CN104902557A - Method for optimizing wireless resources of small cell user - Google Patents

Abstract

The invention provides a method for optimizing wireless resources of a small cell user. The method comprises the following steps of establishing an energy efficiency function mathematical model of the small cell user; secondly, converting an original three-dimensional optimization problem into a one-dimensional optimization problem by utilizing constraint conditions; thirdly, through theoretical derivation, proving that the one-dimensional equivalent energy efficiency function has a curve characteristic of increasing at first and then decreasing, namely existence of a global optimal power point; and lastly, designing a derivative-based dichotomy algorithm to solve the optimal power point. According to the method, the energy efficiency of the small cell user in a heterogeneous network can be improved, and the requirements on green communication are met.

Description

Small cell user radio method for optimizing resources

Technical field

The present invention relates to power of mobile communication control technology, particularly relate to a kind of small cell (little base station) user radio method for optimizing resources.

Background technology

Small cell is lower powered radio access node, that be operated in mandate, unauthorized frequency spectrum, can cover the scope of 10 meters to 200 meters, and small cell is the important component of 3G data distribution, is the effective way of management LTE-A frequency spectrum.

Along with green communications receive the concern of people day by day, how controlling to improve the efficiency of small cell in heterogeneous network by power, is current small cell technology problem demanding prompt solution.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of small cell user radio method for optimizing resources, to improve the efficiency of small cell user.

In order to solve the problems of the technologies described above, technical scheme of the present invention is to provide a kind of small cell user radio method for optimizing resources, it is characterized in that: the method is made up of following 4 steps:

Step 1: in the heterogeneous network containing the little base station of small cell, macrocellular and D2D, set up the target function of small cell user efficiency, shown in (1):

This target function comprises following constraints:

1, the minimum transmission rate request of phone user, namely its minimum transmission rate can not be less than δ _c:

${\log }_2(1+\frac{P_C{h}_C}{P_S{h}_{\mathrm{SC}}+P_D{h}_{\mathrm{DC}}+n_0})\≥{\mathrm{\δ}}_C$

2, the minimum transmission rate request of D2D, namely its minimum transmission rate can not be less than δ _d:

3, the maximum transmission power of small cell user, D2D user and macrocell user limits:

P _S，P _C，P _D≤P _max

A small cell user is comprised in small cell; D2D centering comprises two D2D users, and one of them is for receiving user, and another is for sending user; Wherein: P _srepresent the through-put power of small cell user, h _sDrepresent that small cell user and D2D are to the channel gain received between user, h _sCrepresent the channel gain between small cell user and macro base station, h _srepresent the channel gain between small cell user and little base station, P _drepresent that D2D is to the through-put power of launching user, h _drepresent the channel gain between D2D user, P _crepresent the through-put power of phone user, h _cDrepresent that phone user and D2D are to the channel gain received between user, n ₀represent noise power, P _circuitrepresent the circuit power consumption of D2D user, h _crepresent the channel gain between phone user and macro base station, h _dCrepresent that D2D is to the channel gain launched between user and macro base station, h _dSrepresent that D2D is to the channel gain launched between user and little base station, h _cSrepresent the channel gain between phone user and little base station, max function representation maximizes the target function of small cell user efficiency;

Step 2: because the small cell user efficiency optimization problem being independent variable with phone user's through-put power, D2D user's through-put power and small cell user through-put power is a non-convex problem, directly carries out solving very difficult; For identical P _s, small cell user efficiency U _svalue reduce along with the increase of phone user's through-put power and D2D user's through-put power, therefore, when getting critical value under the minimum capacity meeting phone user and D2D user in constraints 1 and constraints 2 requires situation, small cell user efficiency is maximum; Can be obtained by constraints 1 and constraints 2:

$\left\{\begin{array}{c}{\log }_2(1+\frac{P_C{h}_C}{P_S{h}_{\mathrm{SC}}+P_D{h}_{\mathrm{DC}}+n_0})={\mathrm{\δ}}_C\\ {\log }_2(1+\frac{P_D{h}_D}{P_S{h}_{\mathrm{SD}}+P_C{h}_{\mathrm{CD}}+n_0})={\mathrm{\δ}}_D\end{array}\right.---\left(2\right)$

That is:

$\left\{\begin{array}{c}{P}_C=\frac{(2^{{\mathrm{\δ}}_C}-1)(P_D{h}_{\mathrm{DC}}+P_S{h}_{\mathrm{SC}}+n_0)}{h_C}\\ P_D=\frac{(2^{{\mathrm{\δ}}_D}-1)(P_C{h}_{\mathrm{CD}}+P_S{h}_{\mathrm{SD}}+n_0)}{h_D}\end{array}\right.---\left(3\right)$

Make respectively can in the hope of be independent variable with small cell user through-put power phone user's through-put power and D2D user's through-put power by above formula, as follows respectively:

$\left\{\begin{array}{c}{P}_C=\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{SD}}{h}_{\mathrm{DC}}+{\mathrm{\θ}}_C{h}_{\mathrm{SC}}{h}_D}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}{P}_S+\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{n}_0+{\mathrm{\θ}}_D{h}_C{n}_0}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}\\ P_D=\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{DC}}{h}_{\mathrm{CD}}+{\mathrm{\θ}}_D{h}_{\mathrm{SD}}{h}_C}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}{P}_S+\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{DC}}{n}_0+{\mathrm{\θ}}_C{h}_D{n}_0}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}\end{array}\right.---\left(4\right)$

Again formula (5) is updated to and can obtains equivalent majorized function in former optimization problem formula (1) and be:

$\underset{P_S}{\max }\frac{{\log }_2(1+\frac{P_S{h}_S}{P_S\mathrm{\β}+{\mathrm{\η}}_1})}{P_S+P_{\mathrm{circuit}}}---\left(5\right)$

Now bound for objective function is:

P _S≤P′ _max

Wherein

$\mathrm{\β}=\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D(h_{\mathrm{SD}}{h}_{\mathrm{DC}}{h}_{\mathrm{CS}}+h_{\mathrm{SC}}{h}_{\mathrm{CD}}{h}_{\mathrm{DS}})+{\mathrm{\θ}}_C{h}_{\mathrm{SC}}{h}_D{h}_{\mathrm{CS}}+{\mathrm{\θ}}_D{h}_{\mathrm{SD}}{h}_C{h}_{\mathrm{DS}}}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}---\left(6\right)$

$n_1=\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D(h_{\mathrm{CD}}{h}_{\mathrm{CS}}+h_{\mathrm{DC}}{h}_{\mathrm{DS}})+{\mathrm{\θ}}_C{h}_D{h}_{\mathrm{DS}}+{\mathrm{\θ}}_D{h}_C{h}_{\mathrm{CS}}}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}{n}_0---\left(7\right)$

${P^{\′}}_{\max }=\min \{P_{\max },\frac{P_{\max }-\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{n}_0+{\mathrm{\θ}}_D{h}_C{n}_0}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}}{\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{SD}}{h}_{\mathrm{DC}}+{\mathrm{\θ}}_C{h}_{\mathrm{SC}}{h}_D}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}},\frac{P_{\max }-\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{DC}}{n}_0+{\mathrm{\θ}}_C{h}_D{n}_0}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}}{\frac{{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{SC}}{h}_{\mathrm{CD}}+{\mathrm{\θ}}_D{h}_{\mathrm{SD}}{h}_C}{h_C{h}_D-{\mathrm{\θ}}_C{\mathrm{\θ}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}}\}---\left(8\right)$

Like this, will with P _s, P _cand P _dfor the proper energy effect optimization problem of independent variable is only converted into P _sfor the equivalent efficiency optimization problem of independent variable;

Step 3: utilize the target function of equivalent optimization problem in the provable formula of convex optimum theory (5) about P _spossess and strict first increase the curve characteristic subtracted afterwards;

Step 4: design the dichotomy Algorithm for Solving optimal transmission power points based on derivative.

Preferably, in described step 4, adopt the dichotomy Algorithm for Solving optimal transmission power points based on derivative, specifically comprise the steps:

A). make λ > 1, j=0, convergence threshold value is ε, tries to achieve value;

If b). $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={P_S}^{\left[j\right]}}<0,$ Order ${P_S}^{[j+1]}=\frac{{P_S}^{\left[j\right]}}{\mathrm{\&lambda;}},j=j+1;$

C). otherwise order ${P_S}^{[j+1]}=\mathrm{\&lambda;}{P_S}^{\left[j\right]},j=j+1;$

D). repeat b) .c). until $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={p_S}^{\left[0\right]}}\&CenterDot;\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={P_S}^{\left[j\right]}}<0;$

If e). $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={P_S}^{\left[0\right]}}>0,$ Make P _s ¹=P _s ^[j-1], P _s ²=P _s ^[j], ${\hat{P}}_S=\frac{{P_S}^1+{P_S}^2}{2};$

F). otherwise, make P _s ¹=P _s ^[j], P _s ²=P _s ^[j-1],

If g). $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={\hat{P}}_S}<0,$ Order ${P_S}^2={\hat{P}}_S,{\hat{P}}_S=\frac{{P_S}^1+{P_S}^2}{2},$ Ask $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={\hat{P}}_S};$

H). otherwise order ${P_S}^1={\hat{P}}_S,{\hat{P}}_S=\frac{{P_S}^1+{P_S}^2}{2},$ Ask $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={\hat{P}}_S};$

I). repeat e) .h). until

J). return $P_S^{*}={\hat{P}}_S$

Wherein, λ represents step-length, and j represents cycle-index, P _s ^[j]represent the through-put power of jth time circulation time small cell user, P _s ^[0]represent initial transmission power, represent optimal solution through-put power, γ (P _s) molecule of expression (5) efficiency function first derivative, P _s ¹, P _s ², represent median.

Method provided by the invention has filled up the blank of existing small cell technical research in heterogeneous network, establish the efficiency function Mathematical Modeling of small cell user in the heterogeneous network comprising macrocellular, small cell and D2D first, and be one dimension equivalence optimization problem by former three-dimensional optimized problem reduction, by the Curve Property of Researching The Equivalent optimization problem, demonstrate the existence of optimal power point, devising the dichotomy Algorithm for Solving optimal power point based on derivative, bringing great convenience for solving; Adopt the present invention that the efficiency of the small cell user in heterogeneous network can be made to reach optimal value.

Embodiment

For making the present invention become apparent, hereby with a preferred embodiment, be described in detail below.

The specific implementation process of small cell user radio method for optimizing resources is as follows:

Step 1: in the heterogeneous network containing the little base station of small cell, macrocellular and D2D, set up the target function of small cell user efficiency, shown in (1):

$\underset{P_S,P_D,P_C}{\max }{U}_S(P_S,P_D,P_C)=\frac{{\log }_2(1+\frac{P_S{h}_S}{P_C{h}_{\mathrm{CS}}+P_D{h}_{\mathrm{DS}}+n_0})}{P_S+P_{\mathrm{circuit}}}---\left(1\right)$

This target function comprises following constraints:

1, the minimum transmission rate request of phone user, namely minimum transmission rate can not be less than δ _c:

${\log }_2(1+\frac{P_C{h}_C}{P_S{h}_{\mathrm{SC}}+P_D{h}_{\mathrm{DC}}+n_0})\&GreaterEqual;{\mathrm{\&delta;}}_C$

2, the minimum transmission rate request of D2D, namely minimum transmission rate can not be less than δ _d:

${\log }_2(1+\frac{P_D{h}_D}{P_S{h}_{\mathrm{SD}}+P_C{h}_{\mathrm{CD}}+n_0})\&GreaterEqual;{\mathrm{\&delta;}}_D$

3, the maximum transmission power of small cell user, D2D user and macrocell user limits:

P _S，P _C，P _D≤P _max

A small cell user is comprised in small cell.D2D centering comprises two D2D users, and one of them is for receiving user, and another is for sending user.Wherein: P _srepresent the through-put power of small cell user, h _sDrepresent that small cell user and D2D are to the channel gain received between user, h _sCrepresent the channel gain between small cell user and macro base station, h _srepresent the channel gain between small cell user and little base station, P _drepresent that D2D is to the through-put power of launching user, h _drepresent the channel gain between D2D user, P _crepresent the through-put power of phone user, h _cDrepresent that phone user and D2D are to the channel gain received between user, n ₀represent noise power, P _circuitrepresent the circuit power consumption of D2D user, h _crepresent the channel gain between phone user and macro base station, h _dCrepresent that D2D is to the channel gain launched between user and macro base station, h _dSrepresent that D2D is to the channel gain launched between user and little base station, h _cSrepresent the channel gain between phone user and little base station.(1) the max function representation in formula maximizes the efficiency function of small cell user.

Step 2: because the small cell user efficiency optimization problem being independent variable with phone user's through-put power, D2D user's through-put power and small cell user through-put power is a non-convex problem, directly carries out solving very difficult.For identical P _s, small cell user efficiency U _svalue reduce along with the increase of phone user's through-put power and D2D user's through-put power, therefore, when getting critical value (namely getting equal sign) under the minimum capacity meeting phone user and D2D user in constraints 1 and constraints 2 requires situation, small cell user efficiency is maximum.Can be obtained by constraints 1 and constraints 2:

$\left\{\begin{array}{c}{\log }_2(1+\frac{P_C{h}_C}{P_S{h}_{\mathrm{SC}}+P_D{h}_{\mathrm{DC}}+n_0})={\mathrm{\&delta;}}_C\\ {\log }_2(1+\frac{P_D{h}_D}{P_S{h}_{\mathrm{SD}}+P_C{h}_{\mathrm{CD}}+n_0})={\mathrm{\&delta;}}_D\end{array}\right.---\left(2\right)$

That is:

$\left\{\begin{array}{c}{P}_C=\frac{(2^{{\mathrm{\&delta;}}_C}-1)(P_D{h}_{\mathrm{DC}}+P_S{h}_{\mathrm{SC}}+n_0)}{h_C}\\ P_D=\frac{(2^{{\mathrm{\&delta;}}_D}-1)(P_C{h}_{\mathrm{CD}}+P_S{h}_{\mathrm{SD}}+n_0)}{h_D}\end{array}\right.---\left(3\right)$

Make respectively can in the hope of be independent variable with small cell user through-put power phone user's through-put power and D2D user's through-put power by above formula, as follows respectively:

$\left\{\begin{array}{c}{P}_C=\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{SD}}{h}_{\mathrm{DC}}+{\mathrm{\&theta;}}_C{h}_{\mathrm{SC}}{h}_D}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}{P}_S+\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{n}_0+{\mathrm{\&theta;}}_D{h}_C{n}_0}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}\\ P_D=\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{DC}}{h}_{\mathrm{CD}}+{\mathrm{\&theta;}}_D{h}_{\mathrm{SD}}{h}_C}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}{P}_S+\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{DC}}{n}_0+{\mathrm{\&theta;}}_C{h}_D{n}_0}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}\end{array}\right.---\left(4\right)$

Again formula (5) is updated to and can obtains equivalent optimization problem in former optimization problem formula (1) and be:

$\underset{P_S}{\max }\frac{{\log }_2(1+\frac{P_S{h}_S}{P_S\mathrm{\&beta;}+{\mathrm{\&eta;}}_1})}{P_S+P_{\mathrm{circuit}}}---\left(5\right)$

Now bound for objective function is:

P _S≤P′ _max

Wherein

$\mathrm{\&beta;}=\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D(h_{\mathrm{SD}}{h}_{\mathrm{DC}}{h}_{\mathrm{CS}}+h_{\mathrm{SC}}{h}_{\mathrm{CD}}{h}_{\mathrm{DS}})+{\mathrm{\&theta;}}_C{h}_{\mathrm{SC}}{h}_D{h}_{\mathrm{CS}}+{\mathrm{\&theta;}}_D{h}_{\mathrm{SD}}{h}_C{h}_{\mathrm{DS}}}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}---\left(6\right)$

$n_1=\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D(h_{\mathrm{CD}}{h}_{\mathrm{CS}}+h_{\mathrm{DC}}{h}_{\mathrm{DS}})+{\mathrm{\&theta;}}_C{h}_D{h}_{\mathrm{DS}}+{\mathrm{\&theta;}}_D{h}_C{h}_{\mathrm{CS}}}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}{n}_0---\left(7\right)$

${P^{\&prime;}}_{\max }=\min \{P_{\max },\frac{P_{\max }-\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{n}_0+{\mathrm{\&theta;}}_D{h}_C{n}_0}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}}{\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{SD}}{h}_{\mathrm{DC}}+{\mathrm{\&theta;}}_C{h}_{\mathrm{SC}}{h}_D}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}},\frac{P_{\max }-\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{DC}}{n}_0+{\mathrm{\&theta;}}_C{h}_D{n}_0}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}}{\frac{{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{SC}}{h}_{\mathrm{CD}}+{\mathrm{\&theta;}}_D{h}_{\mathrm{SD}}{h}_C}{h_C{h}_D-{\mathrm{\&theta;}}_C{\mathrm{\&theta;}}_D{h}_{\mathrm{CD}}{h}_{\mathrm{DC}}}}\}---\left(8\right)$

Like this, will with P _s, P _cand P _dthe proper energy effect optimization problem that (three-dimensional independent variable) is independent variable is only converted into P _sthe equivalent efficiency optimization problem that (one dimension independent variable) is independent variable.

Step 3: utilize the target function of equivalent optimization problem in the provable formula of convex optimum theory (5) about P _spossess and strict first increase the curve characteristic subtracted afterwards.Concrete proof procedure is as follows:

Definition: one DUAL PROBLEMS OF VECTOR MAPPING tieed up in real number convex set D is that plan is recessed, if for arbitrary x after becoming the function f of a real number by n ₁, x ₂∈ D and x ₁≠ x ₂have:

f(λx ₁+(1-λ)x ₂)＞min{f(x ₁)，f(x ₂)}， (9)

Wherein 0 < λ < 1, min function representation gets minimum value.

Any strictly monotone function is all that plan is recessed, and strictly concave function is also all that strict plan is recessed arbitrarily, but is generally invalid conversely.

Note $R\left(P_S\right)={\log }_2(1+\frac{P_S{h}_S}{P_S\mathrm{\&beta;}+n_1}),U_S\left(P_S\right)=\frac{{\log }_2(1+\frac{P_S{h}_S}{P_S\mathrm{\&beta;}+n_1})}{P_S+P_{\mathrm{circuit}}},$ Then have:

Theorem: if R is (P _s) for P _sstrict concave function, so U _s(P _s) be exactly that strict plan is recessed, and be first monotonic increase monotone decreasing again, so P _soptimal value be that certain is limited to point.

Prove: first can in the hope of R (P _s) second dervative

$R^{\&prime;\&prime;}\left(P_S\right)=\frac{d^{2}R\left(P_S\right)}{{\mathrm{dP}}_S}=-\frac{[2\mathrm{\&beta;}(\mathrm{\&beta;}+h_S)P_S+n_1(2\mathrm{\&beta;}+h_S)]n_1{h}_S}{{(\mathrm{\&beta;}{P}_S+n_1)}^2{[(\mathrm{\&beta;}+h_S)P_S+n_1]}^2}<0$

So R (P _s) about P _sit is a strictly concave function.Definition U (P _s) superlevel collection as follows:

S _η＝{P _S＞0|U(P _S)≥η}

Known by document, if for any real number η, S _ηa strict convex set, then U (P _s) about P _sit is a strictly quasi-concave function.The S as η < 0 _ηset boundaries does not have a little, when η>=0:

S _η＝{P _S＞0|η·(P _S+P _circuit)-R(P _S)≤0}。

Because R is (P _s) about P _sstrict concave function, so S _ηabout P _sit is strictly convex sets.Demonstrate U (P like this _s) be about P _sstrictly quasi-concave function.U (P again _s) first derivative be:

$U^{\&prime;}\left(P_S\right)=\frac{\mathrm{dU}\left(P_S\right)}{{\mathrm{dP}}_S}=\frac{\frac{h_S{n}_1(P_S+P_{\mathrm{circuit}})}{(\mathrm{\&beta;}{P}_S+n_1)[(\mathrm{\&beta;}+h_s)P_S+n_1]\ln 2}-R\left(P_S\right)}{{(P_S+P_{\mathrm{circuit}})}^2}---\left(10\right)$

Because above formula denominator is greater than zero, so U (P _s) monotonicity only relevant with the sign of molecule, differentiate is carried out to molecule, order $\mathrm{\&gamma;}\left(P_S\right)=\frac{h_S{n}_1(P_S+P_{\mathrm{circuit}})}{(\mathrm{\&beta;}{P}_S+n_1)[(\mathrm{\&beta;}+h_S)P_S+n_1]\ln 2}-R\left(P_S\right),$ Then

$\begin{array}{c}{\mathrm{\&gamma;}}^{\&prime;}\left(P_S\right)=\frac{n_1{h}_S[(\mathrm{\&beta;}+h_S)P_S+n_1](\mathrm{\&beta;}{P}_S+n_1)}{{[(\mathrm{\&beta;}+h_S)P_S+n_1]}^2{(\mathrm{\&beta;}{P}_S+n_1)}^2\ln 2}\\ -\frac{n_1{h}_S(P_S+P_{\mathrm{circuit}})[2\mathrm{\&beta;}(\mathrm{\&beta;}+h_S)P_S+n_1(2\mathrm{\&beta;}+h_S)]}{{[(\mathrm{\&beta;}+h_S)P_S+n_1]}^2{(\mathrm{\&beta;}{P}_S+n_1)}^2}\\ -\frac{(\mathrm{\&beta;}{P}_D+n_1)n_1{h}_D}{[(\mathrm{\&beta;}+h_D)P_D+n_1]{(\mathrm{\&beta;}{P}_D+n_1)}^2\ln 2}\\ =-\frac{n_1{h}_D(P_D+P_{\mathrm{circuit}})[2\mathrm{\&beta;}(\mathrm{\&beta;}+h_D)P_D+n_1(2\mathrm{\&beta;}+h_D)]}{{[(\mathrm{\&beta;}+h_D)P_D+n_1]}^2{(\mathrm{\&beta;}{P}_D+n_1)}^2}\end{array}---\left(11\right)$

Therefore γ ' (P _s) be minus, γ (P _s) monotone decreasing, again P _sγ (P when going to zero _s) be greater than zero, P _sγ (P when being tending towards infinite _s) be minus, so U (P _s) be one and first increase the function subtracted afterwards.

Step 4: design the dichotomy Algorithm for Solving optimal transmission power points based on derivative, specifically comprise the steps:

A). make λ > 1, j=0, convergence threshold value is ε, tries to achieve value;

If b). $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={P_S}^{\left[j\right]}}<0,$ Order ${P_S}^{[j+1]}=\frac{{P_S}^{\left[j\right]}}{\mathrm{\&lambda;}},j=j+1;$

C). otherwise make P _s ^[j+1]=λ P _s ^[j], j=j+1;

D). repeat b) .c). until $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={P_S}^{\left[0\right]}}\&CenterDot;\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={P_S}^{\left[j\right]}}<0;$

If e). $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={P_S}^{\left[0\right]}}>0,$ Make P _s ¹=P _s ^[j-1], P _s ²=P _s ^[j], ${\hat{P}}_S=\frac{{P_S}^1+{P_S}^2}{2};$

F). otherwise, make P _s ¹=P _s ^[j], P _s ²=P _s ^[j-1],

If g). $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={\hat{P}}_S}<0,$ Order ${P_S}^2={\hat{P}}_S,{\hat{P}}_S=\frac{{P_S}^1+{P_S}^2}{2},$ Ask $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={\hat{P}}_S};$

H). otherwise order ${P_S}^1={\hat{P}}_S,{\hat{P}}_S=\frac{{P_S}^1+{P_S}^2}{2},$ Ask $\mathrm{\&gamma;}\left(P_S\right){|}_{P_S={\hat{P}}_S};$

I). repeat e) .h). until

J). return $P_S^{*}={\hat{P}}_S$

Wherein, P _s ^[0]represent initial transmission power, represent optimal solution through-put power, γ (P _s) molecule of expression (5) efficiency function first derivative, P _s ¹, P _s ², represent median.λ represents step-length, and j represents cycle-index, P _s ^[j]represent the through-put power of jth time circulation time small cell user.

Claims (2)

1. a small cell user radio method for optimizing resources, is characterized in that: the method is made up of following 4 steps:

Step 1: in the heterogeneous network containing the little base station of small cell, macrocellular and D2D, set up the target function of small cell user efficiency, shown in (1):

This target function comprises following constraints:

(1) the minimum transmission rate request of phone user, namely its minimum transmission rate can not be less than δ _c:

(2) the minimum transmission rate request of D2D, namely its minimum transmission rate can not be less than δ _d:

(3) maximum transmission power of small cell user, D2D user and macrocell user limits:

P _S，P _C，P _D≤P _max

A small cell user is comprised in small cell; D2D centering comprises two D2D users, and one of them is for receiving user, and another is for sending user; Wherein: P _srepresent the through-put power of small cell user, h _sDrepresent that small cell user and D2D are to the channel gain received between user, h _sCrepresent the channel gain between small cell user and macro base station, h _srepresent the channel gain between small cell user and little base station, P _drepresent that D2D is to the through-put power of launching user, h _drepresent the channel gain between D2D user, P _crepresent the through-put power of phone user, h _cDrepresent that phone user and D2D are to the channel gain received between user, n ₀represent noise power, P _circuitrepresent the circuit power consumption of D2D user, h _crepresent the channel gain between phone user and macro base station, h _dCrepresent that D2D is to the channel gain launched between user and macro base station, h _dSrepresent that D2D is to the channel gain launched between user and little base station, h _cSrepresent the channel gain between phone user and little base station, max function representation maximizes the target function of small cell user efficiency;

Step 2: because the small cell user efficiency optimization problem being independent variable with phone user's through-put power, D2D user's through-put power and small cell user through-put power is a non-convex problem, directly carries out solving very difficult; For identical P _s, small cell user efficiency U _svalue reduce along with the increase of phone user's through-put power and D2D user's through-put power, therefore, when getting critical value under the minimum capacity meeting phone user and D2D user in constraints 1 and constraints 2 requires situation, small cell user efficiency is maximum; Can be obtained by constraints 1 and constraints 2:

That is:

Make respectively can in the hope of be independent variable with small cell user through-put power phone user's through-put power and D2D user's through-put power by above formula, as follows respectively:

Again formula (5) is updated to and can obtains equivalent majorized function in former optimization problem formula (1) and be:

Now bound for objective function is:

P _S≤P′ _max

Wherein

Like this, will with P _s, P _cand P _dfor the proper energy effect optimization problem of independent variable is only converted into P _sfor the equivalent efficiency optimization problem of independent variable;

Step 3: utilize the target function of equivalent optimization problem in the provable formula of convex optimum theory (5) about P _spossess and strict first increase the curve characteristic subtracted afterwards;

Step 4: design the dichotomy Algorithm for Solving optimal transmission power points based on derivative.

2. a kind of small cell user radio method for optimizing resources as claimed in claim 1, is characterized in that: in described step 4, adopts the dichotomy Algorithm for Solving optimal transmission power points based on derivative, specifically comprises the steps:

A). make λ > 1, j=0, convergence threshold value is ε, tries to achieve value;

If b). order j=j+1;

C). otherwise order j=j+1;

D). repeat b) .c). until

If e). order

F). otherwise, order

If g). order ask

H). otherwise order ask

I). repeat e) .h). until

J). return

Wherein, λ represents step-length, and j represents cycle-index, represent the through-put power of jth time circulation time small cell user, represent initial transmission power, represent optimal solution through-put power, γ (P _s) molecule of expression (5) efficiency function first derivative, P _s ¹, P _s ², represent median.