CN104901913A - Transceiver design method for maximizing energy efficiency based on multi-user signal and energy simultaneous interpretation system - Google Patents

Abstract

The invention discloses a transceiver design method for maximizing energy efficiency based on a multi-user signal and energy simultaneous interpretation system. The method is advantageous in that the Dinkelbach algorithm is utilized to simplify complex problems, i.e., original problems are resolved into a series of sub-problems and nonlinear score programming is converted to a common non-fractional programming; and the iterative idea of the Dinklbach algorithm is used for determine optimal transmission precoding and power split factors, thereby finishing design of the multi-user signal and energy simultaneous interpretation system and achieving maximization of the energy efficiency of the system.

Description

Believe simultaneous interpretation EVAC (Evacuation Network Computer Model) efficiency can maximize transceiver design method based on multi-user

Technical field

The present invention relates to wireless communication transmission technique, be specially the transceiver design method of maximize energy efficiency under Multi-users MIS O (Multiple Input Single Output) wireless communication energy simultaneous interpretation EVAC (Evacuation Network Computer Model).

Background technology

At present, the huge energy consumption of communication technology generation and the environmental problem of generation thereof have become the focus of communication industry and even whole society's concern.Radio wave, not only can transmission information as a kind of potential green energy resource, can also transmitting energy.The energy wherein transmitted can effectively utilize, and under the condition not affecting telecommunication service quality, uses transmitting energy can reduce the energy consumption of whole system most effectively, improves the energy efficiency of system.

Current a lot of research work concentrates on the throughput-maximized of wireless communication system, and transmitting power minimizes or the research of wireless collection energy maximization.Its Literature [Q.Shi, W.Xu, T.-H.Chang, Y.Wang and E.Song, " Joint beamforming and power splitting for MISO interference channel with SWIPT:an SOCP relaxation and decentralized algorithm, ", IEEE Trans.Signal Process.vol.62, no.23, pp.6194-6208, and [S.Timotheou Dec.2014.], I.Krikidis, G.Zheng and B.Ottersten, " Beamforming for MISO interference channels with QoS and RF energy transfer, " IEEE Trans.Wireless Commun., vol.13, no.5, pp.2646-2658, May 2014.] be believe energy simultaneous interpretation EVAC (Evacuation Network Computer Model) for multi-user, target is minimised as with through-put power, convex relaxing techniques is utilized to study the co-design method of precoding and power splitting factor.But energy efficiency, be defined as the energy (the every bit of joule) of transmission per unit bit consumption, be also an important evaluation criterion of a judgement systematic function quality, it is the primary study direction of current and following green wireless communication system.Therefore the present invention be directed to multi-user and believe energy simultaneous interpretation EVAC (Evacuation Network Computer Model), be target with maximize energy efficiency, utilize the co-design method of Dinkelbach algorithm research transfer pre-coding and received power splitting factor.

Summary of the invention

The object of the invention is to the deficiency for traditional letter energy simultaneous interpretation EVAC (Evacuation Network Computer Model) technology, propose one and believe the maximized transceiver design method of energy simultaneous interpretation EVAC (Evacuation Network Computer Model) efficiency based on multi-user.

The object of the invention is to be achieved through the following technical solutions: a kind of believe based on multi-user can the maximized transceiver design method of simultaneous interpretation EVAC (Evacuation Network Computer Model) efficiency, comprises the steps:

(1) the following variable of initialization: the constrained objective γ of Signal to Interference plus Noise Ratio _k, gather power constraint target e _k, k=1,2 ..., K, the power constraint target P of each user _k;

(2) multi-user is believed that the maximize energy efficiency problem of energy simultaneous interpretation EVAC (Evacuation Network Computer Model) simplifies, become K subproblem by former PROBLEM DECOMPOSITION; Use Dinkelbach thought, introduce efficiency variable η and nonlinear fractional programming is converted to general non-fractional programming, wherein a kth independent subproblem is as follows:

$\begin{array}{c}\underset{\{p_k,{\mathrm{\&rho;}}_k\}}{\max }\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{p}_k+P_c)\\ s.t.\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2}\&GreaterEqual;{\mathrm{\&gamma;}}_k\\ {\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)(p_k{g}_k+{\mathrm{\&sigma;}}_k^2)\&GreaterEqual;e_k\\ 0<p_k<P_k\\ 0\&le;{\mathrm{\&rho;}}_k\&le;1\end{array}$

Wherein: ρ _kfor the power splitting factor of user k, K is total number of users, P _cfor system fixes total consumed power, for the variance of the additive noise that antenna is introduced, for radiofrequency signal changes the variance of the additive noise caused when baseband signal carries out signal transacting into, for efficiency power amplifier, ζ _kfor the energy conversion efficiency of Acquisition Circuit unit, and define h _kkconjugate channel vector between the transmitter and receiver of expression user k, represent the optimal approach to zero precoding direction vector of user k, η represents efficiency variable;

(3) a kth independent subproblem is with p _k, ρ _kfor unknown number, solve the optimal solution p of each subproblem _k, ρ _k, namely obtain closed solutions set { p _k, ρ _k, k=1,2 ..., K; Pass through formula try to achieve the energy valid value η that this closed solutions set is corresponding; Trying to achieve based on Dinkelbach iteration thought finally can valid value η ⁽ⁿ⁾and it is corresponding

(4) transfer pre-coding vector is calculated the transmitter of user k utilizes v _kprecoding is carried out to signal transmission, simultaneously by control channel by each power splitting factor be sent to corresponding receiver, each receiver user setting power splitting factor, completes the transceiver design of letter energy simultaneous interpretation EVAC (Evacuation Network Computer Model), receives while can carrying out information and energy.

A described K independent subproblem solve based on Dinkelbach alternative manner, specifically comprise following sub-step:

(1.1) initialization iterations n=1, feasible solution and calculate corresponding energy valid value η ⁽ⁿ⁾, wherein represent the through-put power that user k tries to achieve n-th iteration and power splitting factor respectively;

(1.2) upgrade iterations n=n+1, solve a kth subproblem, namely solve four one-dimensional equation corresponding to this subproblem, that is:

Equation one: $\left\{\begin{array}{c}{\mathrm{\&rho;}}_k=1-\frac{e_k}{{\mathrm{\&zeta;}}_k(P_k{g}_k+{\mathrm{\&sigma;}}_k^2)}\\ p_k\left({\mathrm{\&rho;}}_k\right)=P_k\end{array}\right.;$

Equation two: $\left\{\begin{array}{c}{\mathrm{\&rho;}}_k=\frac{{\mathrm{\&delta;}}_k^2{\mathrm{\&gamma;}}_k}{P_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&gamma;}}_k}\\ p_k\left({\mathrm{\&rho;}}_k\right)=P_k\end{array}\right.;$

Equation three: $\left\{\begin{array}{c}{A}_1{\mathrm{\&rho;}}_k^3+B_1{\mathrm{\&rho;}}_k^2+C_1{\mathrm{\&rho;}}_k+D_1=0\\ p_k\left({\mathrm{\&rho;}}_k\right)=l_2\left({\mathrm{\&rho;}}_k\right)=\frac{1}{g_k}(\frac{e_k}{{\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)}-{\mathrm{\&sigma;}}_k^2)\end{array}\right.;$

Wherein:

$\begin{array}{c}{A}_1={\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2\\ B_1=-3{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2+\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2+\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;\&theta;}{e}_k^2}{g_k{\mathrm{\&zeta;}}_k^2}{\mathrm{\&sigma;}}_k^2\\ C_1=-\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^2+3{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2+\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^4-\frac{\mathrm{\&eta;\&theta;}{e}_k^2}{g_k{\mathrm{\&zeta;}}_k^2}{\mathrm{\&delta;}}_k^2\\ D_1=\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^2-{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^4\end{array};$

Equation four: $\left\{\begin{array}{c}{A}_2{\mathrm{\&rho;}}_k+B_2=0\\ p_k\left({\mathrm{\&rho;}}_k\right)=p_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)=\frac{{\mathrm{\&rho;}}_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&rho;}}_k\mathrm{\&eta;\&theta;}-{\mathrm{\&delta;}}_k^2\mathrm{\&eta;\&theta;}}{{\mathrm{\&rho;}}_k{g}_k\mathrm{\&eta;\&theta;}}\end{array}\right.$

Wherein:

$\begin{array}{c}{A}_2=g_k-\mathrm{\&eta;\&theta;}{\mathrm{\&sigma;}}_k^2\\ B_2=-\mathrm{\&eta;\&theta;}{\mathrm{\&delta;}}_k^2\end{array};$

Obtain corresponding closed solutions set { p _k, ρ _k, find out and meet feasible zone 0≤ρ _k≤ 1 and l ₂(ρ _k)≤p _k≤ P _kand make target function corresponding when obtaining maximum be the solution that user k is corresponding, repeat this step until all subproblems all find corresponding optimal solution, energy valid value η now can be calculated ⁽ⁿ⁾, η ⁽ⁿ⁾can be expressed as:

${\mathrm{\&eta;}}^{\left(n\right)}=\frac{\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\log (1+\frac{{\mathrm{\&rho;}}_k^{\left(n\right)}{p}_k^{\left(n\right)}{g}_k}{{\mathrm{\&rho;}}_k^{*}{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})}{\mathrm{\&theta;}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{p}_k^{\left(n\right)}+P_c};$

(1.3) judge whether to meet iterated conditional ε is decision threshold, continues to perform step (1.2), namely also do not find final energy valid value if satisfy condition; Otherwise jump out circulation, export η now ⁽ⁿ⁾with

The invention has the beneficial effects as follows: transmission beam figuration vector sum interference channel matrix effectively combines by the present invention, adopt ZF and the problem of Dinkelbach algorithm to former complexity to simplify.Under the prerequisite meeting telecommunication service quality, transmit while not only achieving information and energy, the more important thing is the energy efficiency maximizing letter energy simultaneous interpretation EVAC (Evacuation Network Computer Model).

Accompanying drawing explanation

Fig. 1 is the system model figure of one embodiment of the invention;

Fig. 2 is the program flow diagram of the key algorithm of one embodiment of the invention;

Fig. 3 is average efficiency and the transmitting power comparison diagram of one embodiment of the invention;

Fig. 4 is average efficiency and the number of transmit antennas comparison diagram of one embodiment of the invention.

Embodiment

In order to make the present invention more reliably clear, hereafter will be specifically addressed embodiments of the present invention.

The model of system as shown in Figure 1, considers that a multi-user believes energy simultaneous interpretation EVAC (Evacuation Network Computer Model), under given band bandwidth W, and each user (T _k) (transmitting terminal altogether K user) be equipped with N _t(N _t>1) individual antenna provision 1 single-antenna subscriber (receiving terminal is K user altogether).Allow s _j~ CN (0,1) represents transmission symbol, v _jrepresent precoding (or claiming wave beam forming vector) j=1 ..., K.Allow h _kjrepresent the conjugation passage vector between transmitter j and receiver k, the signal that so user k accepts can be expressed as:

$y_k=\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{\mathrm{kj}}^H{v}_j{s}_j+n_k,k=1,...,K---\left(1\right)$

Wherein represent the antenna additive noise of user k.

Be different from traditional Multi-users MIS O system, the signal that each user receives will divide two parts, and a part is used for information decoding, and another part is used for energy acquisition.User k receives signal proportionally ρ _kdivide, information decoding part can be expressed as:

$y_k^{\mathrm{ID}}=\sqrt{{\mathrm{\&rho;}}_k}(\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{\mathrm{kj}}^H{v}_j{s}_j+n_k)+z_k,\&ForAll;k---\left(2\right)$

Wherein for radiofrequency signal changes the additive noise caused when baseband signal carries out signal transacting into.

Another part energy acquisition function can be expressed as:

$y_k^{\mathrm{EH}}=\sqrt{1-{\mathrm{\&rho;}}_k}(\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{h}_{\mathrm{kj}}^H{v}_j{s}_j+n_k),\&ForAll;k---\left(3\right)$

Therefore, the Signal to Interference plus Noise Ratio SINR of the channel decoding of user k _kcan be expressed as:

${\mathrm{SINR}}_k=\frac{{\mathrm{\&rho;}}_k{\left|h_{\mathrm{kk}}^H{v}_k\right|}^2}{{\mathrm{\&rho;}}_k(\underset{j\&NotEqual;k}{\mathrm{\&Sigma;}}{\left|h_{\mathrm{kj}}^H{v}_j\right|}^2+{\mathrm{\&sigma;}}_k^2)},\&ForAll;k---\left(4\right)$

The power E that user k gathers _kcan be expressed as:

$E_k={\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)(\underset{j=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|h_{\mathrm{kj}}^H{v}_j\right|}^2+{\mathrm{\&sigma;}}_k^2),\&ForAll;k---\left(5\right)$

Wherein ζ _k∈ (0,1] represent energy conversion efficiency.

According to shannon formula, the message transmission rate R of a kth user _kcan be expressed as:

$R_k\stackrel{\mathrm{\&Delta;}}{=}W\log (1+{\mathrm{SINR}}_k),\&ForAll;k---\left(6\right)$

Therefore, the message transmission rate R that system is total can be expressed as:

$R\stackrel{\mathrm{\&Delta;}}{=}{\mathrm{\&Sigma;}}_{k=1}^K{R}_k---\left(7\right)$

The total power consumption P of system _scan be expressed as:

$P_s=\mathrm{\&theta;}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{\left|\right|v_k\left|\right|}^2+P_c---\left(8\right)$

Wherein Part I represent the power loss (θ>=1 represents the power efficiency of amplifier) of transmitter amplifier, Part II P _crepresenting the Constant power dissipation of receiver signal process, is separate with Part I.

Can simultaneous interpretation EVAC (Evacuation Network Computer Model) for letter, telecommunication service quality require to include two parts, a part is to ensure that proper communication needs Signal to Interference plus Noise Ratio SINR _kreach certain requirement, another part gathers power E _kneed meet some requirements.Suppose SINR _kand E _kdesign object be respectively γ _kand e _k.In order to simplify the design of transceiver, we use modal Wave beam forming scheme-ZF process, and namely make zero multi-user interference signal.Mathematically, this problem can be equivalent to (ignoring constant W):

$\begin{array}{c}\underset{\{v_k,{\mathrm{\&rho;}}_k\}}{\max }\frac{{\mathrm{\&Sigma;}}_{k=1}^K{R}_k}{\mathrm{\&theta;}{\mathrm{\&Sigma;}}_{K=1}^K{\left|\right|v_k\left|\right|}^2+P_c}\\ s.t.{\mathrm{SINR}}_k(v,{\mathrm{\&rho;}}_k)\&GreaterEqual;{\mathrm{\&gamma;}}_k,\&ForAll;k,\\ E_k(v,{\mathrm{\&rho;}}_v)\&GreaterEqual;e_k,\&ForAll;k,\\ h_{\mathrm{jk}}^H{v}_j=0,j\&NotEqual;k,\&ForAll;k\\ 0\&le;p_k\&le;P_k,\\ 0\&le;{\mathrm{\&rho;}}_k\&le;1,\&ForAll;k.\end{array}---\left(9\right)$

Observe the problems referred to above, be very easy to find, this problem is non-convex optimization problem (comprising the target function of non-convex and the constraint set of non-convex), but according to the zero-forcing constraint condition of problem (9) and structure, we can utilize proposition 1 problem (9) to be simplified.

Proposition 1: assuming that $H_k\stackrel{\mathrm{\&Delta;}}{=}[h_{1k},...,h_{(k-1)k},h_{(k+1)k},...,h_{\mathrm{Kk}}],\&ForAll;k,$ U _kbe expressed as interference channel matrix kernel orthogonal basis composition vector, definition g _kbe respectively:

${\tilde{v}}_k\stackrel{\mathrm{\&Delta;}}{=}\frac{U_k{U}_k^H{h}_k}{\left|\right|U_k{U}_k^H{h}_k\left|\right|},g_k\stackrel{\mathrm{\&Delta;}}{=}{\left|h_{\mathrm{kk}}^H{\tilde{v}}_k\right|}^2,\&ForAll;k,---\left(10\right)$

Therefore problem (9) can be reduced to:

$\begin{array}{c}\underset{\{p_k,{\mathrm{\&rho;}}_k\}}{\max }\frac{{\mathrm{\&Sigma;}}_{k=1}^K\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})}{{\mathrm{\&Sigma;}}_{k=1}^K\mathrm{\&theta;}{p}_k+P_c}\\ s.t.\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2}\&GreaterEqual;{\mathrm{\&gamma;}}_k,\&ForAll;k,\\ {\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)(p_k{g}_k+{\mathrm{\&sigma;}}_k^2)\&GreaterEqual;e_k,\&ForAll;k,\\ 0\&le;p_k\&le;P_k,\\ 0\&le;{\mathrm{\&rho;}}_k\&le;1,\&ForAll;k.\end{array}---\left(11\right)$

Wherein $v_k=\sqrt{p_k}{\tilde{v}}_k,k=\mathrm{1,2},...,K.$

Obviously, problem (11) is a non-linear fractional programming, is difficult to be solved.Introducing efficiency variable η uses Dinkelbach algorithm by the form that target function converts molecule to, denominator subtracts each other of problem (11).Therefore, target function can be exchanged into:

$\underset{(p_k,{\mathrm{\&rho;}}_k)\&Element;{\mathrm{\&Omega;}}_k,k\&ForAll;}{\max }{\mathrm{\&Sigma;}}_{k=1}^K\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{p}_k+P_c)---\left(12\right)$

As η=η ^*, η ^*be expressed as:

${\mathrm{\&eta;}}^{*}=\frac{\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\log (1+\frac{p_k^{*}{p}_k^{*}{g}_k}{{\mathrm{\&rho;}}_k^{*}{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})}{\mathrm{\&theta;}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{p}_k^{*}+P_c}---\left(13\right)$

η ^*only maximum energy efficiency, if the optimum value of problem (12) that F (η) represents.Dinkelbach algorithm is a kind of iterative algorithm, and the η of generation converges on maximum energy efficiency η ^*make F (η ^*)=0.Wherein the acquisition of η value as shown in Figure 2.Once η convergence, problem (12) will be resolved, and also just obtain the optimal solution of problem (11), thus achieve the optimization of energy efficiency.

Therefore, what first we needed solution is problem (12).Be different from problem (11), problem (12) is independently for each user.That is, problem (12) can be broken down into K subproblem, and wherein a kth subproblem can be expressed as:

$\begin{array}{c}\underset{\{p_k,{\mathrm{\&rho;}}_k\}}{\max }\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{p}_k+P_c)\\ s.t.\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2}\&GreaterEqual;{\mathrm{\&gamma;}}_k,\\ {\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)(p_k{g}_k+{\mathrm{\&sigma;}}_k^2)\&GreaterEqual;e_k,\\ 0\&le;p_k\&le;P_k,\\ 0\&le;{\mathrm{\&rho;}}_k\&le;1.\end{array}---\left(14\right)$

Conveniently, before deal with problems (14), the first two condition of this problem is first changed by we, namely

$\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2}\&GreaterEqual;{\mathrm{\&gamma;}}_k\&RightArrow;{\mathrm{\&rho;}}_k\&GreaterEqual;\frac{{\mathrm{\&gamma;}}_k({\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2)}{{\mathrm{\&rho;}}_k{g}_k}---\left(15\right)$

${\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)(p_k{g}_k+{\mathrm{\&sigma;}}_k^2)\&GreaterEqual;e_k\&RightArrow;p_k\&GreaterEqual;\frac{1}{g_k}(\frac{e_k}{{\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)}-{\mathrm{\&sigma;}}_k^2)---\left(16\right)$

If $l_1\left({\mathrm{\&rho;}}_k\right)=\frac{{\mathrm{\&gamma;}}_k({\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2)}{{\mathrm{\&rho;}}_k{g}_k},l_2\left({\mathrm{\&rho;}}_k\right)=\frac{1}{g_k}(\frac{e_k}{{\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)}-{\mathrm{\&sigma;}}_k^2),{\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)=\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{p}_k+P_c)$

If by p _kuse ρ _krepresent, i.e. p _k(ρ _k).Problem (14) just becomes the convex problem of single argument with edge-restraint condition, and its optimum value one fixes on extreme point or boundary value point.Therefore, optimum value p _k(ρ _k) can be following four kinds of situations:

1) p _k(ρ _k)=P _k; 2) p _k(ρ _k)=l ₁(ρ _k); 3) p _k(ρ _k)=l ₂(ρ _k); 4) wherein the target function of problem of representation (14) is with p _kfor the extreme point of unknown number.In order to deal with problems (14), we need respectively p to be discussed _k, ρ _keach situation, be now summarized as following 3 kinds of situations:

1) suppose $p_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)\&GreaterEqual;p_k^{\mathrm{up}}\&GreaterEqual;\max (l_1\left({\mathrm{\&rho;}}_k\right),l_2\left({\mathrm{\&rho;}}_k\right))$ ( for p _kupper boundary values), when $p_k\left({\mathrm{\&rho;}}_k\right)=p_k^{\mathrm{up}}=P_k$ Time, target function ψ _k(ρ _k) can be expressed as:

${\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)=\log (1+\frac{{\mathrm{\&rho;}}_k{P}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{P}_k+P_c)---\left(17\right)$

1.1) ask (with ρ _kextreme point for unknown number), so order obtain ρ _kdo not exist.

1.2) ask (ρ _kupper boundary values), problem (14) the 2nd constraints is transformed: therefore ${\mathrm{\&rho;}}_k^{\mathrm{up}}=\min (1-\frac{e_k}{{\mathrm{\&zeta;}}_k(P_k{g}_k+{\mathrm{\&sigma;}}_k^2)},1),$ Namely ${\mathrm{\&rho;}}_k^{\mathrm{up}}=1-\frac{e_k}{{\mathrm{\&zeta;}}_k(P_k{g}_k+{\mathrm{\&sigma;}}_k^2)}$

: $\begin{array}{c}{\mathrm{\&rho;}}_k=1-\frac{e_k}{{\mathrm{\&zeta;}}_k(P_k{g}_k+{\mathrm{\&sigma;}}_k^2)}\\ p_k=P_k\end{array}.$

Verify hypothesis condition whether set up, set up and then there is this solution, be false, ignore this and separate.

1.3) ask (ρ _klower border value), problem (14) first constraintss are transformed: therefore ${\mathrm{\&rho;}}_k^{\mathrm{down}}=\max (\frac{{\mathrm{\&delta;}}_k^2{\mathrm{\&gamma;}}_k}{P_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&gamma;}}_k},0).$

If $\frac{{\mathrm{\&delta;}}_k^2{\mathrm{\&gamma;}}_k}{P_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&gamma;}}_k}>0,$ Then ${\mathrm{\&rho;}}_k=\frac{{\mathrm{\&delta;}}_k^2{\mathrm{\&gamma;}}_k}{P_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&gamma;}}_k},$ ? $\begin{array}{c}{\mathrm{\&rho;}}_k=\frac{{\mathrm{\&delta;}}_k^2{\mathrm{\&gamma;}}_k}{P_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&gamma;}}_k}\\ p_k=P_k\end{array}.$

Verify hypothesis condition whether set up, set up and then there is this solution, be false, ignore this and separate.

If $\frac{{\mathrm{\&delta;}}_k^2{\mathrm{\&gamma;}}_k}{P_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&gamma;}}_k}<0,$ Then ρ _k=0 i.e. ρ _kdo not exist.

2) suppose $p_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)\&le;p_k^{\mathrm{down}}\&le;p_k^{\mathrm{up}}$ ( for p _klower border value), namely $p_k\left({\mathrm{\&rho;}}_k\right)=p_k^{\mathrm{down}}=\max (l_1\left({\mathrm{\&rho;}}_k\right),l_2\left({\mathrm{\&rho;}}_k\right)).$

2.1) l is worked as ₁(ρ _k) > l ₂(ρ _k) > 0 time, target function ψ _k(ρ _k) can be expressed as:

${\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)=\log (1+\frac{{\mathrm{\&rho;}}_k{l}_1\left({\mathrm{\&rho;}}_k\right)g_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{l}_1\left({\mathrm{\&rho;}}_k\right)+P_c)---\left(18\right)$

Ask so order $\frac{d{\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)}{d{\mathrm{\&rho;}}_k}=0,$ Obtain ρ _kdo not exist.

2.2) l is worked as ₂(ρ _k)>=l ₁(ρ _k) > 0 time, target function ψ _k(ρ _k) can be expressed as:

${\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)=\log (1+\frac{{\mathrm{\&rho;}}_k{l}_2\left({\mathrm{\&rho;}}_k\right)g_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{l}_2\left({\mathrm{\&rho;}}_k\right)+P_c)---\left(19\right)$

Ask so order $\frac{d{\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)}{d{\mathrm{\&rho;}}_k}=0,$ :

$A_1{\mathrm{\&rho;}}_k^3+B_1{\mathrm{\&rho;}}_k^2+C_1{\mathrm{\&rho;}}_k+D_1=0---\left(20\right)$

Wherein:

$\begin{array}{c}{A}_1={\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2\\ B_1=-3{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2+\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2+\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;\&theta;}{e}_k^2}{g_k{\mathrm{\&zeta;}}_k^2}{\mathrm{\&sigma;}}_k^2\\ C_1=-\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^2+3{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2+\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^4-\frac{\mathrm{\&eta;\&theta;}{e}_k^2}{g_k{\mathrm{\&zeta;}}_k^2}{\mathrm{\&delta;}}_k^2\\ D_1=\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^2-{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;\&theta;}{e}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^4\end{array}$

Now $p_k=l_2\left({\mathrm{\&rho;}}_k\right)=\frac{1}{g_k}(\frac{e_k}{{\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)}-{\mathrm{\&sigma;}}_k^2).$

Verify hypothesis condition 1 (l respectively ₂(ρ _k)>=l ₁(ρ _k) > 0) and assumed condition 2 whether set up, set up and then there is this solution, be false, ignore this and separate.

3) suppose $p_k^{\mathrm{down}}\&le;p_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)\&le;p_k^{\mathrm{up}},$ Order $\frac{d{\mathrm{\&psi;}}_k\left({p_k,\mathrm{\&rho;}}_k\right)}{d{p}_k}=0$ :

$p_k\left({\mathrm{\&rho;}}_k\right)=p_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)=\frac{{\mathrm{\&rho;}}_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&rho;}}_k\mathrm{\&eta;\&theta;}-{\mathrm{\&delta;}}_k^2\mathrm{\&eta;\&theta;}}{{\mathrm{\&rho;}}_k{g}_k\mathrm{\&eta;\&theta;}}---\left(21\right)$

Therefore, target function ψ _k(ρ _k) can be expressed as:

${\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)=\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)g_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}(\mathrm{\&theta;}{p}_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)+P_c)---\left(22\right)$

Ask so order $\frac{d{\mathrm{\&psi;}}_k\left({\mathrm{\&rho;}}_k\right)}{d{\mathrm{\&rho;}}_k}=0,$ :

A ₂ρ _k+B ₂＝0 (23)

Wherein:

$\begin{array}{c}{A}_2=g_k-\mathrm{\&eta;\&theta;}{\mathrm{\&sigma;}}_k^2\\ B_2=-\mathrm{\&eta;\&theta;}{\mathrm{\&delta;}}_k^2\end{array}$

Now $p_k=p_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)=\frac{{\mathrm{\&rho;}}_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&rho;}}_k\mathrm{\&eta;\&theta;}-{\mathrm{\&delta;}}_k^2\mathrm{\&eta;\&theta;}}{{\mathrm{\&rho;}}_k{g}_k\mathrm{\&eta;\&theta;}}.$

Verify hypothesis condition whether set up, set up and then there is this solution, be false, ignore this and separate.

Closed solutions { the ρ that often kind of situation is obtained _kand corresponding { p _k, in generation to problem (14), then obtain and make ψ _k(ρ _k) obtain (ρ corresponding to maximum _k, p _k), be problem (14) and solve, more in like manner solve other subproblems, finally obtain the feasible solution { ρ of problem (11) _k, p _k.

To sum up, the transmitter of user k utilizes v _kprecoding is carried out to signal transmission, by control channel, each power splitting factor is sent to corresponding receiver simultaneously, make each receiver user setting power splitting factor, receive while reaching information and energy, thus achieve the maximization of energy efficiency.

As shown in Figure 2, describe the concrete grammar using Dinkelbach algorithm iteration to go out η value, comprise the following steps:

(1) initialization iterations n=1, feasible solution and calculate corresponding energy valid value η ⁽ⁿ⁾, wherein represent the through-put power that user k tries to achieve n-th iteration and power splitting factor (initial value η respectively ⁽¹⁾, η ⁽²⁾be set as 10 respectively ^-3with );

(2) corresponding closed solutions set { p is obtained _k, ρ _k, find out and meet feasible zone 0≤ρ _k≤ 1 and max (l ₁(ρ _k), l ₂(ρ _k))≤p _k≤ P _kand make target function corresponding when obtaining maximum be the solution that user k is corresponding, repeat this step until all subproblems all find corresponding optimal solution, energy valid value η now can be calculated ⁽ⁿ⁾, η ⁽ⁿ⁾can be expressed as:

${\mathrm{\&eta;}}^{\left(n\right)}=\frac{\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\log (1+\frac{{\mathrm{\&rho;}}_k^{\left(n\right)}{p}_k^{\left(n\right)}{g}_k}{{\mathrm{\&rho;}}_k^{*}{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})}{\mathrm{\&theta;}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{p}_k^{\left(n\right)}+P_c};$

(3) judge whether to meet iterated conditional ε is decision threshold, is set as 10 ^-4if satisfy condition and continue to perform step (1.2), namely also do not find final energy valid value; Otherwise jump out circulation, export η now ⁽ⁿ⁾with

Fig. 3 and Fig. 4 is that the present invention is by the simulating, verifying of Matlab to designed scheme.Parameter is specifically set to: transmitting terminal antenna number N _t=8, the quantity K=4 of receiver, energy conversion factor ξ=0.65, antenna noise power transmitted noise power efficiency power amplifier θ=5, bandwidth W=15KHz, in addition, supposes that all information receivers have identical SINR _kand E _kthreshold value, i.e. γ ₁=...=γ _k=γ and e ₁=...=e _k=e.If do not make specified otherwise, overall transmission power P is set in simulations _k=40dBm, γ=20dBm, e=-20dBm.The total permanent circuit of transceiver herein consumes P _cvalue as follows:

P _C＝N _t(P _DAC+P _mix+P _filt)+2P _syn+K(P _LNA+P _mix+P _IFA+P _filr+P _ADC) (24)

Wherein: P _dAC, P _mix, P _filt, P _syn, P _lNA, P _iFA, P _aDCrepresent the power that digital-to-analogue conversion, blender, the filter of transmitter terminal, frequency mixer, low noise amplifier, intermediate frequency amplifier, receiver end filter and analog-to-digital conversion consume respectively.In simulations, the value of each parameter is as form 1:

Each parameter value during the total permanent circuit of form 1 transceiver consumes

Blender P mix	30.3mW
		Filter P filt＝P filr	2.5mW
Frequency mixer P syn	50mW
		Low noise amplifier P LNA	20mW
Intermediate frequency amplifier P IFA	3mW
		Digital-to-analogue transforms P DAC	15.44mW
Analog-to-digital conversion P ADC	6.76mW

Fig. 3 gives the comparison diagram of average energy valid value and through-put power.The parameter arranged respectively in figure is: γ=20dBm, e=-20dBm, and γ=10dBm, e=-10dBm.The continuous increase along with through-put power can be found out by the curve of two in figure, average energy valid value constantly increases, but when the through-put power of two curves is more than or equal to 16dBm and 26dBm respectively, average energy valid value all no longer increases and keeps in the same horizontal line, means that now through-put power is no longer the important parameter affecting average efficiency.

Fig. 4 gives the comparison diagram of average energy valid value and antenna number, and the parameter arranged in figure is: γ=20dBm, e=-20dBm, consumes P by the total permanent circuit of formula (24) known transceiver _cincrease along with antenna number is increased.As seen from the figure as antenna number N _twhen increasing to 16 from 4, average energy valid value constantly increases, but when antenna number increases to 60 from 16, average energy valid value but reduces gradually, this means that should carry out day line options when transmitter terminal will adopt large-scale antenna array time could obtain good performance efficiency.

Compared by performance simulation above, the present invention can not only controls transfer power realize efficiency maximize, and can to antenna number carry out choose reasonable realize efficiency maximize, can play an important role in the large-scale antenna array of following 5G technology.

The present invention is not only confined to above-mentioned embodiment, and persons skilled in the art, according to content disclosed by the invention, can adopt other multiple specific embodiments to implement the present invention.Therefore, every employing project organization of the present invention and thinking, do the design that some simply change or change, all fall into scope.

Claims (2)

1. believe simultaneous interpretation EVAC (Evacuation Network Computer Model) efficiency can maximize a transceiver design method based on multi-user, it is characterized in that, comprise the steps:

(1) the following variable of initialization: the constrained objective γ of Signal to Interference plus Noise Ratio _k, gather power constraint target e _k, k=1,2 ..., K, the power constraint target P of each user _k;

(2) multi-user is believed that the maximize energy efficiency problem of energy simultaneous interpretation EVAC (Evacuation Network Computer Model) simplifies, become K subproblem by former PROBLEM DECOMPOSITION; Use Dinkelbach thought, introduce efficiency variable η and nonlinear fractional programming is converted to general non-fractional programming, wherein a kth independent subproblem is as follows:

$\underset{\{p_k,{\mathrm{\&rho;}}_k\}}{\max }\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}({\mathrm{\&theta;p}}_k+P_c)$

$s.t.\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2}\&GreaterEqual;{\mathrm{\&gamma;}}_k$

${\mathrm{\&xi;}}_k(1-{\mathrm{\&rho;}}_k)(p_k{g}_k+{\mathrm{\&sigma;}}_k^2)\&GreaterEqual;e_k$

0＜p _k＜P _k

0≤ρ _k≤1

Wherein: ρ _kfor the power splitting factor of user k, K is total number of users, P _cfor system fixes total consumed power, for the variance of the additive noise that antenna is introduced, for radiofrequency signal changes the variance of the additive noise caused when baseband signal carries out signal transacting into, for efficiency power amplifier, ζ _kfor the energy conversion efficiency of Acquisition Circuit unit, and define h _kkconjugate channel vector between the transmitter and receiver of expression user k, represent the optimal approach to zero precoding direction vector of user k, η represents efficiency variable;

(3) a kth independent subproblem is with p _k, ρ _kfor unknown number, solve the optimal solution p of each subproblem _k, ρ _k, namely obtain closed solutions set { p _k, ρ _k, k=1,2 ..., K; Pass through formula try to achieve the energy valid value η that this closed solutions set is corresponding; Trying to achieve based on Dinkelbach iteration thought finally can valid value η ⁽ⁿ⁾and it is corresponding

(4) transfer pre-coding vector is calculated the transmitter of user k utilizes v _kprecoding is carried out to signal transmission, simultaneously by control channel by each power splitting factor be sent to corresponding receiver, each receiver user setting power splitting factor, completes the transceiver design of letter energy simultaneous interpretation EVAC (Evacuation Network Computer Model), receives while can carrying out information and energy.

2. a kind ofly according to claim 1 believe simultaneous interpretation EVAC (Evacuation Network Computer Model) efficiency can maximize transceiver design method based on multi-user, it is characterized in that, a described K independent subproblem solve based on Dinkelbach iterative algorithm, specifically comprise following sub-step:

(1.1) initialization iterations n=1, feasible solution and calculate corresponding energy valid value η ⁽ⁿ⁾, wherein represent the through-put power that user k tries to achieve n-th iteration and power splitting factor respectively;

(1.2) upgrade iterations n=n+1, solve a kth subproblem, namely solve four one-dimensional equation corresponding to this subproblem, that is:

Equation one: $\left\{\begin{array}{c}{\mathrm{\&rho;}}_k=1-\frac{e_k}{{\mathrm{\&zeta;}}_k(P_k{g}_k+{\mathrm{\&sigma;}}_k^2)}\\ p_k\left({\mathrm{\&rho;}}_k\right)=P_k\end{array}\right.;$

Equation two: $\left\{\begin{array}{c}{\mathrm{\&rho;}}_k=\frac{{\mathrm{\&delta;}}_k^2{\mathrm{\&gamma;}}_k}{P_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&gamma;}}_k}\\ p_k\left({\mathrm{\&rho;}}_k\right)=P_k\end{array}\right.;$

Equation three: $\left\{\begin{array}{c}{A}_1{\mathrm{\&rho;}}_k^3+B_1{\mathrm{\&rho;}}_k^2+C_1{\mathrm{\&rho;}}_k+D_1=0\\ p_k\left({\mathrm{\&rho;}}_k\right)=l_2\left({\mathrm{\&rho;}}_k\right)=\frac{1}{g_k}(\frac{e_k}{{\mathrm{\&zeta;}}_k(1-{\mathrm{\&rho;}}_k)}-{\mathrm{\&sigma;}}_k^2)\end{array}\right.;$

Wherein:

$A_1={\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2$

$B_1=-3{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2+\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2+\frac{\mathrm{\&eta;}{\mathrm{\&theta;e}}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;}{\mathrm{\&theta;e}}_k^2}{g_k{\mathrm{\&zeta;}}_k^2}{\mathrm{\&sigma;}}_k^2$ $C_1=-\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^2+3{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;}{\mathrm{\&theta;e}}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2+\frac{\mathrm{\&eta;}{\mathrm{\&theta;e}}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&sigma;}}_k^4-\frac{\mathrm{\&eta;}{\mathrm{\&theta;e}}_k^2}{g_k{\mathrm{\&zeta;}}_k^2}{\mathrm{\&delta;}}_k^2;$

$D_1=\frac{e_k}{{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^2-{\mathrm{\&sigma;}}_k^2{\mathrm{\&delta;}}_k^2-\frac{\mathrm{\&eta;}{\mathrm{\&theta;e}}_k}{g_k{\mathrm{\&zeta;}}_k}{\mathrm{\&delta;}}_k^4$

Equation four: $\left\{\begin{array}{c}{A}_2{\mathrm{\&rho;}}_k+B_2=0\\ p_k\left({\mathrm{\&rho;}}_k\right)=p_k^{\mathrm{ex}}\left({\mathrm{\&rho;}}_k\right)=\frac{{\mathrm{\&rho;}}_k{g}_k-{\mathrm{\&sigma;}}_k^2{\mathrm{\&rho;}}_k\mathrm{\&eta;\&theta;}-{\mathrm{\&delta;}}_k^2\mathrm{\&eta;\&theta;}}{{\mathrm{\&rho;}}_k{g}_k\mathrm{\&eta;\&theta;}}\end{array}\right.$

Wherein:

$A_2=g_k-\mathrm{\&eta;\&theta;}{\mathrm{\&sigma;}}_k^2$

$B_2=-\mathrm{\&eta;\&theta;}{\mathrm{\&delta;}}_k^2;$

Obtain corresponding closed solutions set { p _k, ρ _k, find out and meet feasible zone 0≤ρ _k≤ 1 and l ₂(ρ _k)≤p _k≤ P _kand make target function $\log (1+\frac{{\mathrm{\&rho;}}_k{p}_k{g}_k}{{\mathrm{\&rho;}}_k{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})-\mathrm{\&eta;}({\mathrm{\&theta;p}}_k+P_c)$ Corresponding when obtaining maximum be the solution that user k is corresponding, repeat this step until all subproblems all find corresponding optimal solution, energy valid value η now can be calculated ⁽ⁿ⁾, η ⁽ⁿ⁾can be expressed as:

${\mathrm{\&eta;}}^{\left(n\right)}=\frac{\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\log (1+\frac{{\mathrm{\&rho;}}_k^{\left(n\right)}{p}_k^{\left(n\right)}{g}_k}{{\mathrm{\&rho;}}_k^{*}{\mathrm{\&sigma;}}_k^2+{\mathrm{\&delta;}}_k^2})}{\mathrm{\&theta;}\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}{p}_k^{\left(n\right)}+P_c};$

(1.3) judge whether to meet iterated conditional ε is decision threshold, continues to perform step (1.2), namely also do not find final energy valid value if satisfy condition; Otherwise jump out circulation, export η now ⁽ⁿ⁾with