecewise function, and in B_kThere is breakpoint, forDirectly interference price y differentiations can not be solved to disturb the optimization problem of price y, discussed first optimal Interference price y values whether there is, and formula (17) is divided into two parts on each subcarrier on interference price y, be respectivelyWithUnderstood according to formula (18),It is the convex letter for disturbing price y Number, therefore, we only need to study L_PThe property of (y).

Step 7.1：By B_k(k=1,2 ..., K) is arranged by ascending order, without loss of generality, makes B₁≤B₂≤…≤B_K, so that shape Into K interval (0, B₁)(B₁,B₂),…(B_K-1,B_K)；With (0, B₁) as a example by, when y → 0, can be with derived expression (19):

Step 7.2：Draw L_PShown in the second dervative of (y) on y, such as formula (20)：

Except non-point B that can be micro-₁, L_PY () is a convex function, and haveOr

Step 7.3：Analysis can draw more than, except point B_k, L (P_k,λ,ν_n) it is the convex function on y.

The problem that the present invention is difficult to solve for non-convex problem of resource allocation etc., sets up two-stage Stackelberg game moulds Type, makes macrocellular network and microcellulor network that respective income is maximized under the conditions of in a balanced way.

The present invention proposes that different optimization problems are solved respectively for macrocellular network and the different characteristics of microcellulor network Scheme.LDDM algorithms are used for macrocellular network, optimum allocation side is then obtained using LDDM algorithms for microcellulor network Case.

In the way of price be incorporated into the optimization problem of high energy efficiency resource allocation jamming power by the present invention, used as problem Constraints, realize improve network data rate while, cost of energy and interference cost can be taken into account, realize The resource allocation policy of the low interference of high energy efficiency.

The present invention introduces jamming power constraints in the power distribution problems for pursuing high energy efficiency, proposes to maximize efficiency The non-convex problem of function, and the problem is decomposed by setting up two-stage Stackelberg betting models, respectively for grand honeybee Nest network (Macrocell) sets up different efficiency majorized functions from microcellulor network (Picocell)；To macrocellular network with The efficiency majorized function of microcellulor network proposes that Lagrange duality decomposes (LDDM) method and optimizes, and interference price is entered Row optimization, eventually finds the optimization solution of high energy efficiency power distribution problems.

Above-described embodiment is only that protection scope of the present invention of enumerating of present inventive concept way of realization is not limited only to Embodiment is stated, it is thinkable according to technology design of the invention institute that protection scope of the present invention may extend to those skilled in the art Equivalent technologies mean.

Claims (2)

1. the heterogeneous network high energy efficiency power distribution method of game theory is based on, it is characterised in that comprised the following steps：

Step 1：Heterogeneous network topology is set up

A two-layer heterogeneous network, a center macrocellular network and N number of microcellulor network are set up, whole frequency band is divided into K Subcarrier, all of microcellulor network and macrocellular network share identical frequency spectrum together, and interference includes cross-layer interference and same layer Interference；

Step 2：Power distribution efficiency function is set up

Macrocellular network and n-th microcellulor network energy ezpenditure use P respectively_mAnd P_nRepresent, such as shown in formula (1)：Macrocellular net Network and n-th microcellulor network energy ezpenditure formula can also be expressed as income：

$\left\{\begin{array}{c}{P}_m=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{k}_m{P}_k+P_{cm}\\ P_n=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{k}_n{P}_k^n+P_{cn}\end{array}\right.---\left(1\right)$

Wherein, k_mAnd k_nMacrocellular network and n-th efficiency of the power amplifier of microcellulor network are represented respectively；P_kWithPoint Biao Shi not the power that is distributed on k-th subcarrier of macrocellular network and n-th microcellulor network；P_cmAnd P_cnRepresent respectively grand Cellular network and n-th circuit power of microcellulor network and be separate with transmission power between being；

Therefore, it is η (y, P to set up and maximize efficiency function η_n,P_m), wherein y represents interference price；

Step 3：Maximize efficiency function

The problem for pursuing high energy efficiency is converted into maximization efficiency function η (y, P_n,P_m), such as shown in formula (2)：

$\begin{array}{cc}s.t.& P_k^n\≥0,\∀k,\∀n,\end{array}---\left(3\right)$

$\underset{k=1}{\overset{K}{\Σ}}{P}_k\≤P_{max},\∀k,---\left(4\right)$

$\underset{k=1}{\overset{K}{\Σ}}{P}_k^n\≤P_{max}^n,\∀k,\∀n,---\left(5\right)$

$P_k\≥0,\∀k,---\left(6\right)$

$\underset{k=1}{\overset{K}{\Σ}}(x_k^n{P}_k+\underset{j\≠n}{\overset{N}{\mathrm{\Σ}}}{h}_k^{n,j}{P}_k^j)\≤I_n^{th},\∀n,---\left(7\right)$

Wherein, β_RIIt is the compromise and β of data transfer rate and interference income_RI>0；β_PIIt is the compromise and β of energy ezpenditure and interference cost_PI> 0；Introduce β_RI、β_PIThe purpose of the two weight factors be by the unit-normalization of efficiency function be bit/joule；Y represents interference Price and y>0, the unit of price is disturbed for the price of per unit jamming power；It is n-th microcellulor on k-th subcarrier Total interference that network is received in macrocellular network；P_maxWithIt is respectively the total of macrocellular network and n-th microcellulor network Maximum transmission power,It is the jamming power upper limit that n-th microcellulor network can be tolerated,R_kTable Show the data transfer rate of macrocellular network, wherein σ²Represent additive white Gaussian noise of the macrocellular network in each subcarrier, h_kIt is grand honeybee Nest network arrives the channel gain of macrocell user on k-th subcarrier, N-th data transfer rate of microcellulor network is represented, whereinIt is macrocellular network to n-th microcellulor network channel gain, Represent on sub-carrierk, microcellulor network j (j ≠ n) to n-th channel gain of microcellulor network,It is microcellulor network n In the bandwidth that the additive white Gaussian noise of each subcarrier, W are distributed to each subcarrier,Represent the n-th microcellulor network n To the channel gain of microcellulor user on k subcarrier)；Represent that j-th microcellulor network is distributed on k-th subcarrier Power；

Then, maximizing the optimization problem of efficiency can then be write as the maximization function constrained with jamming power and transmission power The problem of η；

Step 4：Set up two-stage Stackelberg betting models

Drawn by the definition of η, optimization problem is a non-convex problem, and this fractional order function is converted into the equivalent of fractional programming This fractional programming problems is being further broken into two subproblems by subtraction, and suboptimal solution is obtained by energy by the method for game Used as follower, microcellulor network forms a two-stage to macrocellular network in effect optimization problem as leader Stackelberg betting models, it is noted that although this optimization problem is divided into two benches, they are by disturbing price Cost close-coupled is together；

Step 5：The efficiency optimization of macrocellular network

Because macrocellular network benefit function model is one on P_kConvex function, its all of constraints be all it is linear, Formula (11) is a convex optimization problem, introduces Lagrange duality decomposition algorithm (LDDM) to solve, Lagrangian, such as Shown in formula (12)：

$\begin{array}{c}L\left(P_k,\mathrm{\λ},{\mathrm{\ν}}_n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\left(R_k-k_m{P}_k-{\mathrm{\β}}_{PI}\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{yx}}_k^n{P}_k\right)-P_{cm}\\ -\mathrm{\λ}\left(\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{P}_k-P_{\max }\right)-\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{v}_n\left(\mathrm{\Σ}\left(x_k^n{P}_k+\underset{j\≠n}{\overset{N}{\mathrm{\Σ}}}{h}_k^{n,j}{P}_k^j\right)-I_n^{th}\right)\end{array}---\left(12\right)$

Wherein λ and v_nIt is non-negative dual variable corresponding with constraints (3) and (6), dual function g (λ, ν_n) as formula (11) shown in the upper bound of optimal value, such as formula (13)：

$g(\mathrm{\λ},{\mathrm{\ν}}_n)=\underset{P_k\≥0,\∀k}{max}L(P_k,\mathrm{\λ},{\mathrm{\ν}}_n)---\left(13\right)$

Dual definition is shown in formula (14)：

$\begin{array}{cc}\underset{\mathrm{\λ}\≥0,v_n\≥0,\∀k,\∀n}{\min }& g\left(\mathrm{\λ},v_n\right)\\ s.t.& \left(7\right)\end{array}---\left(14\right)$

When the quantity of subcarrier is sufficiently large, the duality gap between primal problem and dual problem is almost zero, antithesis Problem just can on each subcarrier be broken down into K independent subproblem, and independent subproblem just corresponds to subcarrier, there is K son Carrier wave, so have K subproblem, such as shown in formula (15)：

$g(\mathrm{\λ},{\mathrm{\ν}}_n)=W{\log }_2(1+\frac{h_k{P}_k}{{\mathrm{\σ}}^2})-{\mathrm{YP}}_k---\left(15\right)$

Wherein,By KKT conditionsMacrocellular network can be drawn Optimization power distribution strategiesAs shown in formula (16)：

$P_k^{*}={(\frac{W}{Yln2}-\frac{{\mathrm{\σ}}^2}{h_k})}^{+}---\left(16\right)$

Wherein, (A)⁺=max (0, A)；

Order

Be can be observed how by formula (16), if jamming power price y>B_k, macrocellular can stop at the biography on k-th subcarrier It is defeated；

Step 6：The efficiency optimization of microcellulor network n

In order to obtain maximization benefit, microcellulor network n can be dry according to the appropriate adjustment of the power allocation case of macrocellular network Price y is disturbed, introduces Lagrange duality decomposition algorithm (LDDM) to solve, such as shown in formula (17)：

Wherein ρ andIt is non-negative dual variable corresponding with constraints (5) and (7),

By KKT conditions, the optimization power distribution problems of microcellulor network nCan be written as shown in formula (18)：

$P_k^{n*}={(\frac{W}{(k_n+\mathrm{\ρ})ln2}-\frac{x_k^n{P}_k+\underset{j\≠n}{\overset{N}{\mathrm{\Σ}}}{h}_k^{n,j}{P}_k^{j*}+{\mathrm{\σ}}_n^2}{h_k^n})}^{+}---\left(18\right)$

It is the j-th optimization power of microcellulor network.

Step 7：The optimization of interference price y

Understood according to step 5,It is a piecewise function, and in B_kThere is breakpoint, forNo Directly interference price y differentiations can be solved to disturb the optimization problem of price y, discuss that optimal interference price y values are first No presence, two parts are divided into by formula (17) on each subcarrier on interference price y, are respectivelyWithUnderstood according to formula (18),It is the convex function for disturbing price y, therefore, we only need Study L_PThe property of (y).

Step 7.1：By B_k(k=1,2 ..., K) is arranged by ascending order, without loss of generality, makes B₁≤B₂≤…≤B_K, so as to form K Interval (0, B₁)(B₁,B₂),…(B_K-1,B_K)；With (0, B₁) as a example by, when y → 0, can be with derived expression (19):

$\frac{\∂L_P\left(y\right)}{\∂y}{|}_{y\→0}>{\mathrm{\β}}_{PI}{x}_k^n(\frac{W}{Yln2}-\frac{{\mathrm{\σ}}^2}{h_k})>0---\left(19\right)$

Step 7.2：Draw L_PShown in the second dervative of (y) on y, such as formula (20)：

$\frac{{\&part;}^2{L}_P\left(y\right)}{\&part;y^2}<0---\left(20\right)$

Except non-point B that can be micro-₁, L_PY () is a convex function, and haveOr

Step 7.3：Analysis can draw more than, except point B_k, L (P_k,λ,ν_n) it is the convex function on y.

2. the heterogeneous network high energy efficiency power distribution method based on game theory according to claim 2, it is characterised in that institute Stating step 4 includes following steps：

Step 4.1：The foundation of microcellulor network efficiency function model

Microcellulor network will suppress cross-layer and disturb, so that most as leader by asking for interference price to macrocellular network Improve the income of its own, n-th benefit function of microcellulor network in limits groundAs shown in formula (8)：

$U_n(y,P_k^n)=\underset{k=1}{\overset{K}{\&Sigma;}}{R}_k^n-(\underset{k=1}{\overset{K}{\&Sigma;}}{k}_n{P}_k^n+P_{cn})+{\mathrm{y\&beta;}}_{RI}\underset{k=1}{\overset{K}{\&Sigma;}}{x}_k^n{P}_k---\left(8\right)$

Wherein,It is power allocation vector of n-th microcellulor network in subcarrier K, therefore, for the efficiency of microcellulor network n Shown in function optimization, such as formula (9)：

$\begin{array}{cc}\underset{y,P_k^n}{\max }& U_n\left(y,P_k^n\right)\\ s.t.& \left(3\right),\left(5\right),\left(7\right)\end{array}---\left(9\right)$

(3), s.t. (5), 7) represent meet formula (3), (5), the condition of (7)；

Step 4.2：The foundation of macrocellular network benefit function model

Macrocellular network maximizes its effect according to microcellulor network as follower according to the provided interference of interference quotation With the benefit function U of macrocellular network_m(P_k), such as shown in formula (10)：

$U_m\left(P_k\right)=\underset{k=1}{\overset{K}{\&Sigma;}}{R}_k-(\underset{k=1}{\overset{K}{\&Sigma;}}{k}_m{P}_k+P_{cm})+{\mathrm{y\&beta;}}_{PI}\underset{n=1}{\overset{N}{\&Sigma;}}\underset{k=1}{\overset{K}{\&Sigma;}}{x}_k^n{P}_k---\left(10\right)$

Therefore, the EE for macrocellular network optimizes as shown in formula (11)：

$\begin{array}{cc}\underset{P_k}{\max }& U_m\left(P_k\right)\\ s.t.& \left(4\right),\left(6\right),\left(7\right)\end{array}---\left(11\right)$

(6), (4), s.t. (7) represent and meet formula (3), (5), the condition of (7).