CN104618999A - Small cellular system high-energy-efficiency power control method - Google Patents

Abstract

The invention discloses a small cellular system high-energy-efficiency power control method. The small cellular system high-energy-efficiency power control method solves the power control problem through game theories, parameter-free fractional programming and ideas of mixed penalty function theories, wherein, through the game theories, every small base station optimizes the energy efficiency through the power distribution of other base stations to achieve power control distribution; then through the concepts of perspective functions and according to the theories of the parameter-free fractional programming, distributed nonconvex energy efficiency optimization problems are converted into convex optimization problems through variable substitution; lastly, a mixed penalty function method integrating an internal penalty function method and an external penalty function method is utilized to solve the converted convex optimization problem which contains non-equation constraint and equation constraint simultaneously. The small cellular system high-energy-efficiency power control method can not only improve the system energy efficiency, but also through distributed algorithm implementation, effectively reduce complexity.

Description

Cellulor system high energy efficiency Poewr control method

Technical field

The present invention relates to mobile communication resources to distribute and power control techniques field, be specifically related to the high energy efficiency optimization method based on game theory, printenv fractional programming and mixed punished function method in a kind of cellulor system.

Background technology

Flourish along with wireless communication technology, capacity requirement sharply increases, and energy ezpenditure increases fast, and following 5G mobile communication system faces a severe challenge.Effectively can be solved the problem such as capacity boost and efficiency raising of mobile communications network by cellulor technology, realize the double goal of more spectral efficient and green communications, be therefore subject to industry extensive concern.Simultaneously because the high energy consumption of the communications industry creates serious negative effect to environment, therefore how to reduce energy consumption, improve the study hotspot that efficiency becomes people.Therefore, based on the problems referred to above, the invention provides the high energy efficiency Poewr control method based on game theory, printenv fractional programming and mixed punished function method in a kind of cellulor system.

Summary of the invention

Technical problem: the invention provides the high energy efficiency optimization method based on game theory, printenv fractional programming and mixed punished function method in a kind of cellulor system, to improve the efficiency of cellulor system.

Technical scheme: based on the high energy efficiency optimization method of game theory, printenv fractional programming and mixed punished function method in a kind of cellulor system, comprise the following steps:

1) participate in formation non-cooperating power to all little base station under cellulor scene and control game, each little base station maximizes respective efficiency according to the power distribution strategies of other little base stations, obtains respective non-convex optimization problem

2) according to printenv fractional programming thought, by introducing and little base station power allocation strategy $p_k=\{P_k^1,P_k^2,...,P_k^i,...,P_k^N\}$ Relevant auxiliary variable $y_k=\{y_k^0,y_k^1,...,y_k^i,...,y_k^N\},$ The non-convex optimization problem obtained in the first step is converted into a convex optimization problem

3) the quadratic penalty function φ of equality constraint in the convex optimization problem obtained is calculated ₁the logarithm barrier function φ retrained with inequation ₂;

4) quadratic penalty function of gained and logarithm barrier function are added in target function, thus obtain a unconfined convex optimization problem min Ψ;

5) utilize alternative manner the solving without constrained convex optimal problem gained in penalty function method, obtain final power distribution strategies p ^*.

Wherein, for the efficiency optimization problem of each little base station, EE _kfor the efficiency of a kth little base station, C is its feasible zone, represent the through-put power set describing a kth base station, represent the power that little base station k launches on channel i, represent the auxiliary variable relevant to a kth little base station power allocation strategy introduced, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, relevant to the gross power of a kth little base station, N represents variable number, for the efficiency optimization problem after variable replacement, f _kfor the target function after variable replacement, S is the feasible zone after variable is replaced; φ ₁for the quadratic penalty function of equality constraint, φ ₂for the logarithm barrier function of inequation constraint, min Ψ is final without constrained convex optimal problem, p ^*for final power distribution strategies.

Described a kind of cellulor system high energy efficiency Poewr control method, it is characterized in that: first, described employing Noncooperative game opinion method makes resource optimize problem distribution, thus reduces the complexity of algorithm; Secondly, by printenv fractional programming, original non-convex optimization problem is transformed in order to convex optimization problem, thus make power control game to exist and the Nash Equilibrium of only existence anduniquess, ensure that its convergence; Again, the variable replacement in printenv fractional programming is that the concept by having an X-rayed function realizes, and concrete variable replacement formula is $y_k^i=P_k^i/(\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{P}_k^j+P_k^c)$ With $y_k^0=1/(\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{P}_k^j+P_k^c);$ Finally, the inequation constraint g in the convex optimization problem of gained ₁(y _k), g ₂(y _k) ..., g _m(y _k) the form of logarithm barrier function be equality constraint g _m+1(y _k), g _m+2(y _k) ..., g _m+n(y _k) quadratic penalty function form be wherein, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, it is relevant to the gross power of a kth little base station, represent the power that little base station k launches on channel i, represent the power that little base station k launches on channel j, represent the loop power that little base station k consumes, N represents variable number, and m is the number of the inequation constraints of the convex optimization problem of gained, n for the number of equality constraint of convex optimization problem, the auxiliary variable relevant to little base station power allocation strategy introduced.

Beneficial effect: based on the high energy efficiency optimization method of game theory, printenv fractional programming and mixed punished function method in cellulor system provided by the invention, by game theory thought, the non-cooperating power establishing little base station controls game, thus realize the distribution of power control, reduce the complexity of algorithm; And by printenv fractional programming and compound penalty function, former optimization problem is transformed in order to unconfined convex optimization problem, thus bring great convenience for solving of optimization problem.

Adopt this efficiency prioritization scheme that the overall efficiency of cellulor system is obtained significantly to improve.

Accompanying drawing explanation

Fig. 1 is cellulor application scenarios schematic diagram of the present invention, and wherein macrocell user and cellulor are with being randomly dispersed in community per family.

Fig. 2 is the method for optimizing resources schematic diagram of cellulor system.Wherein, for the efficiency optimization problem of each little base station, C is its feasible zone; for the efficiency optimization problem after variable replacement, S is the feasible zone after variable is replaced; φ ₁for the quadratic penalty function of equality constraint, φ ₂for the logarithm barrier function of inequation constraint; Min Ψ is final without constrained convex optimal problem; p ^*for final power distribution strategies.

Fig. 3 is algorithm flow chart when carrying out resource optimization to cellulor system in the present invention.Wherein, p ₀for the power distribution strategies of initialized all little base stations, n represents game number of times, and M is total little base station number, EE _k(p _k, p _-k) represent the efficiency of a kth base station, represent the through-put power set of a kth base station, represent the power that little base station k launches on channel i, N is the carrier number of each little base station, and C represents the feasible zone of through-put power, p _-kfor the power distribution strategies of the every other base station except the k of base station, represent the loop power that little base station k consumes, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, relevant to the gross power of a kth little base station, g _i(y _k) (i=1,2,3) be inequation constraints, g ₄(y _k) be equality constraint, φ ₁(y _k) be the quadratic penalty function of equality constraint, φ ₂(y _k) for inequation constraint logarithm barrier function, f (y _k) be the target function after variable replacement, Ψ _μ(y _k) be final target function; μ is that (order of magnitude is 10 to a very large positive number ⁴). the result of calculation of the auxiliary variable obtained after being n-th game, the power distribution strategies result obtained after being n-th game, p ^*for final power distribution strategies.

Embodiment

Consider a two-tier network comprising a macrocellular and M cellulor, adopt OFDM scheme, wherein, macrocellular and this M cellulor share frequency spectrum, and N number of user is served in each little base station.

Below in conjunction with above-mentioned instantiation, of the present invention providing in a kind of cellulor system is elaborated based on the high energy efficiency optimization method of game theory, printenv fractional programming and mixed punished function method:

(1) adopt Noncooperative game opinion method, form a non-cooperating power and control game, in this game, each little base station maximizes respective efficiency respectively, represents as follows:

$\underset{p_k\∈C}{\max }{\mathrm{EE}}_k(p_k,p_{-k}),k\∈\{\mathrm{1,2},\·\·\·,M\}$

Wherein, represent the through-put power set describing a kth base station, represent the power that little base station k launches on channel i, C represents the feasible zone of through-put power, p _-kfor the power distribution strategies of the every other base station except the k of base station, EE _k(p _k, p _-k) representing the efficiency of a kth base station, M is the number of little base station.

Namely for little base station k, have:

$\begin{array}{c}\max {\mathrm{EE}}_k(p_k,p_{-k})=\frac{R_k}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_k^i+P_k^c}=\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\log }_2(1+\frac{H_{k,k}^i{P}_k^i}{N_0+H_{0,k}^i{P}_0^i+\underset{l\≠k}{\mathrm{\Σ}}{H}_{l,k}^i{P}_l^i})}{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_k^i+P_k^c}\\ \begin{array}{ccc}s.t.& C_1:P_k^i\≥0,& i=\mathrm{1,2},...,N\\ & C_2:\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{P}_k^i\≤P_T& \\ & C_3:\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{r}_k^i\≥R_T& \end{array}\end{array}---\left(1\right)$

Wherein, EE _k(P _k, P _-k) be the efficiency of each little base station, represent the through-put power set describing a kth base station, C represents the feasible zone of through-put power, p _-kfor the power distribution strategies of the every other base station except the k of base station, s.t. represents constraints, molecule R _krepresent the transmission rate of the user that all little base station k serve and, denominator represents the power that little base station k consumes; The Section 1 of denominator represents the transmitting power of little base station, represent that the power that little base station k launches on channel i, N are the carrier number of each little base station; Section 2 represent the loop power that little base station consumes, it is not by the impact of transmission rate; represent the link gain between a kth base station and the user of its busy channel i served; interfering link gain between the user representing the busy channel i that l base station and a kth base station are served, l ≠ k, represent the power that little base station l launches on channel i; interfering link gain between the user of the busy channel i that expression macro base station and a kth base station are served, represent the power that macro base station is launched on channel i; represent the transmission rate of little base station k on channel i; N ₀represent noise, in constraints, C ₁and C ₂that the through-put power of little base station is limited, C ₃ensure that the minimum transmission rate of little base station, P _trepresent the limits value of the through-put power that little base station is total, R _tfor the transmission rate recommended minimum value that little base station is total;

The specific implementation method that non-cooperating power controls game is as follows:

1) power distribution strategies of all little base stations of initialization with iterations n=1;

2) following operation is repeated:

A) for each little base station k ∈ 1,2 ..., M}, according to the power distribution strategies of other little base stations of gained after n-th game calculate distribution of work strategy during (n+1)th game

${\tilde{p}}_k(n+1)=\arg \underset{p_k\∈C}{\max }{\mathrm{EE}}_k(p_k,{\tilde{p}}_{-k}\left(n\right))$

b)n＝n+1

If c) convergence is with regard to end loop

3) final power distribution strategies p is obtained ^*.

Wherein, for the initialization power allocation strategy of little base station, for the power distribution strategies of other little base stations except kth little base station of gained after being n-th game, a kth little base station distribution of work strategy of gained after being (n+1)th game, for the efficiency of a kth little base station, p _krepresent the through-put power set describing a kth base station, C represents the feasible zone of through-put power.

(2) after by resource optimize problem distribution, according to printenv fractional programming thought, replaced by variable and obtained non-convex optimization problem is converted into convex optimization problem, specific implementation method is as follows:

By the concept of perspective function, by introducing and transmitting power relevant auxiliary variable $y_k=\{y_k^0,y_k^1,...,y_k^i,...,y_k^N\},$ Carry out variable replacement

$y_k^i=\frac{P_k^i}{P_k^c+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{P}_k^j},i=\mathrm{1,2},...,N---\left(2\right)$

${\mathrm{yy}}_k^0=\frac{1}{P_k^c+\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{P}_k^j}---\left(3\right)$

Wherein, N is the carrier number of each little base station, represent the loop power that little base station k consumes, represent the power that little base station k launches on channel i, represent the power that little base station k launches on channel j, represent the auxiliary variable relevant to a kth little base station power allocation strategy introduced, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, relevant to the gross power of a kth little base station.

Former optimization problem is converted into a convex optimization problem of equal value:

$\begin{array}{c}\max f\left(y_k\right)=y_k^0\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\log }_2(1+\frac{H_{k,k}^i\frac{y_k^i}{y_k^0}}{N_0+H_{0,k}^i{P}_0^i+\underset{l\≠k}{\mathrm{\Σ}}{H}_{l,k}^i{P}_l^i})\\ \begin{array}{ccc}s.t.& S_1:g_1\left(y_k\right)=y_k^i\≥0,& i=\mathrm{0,1,2},...,N\\ & S_2:g_2\left(y_k\right)=y_k^0{P}_T-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_k^i\≥0& \\ & S_3:g_3\left(y_k\right)=R_k-R_T\≥0& \\ & S_4:g_4\left(y_k\right)=P_k^c{y}_k^0+\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_k^i-1=0& \end{array}\end{array}---\left(4\right)$

Wherein, f (y _k) for variable replace it after target function, the variable relevant to the gross power of a kth little base station, be the variable relevant to the gross power of the power that kth little base station is launched on channel i and a kth little base station, N is the carrier number of each little base station, represent the link gain between a kth base station and the user of its busy channel i served, interfering link gain between the user of the busy channel i that expression macro base station and a kth base station are served, interfering link gain between the user representing the busy channel i that l base station and a kth base station are served, represent the power that macro base station is launched on channel i, represent the power that little base station l launches on channel i, N ₀represent noise.S.t. constraints is represented, S ₁, S ₂, S ₃and S ₄the feasible zone of the new optimization problem after variable is replaced, g ₁(y _k), g ₂(y _k), g ₃(y _k) and g ₄(y _k) be corresponding constraints, for the transmission rate of a kth little base station, P _trepresent the limits value of the through-put power that little base station is total, R _tfor the transmission rate recommended minimum value that little base station is total;

(3) by compound penalty function, the equality constraint in former optimization problem is joined in target function with the form of quadratic penalty function, inequation constraint in above-mentioned optimization problem is joined in target function with the form of logarithm barrier function, thus the equality constraint removed in optimization problem and inequation constraint, concrete grammar is as follows:

By the inequation constraint g in step (2) ₁(y _k), g ₂(y _k), g ₃(y _k) write as logarithm barrier function form as follows:

${\mathrm{\φ}}_1\left(y_k\right)=-\underset{i=0}{\overset{N}{\mathrm{\Σ}}}\log y_k^i-\log (y_k^0{P}_T-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_k^i)-\log (R_T-R_k)---\left(5\right)$

By the equality constraint g in step (2) ₄(y _k) write as quadratic penalty function form as follows:

${\mathrm{\φ}}_2\left(y_k\right)={(P_k^x{y}_k^0+\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{y}_k^i-1)}^2---\left(6\right)$

Wherein, N is the carrier number of each little base station, represent the auxiliary variable relevant to a kth little base station power allocation strategy introduced, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, relevant to the gross power of a kth little base station, P _trepresent the limits value of the through-put power that little base station is total, R _tfor the transmission rate recommended minimum value that little base station is total, R _kfor the transmission rate of a kth little base station, represent the loop power that little base station k consumes.

4) quadratic penalty function of gained and logarithm barrier function are added in target function,

$\min {\mathrm{\ψ}}_{\mathrm{\μ}}\left(y_k\right)=-f\left(y_k\right)+\mathrm{\μ}{\mathrm{\φ}}_1\left(y_k\right)+\frac{1}{\mathrm{\μ}}{\mathrm{\φ}}_2\left(y_k\right)---\left(7\right)$

Obtain a unconfined non-convex optimization problem.Wherein, f (y _k) be through printenv fractional programming conversion after target function, Ψ _μ(y _k) be final target function, represent the auxiliary variable relevant to a kth little base station power allocation strategy introduced, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, relevant to the gross power of a kth little base station, μ is that (order of magnitude is 10 to a very large positive number ⁴).

5) utilize alternative manner the solving without constrained convex optimal problem gained in penalty function method, obtain final power distribution strategies p ^*.

According to above description, the performing step that can obtain resource optimization algorithm in cellulor system is as follows:

1) participate in formation non-cooperating power to all little base station under cellulor scene and control game, each little base station maximizes respective efficiency according to the power distribution strategies of other little base stations, obtains respective non-convex optimization problem

2) according to printenv fractional programming thought, by introducing and little base station power allocation strategy $p_k=\{P_k^1,P_k^2,...,P_k^i,...,P_k^N\}$ Relevant auxiliary variable $y_k=\{y_k^0,y_k^1,...,y_k^i,...,y_k^N\},$ The non-convex optimization problem obtained in the first step is converted into a convex optimization problem

3) the quadratic penalty function φ of equality constraint in the convex optimization problem obtained is calculated ₁the logarithm barrier function φ retrained with inequation ₂;

4) quadratic penalty function of gained and logarithm barrier function are added in target function, thus obtain a unconfined convex optimization problem min Ψ;

5) utilize alternative manner the solving without constrained convex optimal problem gained in penalty function method, obtain final power distribution strategies p ^*.

Wherein, for the efficiency optimization problem of each little base station, EE _kfor the efficiency of a kth little base station, C is its feasible zone, represent the through-put power set describing a kth base station, represent the power that little base station k launches on channel i, represent the auxiliary variable relevant to a kth little base station power allocation strategy introduced, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, relevant to the gross power of a kth little base station, N represents variable number, for the efficiency optimization problem after variable replacement, f _kfor the target function after variable replacement, S is the feasible zone after variable is replaced; φ ₁for the quadratic penalty function of equality constraint, φ ₂for the logarithm barrier function of inequation constraint, min Ψ is final without constrained convex optimal problem, p ^*for final power distribution strategies.

Claims (2)

1. a cellulor system high energy efficiency Poewr control method, is characterized in that this Poewr control method is:

1) participate in formation non-cooperating power to all little base station under cellulor scene and control game, each little base station maximizes respective efficiency according to the power distribution strategies of other little base stations, obtains respective non-convex optimization problem

2) according to printenv fractional programming thought, by introducing and little base station power allocation strategy $p_k=\{P_k^1,P_k^2,...,P_k^i,...,P_k^N\}$ Relevant auxiliary variable $y_k=\{y_k^0,y_k^1,...,y_k^i,...,y_k^N\},$ The non-convex optimization problem obtained in the first step is converted into a convex optimization problem

3) the quadratic penalty function φ of equality constraint in the convex optimization problem obtained is calculated ₁the logarithm barrier function φ retrained with inequation ₂;

4) quadratic penalty function of gained and logarithm barrier function are added in target function, thus obtain a unconfined convex optimization problem min Ψ;

5) utilize alternative manner the solving without constrained convex optimal problem gained in penalty function method, obtain final power distribution strategies p ^*.

Wherein, for the efficiency optimization problem of each little base station, EE _kfor the efficiency of a kth little base station, C is its feasible zone, represent the through-put power set describing a kth base station, represent the power that little base station k launches on channel i, represent the auxiliary variable relevant to a kth little base station power allocation strategy introduced, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, relevant to the gross power of a kth little base station, N represents variable number, for the efficiency optimization problem after variable replacement, f _kfor the target function after variable replacement, S is the feasible zone after variable is replaced; φ ₁for the quadratic penalty function of equality constraint, φ ₂for the logarithm barrier function of inequation constraint, min Ψ is final without constrained convex optimal problem, p ^*for final power distribution strategies.

2. a kind of cellulor system high energy efficiency Poewr control method according to claim 1, it is characterized in that: first, described employing Noncooperative game opinion method makes resource optimize problem distribution, thus reduces the complexity of algorithm; Secondly, by printenv fractional programming, original non-convex optimization problem is transformed in order to convex optimization problem, thus make power control game to exist and the Nash Equilibrium of only existence anduniquess, ensure that its convergence; Again, the variable replacement in printenv fractional programming is that the concept by having an X-rayed function realizes, and concrete variable replacement formula is with finally, the inequation constraint g in the convex optimization problem of gained ₁(y _k), g ₂(y _k) ..., g _m(y _k) the form of logarithm barrier function be equality constraint g _m+1(y _k), g _m+2(y _k) ..., g _m+n(y _k) quadratic penalty function form be ${\mathrm{\φ}}_2\left(y_k\right)=\underset{i=m+1}{\overset{m+n}{\mathrm{\Σ}}}{\left(g_i\left(y_k\right)\right)}^2.$

Wherein, it is relevant to the gross power of the power that a kth little base station is launched on channel i and a kth little base station, it is relevant to the gross power of a kth little base station, represent the power that little base station k launches on channel i, represent the power that little base station k launches on channel j, represent the loop power that little base station k consumes, N represents variable number, and m is the number of the inequation constraints of the convex optimization problem of gained, n for the number of equality constraint of convex optimization problem, the auxiliary variable relevant to little base station power allocation strategy introduced.