CN105553513A - Multicarrier PLC relay system power optimization method guaranteeing system rate - Google Patents

Abstract

The invention discloses a multicarrier PLC relay system power optimization method guaranteeing a system rate, and the method comprises the following steps: firstly setting subcarriers and a system total rate target value which are used by a system, and initializing a system power assigned value; secondly employing the thought of concave-convex optimization to roughly convert a problem of maximization of non-convex system power into a convex problem, employing a Lagrange dual method to solve an approximate system power minimization problem, and obtaining a final system emission power assigned value; finally setting the emission power of a source end and a relay according to the calculated emission power, and achieving the signal transmission of a multicarrier PLC system. The method designs the power distribution of the PLC relay system through employing the concave-convex optimization method and the Lagrange dual method, thereby reducing the total power of the PLC relay system while meeting the requirement of the system total rate.

Description

A kind of multicarrier PLC relay system power optimization method ensureing system velocity

Technical field

The present invention relates to power line communication (PLC, PowerLineCommunication) technical field, the multicarrier power line relay communications system power allocation scheme be specially based on OFDM (OFDM, OrthogonalFrequencyDivisionMultiplexing) technology designs.

Background technology

Power line communication refers to using power line as transmission medium, realizes exchanges data and information transmission between each node of power line communication network and between power line communication network and other communication networks.Especially, the research that indoor power line communication technology causes numerous scholar is especially noted.As everyone knows, the manufacture of electric power cable is not intended to transmitting high-frequency signal, and this is very disadvantageous for the broadband connections based on power line.But on the other hand, we also know that the Signal transmissions based on power line has similar broadcast characteristic to radio communication.But through literature search, [L.LampeandA.J.HanVinck, " Cooperativemultihoppowerlinecommunications; " IEEEthe16thInternationalSymposiumonPowerLineCommunicatio nsanditsApplications (ISPLC), Beijing, China, March2012, pp.1-6.] indicate the difference of power line communication trunk channel and wireless relay system.In radio systems, source node is to destination node, therefore source node all can be considered separate to via node and via node to the path of destination node can easily obtain its space diversity gain, and in a power line communication system, this three paths is but highly allo.Therefore, being people's service to allow electric line communication system better, the relaying auxiliary system of some advanced persons can being introduced in electric line communication system.

Therefore, for PLC relay system, first the present invention considers that source node arrives destination node, source node is all equal to the transmitting power of destination node to via node and via node, then based on a kind of power allocation scheme of concavo-convex optimization method and Lagrange duality method design, the object reducing PLC relay system gross power while the total rate requirement of the system that reaches is achieved.The core concept of the method is: utilize concavo-convex optimization thought that the system power minimization problem of non-convex is approximately convex problem, and utilize Lagrange duality method to solve approximate system power minimization problem iteratively to obtain last system emission power apportioning cost, the method can ensure system power monotone decreasing in an iterative process, thus not only achieve the information transmission of PLC system, also make while the total rate requirement of the system that reaches, reduce PLC relay system gross power.

Summary of the invention

The object of the invention is to for the deficiencies in the prior art, a kind of multicarrier PLC relay system power optimization method ensureing system velocity be provided, comprise the following steps:

Step 1: the t easet ofasubcarriers of system determination choice for use, total sub-carrier number is K; The channel coefficients utilizing pilot frequency system to carry out channel estimating to obtain on each subcarrier k=1,2...K, wherein represent L ₁∈ { S, R} to L ₂∈ the channel coefficients of a kth subcarrier between R, D}, S represents source node, and R represents via node, and D represents destination node, sets total rated design desired value q;

Step 2: initialization iterations: n=0, first makes k=1,2...K, P ^[1]=P ^[2]=...=P ^[K]and C ({ P ^[k])=q, adopt dichotomy to try to achieve initial power to it and distribute (P ^[k]) ^*, k=1,2...K.Order ${\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}={\left(P^{\[k\]}\right)}^{*},$ K=1,2...K, and calculate $P_{\mathrm{\Σ}}^{\left(n\right)}=\underset{k=1}{\overset{K}{\Σ}}\[{\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}\],$ Wherein the system overall transmission power value of n-th iteration, with the transmitting power of the via node of system, source node first stage, a source node second stage kth subcarrier respectively; C ({ P ^[k]) represent the total rate function of system;

Step 3: place, carries out convex approaching to the total rate constraint of system in system total power minimization problem, obtains thus former problem is approximately following convex problem:

$\begin{array}{cc}\underset{\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}}{\min }& \underset{k=1}{\overset{K}{\Σ}}\left(P_R^{\[k\]}+P_{S,2}^{\[k\]}+P_{S,1}^{\[k\]}\right)\end{array}$

$\begin{array}{cc}s.t.& \tilde{C}\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)\≥q\end{array}$

$P_R^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0,k=1,2,...,K$

Wherein,

$\tilde{C}\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)\stackrel{\mathrm{\Δ}}{=}\frac{1}{2}\underset{k=1}{\overset{K}{\Σ}}{\log }_2\left(a^{\[k\]}{P}_{S,1}^{\[k\]}+b^{\[k\]}\sqrt{P_{S,1}^{\[k\]}{P}_R^{\[k\]}}+c^{\[k\]}\sqrt{P_{S,2}^{\[k\]}\left(1+P_{S,1}^{\[k\]}{d}^{\[k\]}\right)}+e^{\[k\]}{P}_R^{\[k\]}+f^{\[k\]}\right)$ $a^{\[k\]}={\mathrm{\γ}}_{SD}^{\[k\]}-\frac{x_0^2}{t_0^2}{\mathrm{\λ}}_{SR}^{\[k\]},b^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SR}^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}},c^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SD}^{\[k\]}},d^{\[k\]}={\mathrm{\γ}}_{SR}^{\[k\]},e^{\[k\]}=-\frac{x_0^2}{t_0^2}{\mathrm{\γ}}_{RD}^{\[k\]},f^{\[k\]}=1-\frac{x_0^2}{t_0^2}$ $x_0=\sqrt{{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}}+\sqrt{{\tilde{P}}_{S,2}^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}\left(1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}\right)},t_0=1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}+{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]},$ Node L ₁∈ { S, R} to L ₂∈ { the channel normalized gain of a kth subcarrier between R, D} l ₂∈ { the noise power on a kth subcarrier of R, D};

Step 4: the optimal solution utilizing Dual Method to solve to obtain above-mentioned convex Approximation Problem upgrade iterations: n=n+1, order ${\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_R^{\[k\]}\right)}^{(*)},{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{(*)},{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{(*)}$ K=1,2...K, and calculate $P_{\mathrm{\Σ}}^{\left(n\right)}=\underset{k=1}{\overset{K}{\Σ}}\[{\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}\];$

Step 5: judge whether set up, wherein ε ₁represent decision threshold, its value, between 0.001 ~ 0.000001, if set up, repeats step 3-5; Otherwise the solution that the problem of output is last ${\left(P_R^{\[k\]}\right)}^{*}={\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)},{\left(P_{S,1}^{\[k\]}\right)}^{*}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)},$ ${\left(P_{S,2}^{\[k\]}\right)}^{*}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)},$ k＝1,2...K；

Step 6: in multicarrier PLC relay system source node according to set the transmitting power of first and second each subcarriers of stage, relaying according to set the transmitting power of each subcarrier, thus realize the information transmission of PLC system transmitting-receiving two-end.

Further, the Dual Method in described step 4, specifically comprises the following steps:

Step 4.1: the system velocity constraint after pairing approximation is introduced Lagrange multiplier λ and obtained part Lagrangian:

And dual problem:

$\begin{array}{cc}\underset{\mathrm{\λ}\≥0}{\max }& d\left(\mathrm{\λ}\right)\end{array}$

D (λ) is dual function, is defined as:

$\begin{array}{cc}s.t.& P_R^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0,k=1,2...K\end{array}$

Wherein, P _∑represent systems radiate gross power;

Step 4.2: according to dichotomy thought, the lower bound λ of the bright multiplier of initialization glug _min=0 and upper bound λ _max=Λ, Λ represent and make d (λ) subgradient be the minimum real number of negative; Make the bright multiplier of glug

Step 4.3: then will the PROBLEM DECOMPOSITION of d (λ) be asked to be K subproblem, wherein a kth subproblem can be expressed as:

Here utilize block coordinate descent (BlockCoordinateDecent, the BCD) overall situation to solve optimal solution that these subproblems obtain K subproblem wherein, a ^[k], b ^[k], c ^[k], d ^[k], e ^[k], f ^[k]as defined in step 3.

Step 4.4: the subgradient calculating dual function if make λ _min=λ, if λ _max=λ;

Step 4.5: judge whether set up, wherein ε ₂represent decision threshold, its value is between 0.001 ~ 0.000001.If set up and then upgrade the bright multiplier of glug then step 4.3 ~ 4.4 are repeated; Otherwise export dual problem optimal solution, thus obtain the optimal solution of above-mentioned convex Approximation Problem

Further, the BCD method in described step 4.3, specifically comprises the following steps:

4.3.1 iterations m=0 is made, initialization for any arithmetic number, initialization points is substituted into the target function in step 4.3 obtain initial target functional value

4.3.2 first fixing according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution

4.3.4 secondly fixing according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution

4.3.3 then fix according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution and will substitute into the target function in step 4.3 obtain current target function value

4.3.5 iterations m=m+1 is upgraded, order ${\left(P_R^{\[k\]}\right)}^{\left(m\right)}={\left(P_R^{\[k\]}\right)}^{opt},{\left(P_{S,1}^{\[k\]}\right)}^{\left(m\right)}={\left(P_{S,1}^{\[k\]}\right)}^{opt},$ ${\left(P_{S,2}^{\[k\]}\right)}^{\left(m\right)}={\left(P_{S,2}^{\[k\]}\right)}^{opt},$ Judge whether set up, wherein ε ₃represent decision threshold, its value is between 0.001 ~ 0.000001.If set up, repeat step 4.3.2-4.3.5; Otherwise complete BCD method for solving, export the optimal solution of problem in step 4.3 ${\left({\tilde{P}}_R^{\left(k\right)}\right)}^{\left(bcd\right)}={\left(P_R^{\[k\]}\right)}^{\left(m\right)},{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(bcd\right)}={\left(P_{S,1}^{\[k\]}\right)}^{\left(m\right)},{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(bcd\right)}={\left(P_{S,2}^{\[k\]}\right)}^{\left(m\right)}.$

Beneficial effect of the present invention: the inventive method is first equal thus simplify design complexities to the transmitting power of destination node to via node and via node to destination node, source node by setting source node, and then the power distribution method of relay system is designed based on a kind of PLC of concavo-convex optimization method and Lagrange duality method design, the method can ensure system transfers power monotone decreasing always in an iterative process, thus realizes the object reducing PLC relay system gross power while the total rate requirement of the system that reaches.

Accompanying drawing explanation

Fig. 1 is the system model figure that the embodiment of the present invention adopts the method.

Fig. 2 is the particular flow sheet of the concavo-convex optimization method of the embodiment of the present invention.

Fig. 3 is the particular flow sheet of embodiment of the present invention Dual Method.

Fig. 4 is the particular flow sheet of embodiment of the present invention BCD method.

Fig. 5 is the graph of a relation of embodiment of the present invention system total power and average subcarrier speed.

Embodiment

In order to make object of the present invention and effect clearly, below multicarrier PLC relay system and the inventive method are described in detail.

The present invention considers three node PLC relay system models, and as shown in Figure 1, three nodes are respectively source node (S), via node (R) and destination node (D), wherein Φ _sP, Φ _rP, Φ _dPrepresent that three nodes divide the abcd matrix being clipped to P node respectively, P node represents the crosspoint of backbone network and via node place branch.So source node can be obtained to the channel transfer function of destination node, and use H to via node, via node respectively to destination node, source node _sD, H _sRand H _rDrepresent.Be different from general PLC relay system model, will adopt OFDM multi-carrier modulation technology in the present invention, therefore, system bandwidth is divided into K subcarrier, and wherein the decay of each subcarrier can regard as a channel coefficients.Then be defined as represent from node L ₁to node L ₂kth (k=1 ..., K) frequency response of individual subcarrier, and have L ₁∈ { S, R} and L ₂∈ { R, D}.Use simultaneously with represent respectively source node, via node kth (k=1 ..., K) transmitting power on individual subcarrier.In order to distinguish the through-put power of source node in first stage and second stage, we use symbol respectively with represent, namely have: the then transmitting power P of whole system _Σcan mathematical expression be expressed as:

$P_{\mathrm{\Σ}}=\underset{k=1}{\overset{K}{\Σ}}{P}_S^{\[k\]}+\underset{k=1}{\overset{K}{\Σ}}{P}_R^{\[k\]}=\underset{k=1}{\overset{K}{\Σ}}{P}_{S,1}^{\[k\]}+\underset{k=1}{\overset{K}{\Σ}}{P}_{S,2}^{\[k\]}+\underset{k=1}{\overset{K}{\Σ}}{P}_R^{\[k\]}---\left(1\right)$

According to OFDM modulation principle, by transmitting information coding being K, to obey average be 0, variance be 1 independent complex number type launch symbol X ^[k](k=1 ..., K).In order to complete the transmission of information from source to destination, the present invention adopts a kind of trunking method, and therefore whole transmission is divided into following two stages.

First stage: source node will launch symbol X by a kth subcarrier ^[k](k=1 ..., K) be transferred to via node and destination node, if transmitting power is so can be expressed as at the signal received of two nodes:

$Y_{R,1}^{\[k\]}=H_{SR}^{\[k\]}\sqrt{P_{S,1}^{\[k\]}}{X}^{\[k\]}+N_{R,1}^{\[k\]}---\left(2\right)$

$Y_{D,1}^{\[k\]}=H_{SD}^{\[k\]}\sqrt{P_{S,1}^{\[k\]}}{X}^{\[k\]}+N_{D,1}^{\[k\]}---\left(3\right)$

Wherein: with be illustrated respectively in node L ₂{ R, D} are at the n-th ∈ { Received signal strength in 1,2} stage and noise for ∈.

Second stage: transmitting symbol is sent to destination node by via node, meanwhile, another is launched symbol and is transmitted to destination node again, if the transmitting power of via node is by source node and the transmitting power of source node is now at destination node Received signal strength be so:

$Y_{D,2}^{\[k\]}=H_{RD}^{\[k\]}{g}^{\[k\]}\exp \left({\mathrm{j\θ}}^{\[k\]}\right)Y_{R,1}^{\[k\]}+H_{SD}^{\[k\]}\sqrt{P_{S,2}^{\[k\]}}{X}^{\[k\]}+N_{D,2}^{\[k\]}---\left(4\right)$

Wherein: $g^{\[k\]}=\sqrt{\frac{P_R^{\[k\]}}{P_{S,1}^{\[k\]}|H_{S,R}^{\[k\]}{|}^2+W_R^{\[k\]}}}$ With ${\mathrm{\θ}}^{\[k\]}=\∠H_{SD}^{\[k\]}-H_{SR}^{\[k\]}-H_{RD}^{\[k\]}$ Represent amplitude gain and phase gain respectively, represent noise ) power, ∠ a represents the phase angle of a plural a.

Therefore, according to (2)-(4) formula, destination node end is expressed as in a kth subcarrier, the signal to noise ratio in the n-th stage (SNR):

${\mathrm{SNR}}_{D,1}^{\[k\]}=P_{S,1}^{\[k\]}{\mathrm{\γ}}_{SD}^{\[k\]}---\left(5\right)$

${\mathrm{SNR}}_{D,2}^{\[k\]}=\frac{{\left(\sqrt{P_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}{P}_R^{\[k\]}{\mathrm{\γ}}_{RS}^{\[k\]}}+\sqrt{P_{S,2}^{\[k\]}{\mathrm{\γ}}_{SD}^{\[k\]}\left(1+P_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}\right)}\right)}^2}{1+P_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}+P_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}}---\left(6\right)$

Wherein: node L ₁∈ { S, R} to L ₂{ the channel normalized gain of R, D} is ∈

So, at known channel state information (Channelstateinformation, CSI) in situation, adopt maximum merging can obtain data link than (Maximumratiocombination, MRC) from S node to the total speed (unit: bit/sec/Hz) of the system of D node to be:

$C=\frac{1}{2}\underset{k=1}{\overset{K}{\Σ}}{\log }_2\left(1+{\mathrm{SNR}}_{D,1}^{\[k\]}+{\mathrm{SNR}}_{D,2}^{\[k\]}\right)---\left(7\right)$

Wherein coefficient because the PLC system related in the present invention is a half-duplex system.

For multicarrier PLC relay system, service quality decides primarily of the total speed of system, and therefore, a kind of power division optimization problem meeting service quality can be described as:

$\begin{array}{cc}\underset{\left\{P_R^{\[k\]},P_{S,1}^{\[k\]},P_{S,2}^{\[k\]}\right\}}{\min }& \underset{k=1}{\overset{K}{\Σ}}\left(P_R^{\[k\]}+P_{S,2}^{\[k\]}+P_{S,1}^{\[k\]}\right)\end{array}$

$\begin{array}{cc}s.t.& C\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)\≥q\end{array}---\left(8\right)$

$P_R^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,k=1,2,...,K$

Wherein: in problem (8), target function represents the transmitting power of whole system, q is expressed as the total rate target value of minimum system supported needed for whole system normal operation.

In the present invention, problem (8) is non-convex problem, is mathematically difficult to direct solution.Especially, first constraints in problem analysis (8), the i.e. total rate constraint of system, be difficult to directly find meet equation feasible solution for so complicated problem, the present invention devises a kind of power allocation scheme based on concavo-convex optimization method and Lagrange duality method, achieves the object of the gross power reducing PLC relay system while the total rate requirement of the system that reaches.The core concept of the method is: utilize concavo-convex optimization thought that the system power minimization problem of non-convex is approximately convex problem, and utilizes Lagrange duality method to solve approximate system power minimization problem iteratively to obtain last system emission power apportioning cost.According to the thought of the method, be specifically implemented as follows:

First, according to the first-order characteristics of convex function, namely Taylor series expansion we know:

$\begin{array}{cc}\frac{x^2}{t}\≥\frac{x_0^2}{t_0}+2\frac{x_0}{t_0}(x-x_0)-\frac{x_0^2}{t_0^2}(t-t_0)& \∀x,x_0,t_0\end{array}---\left(9\right)$

Therefore above formula can be utilized to transform the total rate constraints of system is approximate according to concavo-convex optimization (Concave-ConvexProcedure) thought, namely the total rate constraints of system is in feasible solution place approach for:

$\tilde{C}\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)\stackrel{\mathrm{\Δ}}{=}\frac{1}{2}\underset{k=1}{\overset{K}{\Σ}}{\log }_2\left(a^{\[k\]}{P}_{S,1}^{\[k\]}+b^{\[k\]}\sqrt{P_{S,1}^{\[k\]}{P}_R^{\[k\]}}+c^{\[k\]}\sqrt{P_{S,2}^{\[k\]}\left(1+P_{S,1}^{\[k\]}{d}^{\[k\]}\right)}+e^{\[k\]}{P}_R^{\[k\]}+f^{\[k\]}\right)---\left(10\right)$ Wherein: $a^{\[k\]}={\mathrm{\γ}}_{SD}^{\[k\]}-\frac{x_0^2}{t_0^2}{\mathrm{\λ}}_{SR}^{\[k\]},b^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SR}^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}},c^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SD}^{\[k\]}},d^{\[k\]}={\mathrm{\γ}}_{SR}^{\[k\]},e^{\[k\]}=-\frac{x_0^2}{t_0^2}{\mathrm{\γ}}_{RD}^{\[k\]},$ $\begin{array}{cc}{f}^{\[k\]}=1-\frac{x_0^2}{t_0^2}& x_0=\sqrt{{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}}+\sqrt{{\tilde{P}}_{S,2}^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}\left(1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}\right)},t_0=1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}+{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]},\end{array}$ Node L ₁∈ { S, R} to L ₂∈ { the channel normalized gain of a kth subcarrier between R, D} l ₂∈ { the noise power on R, a D} place kth subcarrier;

Therefore, problem (8) can be approximately following convex problem:

$\begin{array}{cc}\underset{\left\{P_R^{\[k\]},P_{S,1}^{\[k\]},P_{S,2}^{\[k\]}\right\}}{\min }& \underset{k=1}{\overset{K}{\Σ}}\left(P_R^{\[k\]}+P_{S,2}^{\[k\]}+P_{S,1}^{\[k\]}\right)\end{array}$

$\begin{array}{cc}s.t.& \tilde{C}\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)\≥q\end{array}---\left(11\right)$

$P_R^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,k=1,2,...,K$

In order to Solve problems (11), the present invention devises a kind of Dual Method.The method main thought is as follows:

First introduce Lagrange multiplier λ, obtain the part Lagrangian of problem (11):

Then its dual problem is:

$\begin{array}{cc}\underset{\mathrm{\λ}\≥0}{\max }& d\left(\mathrm{\λ}\right)\end{array}---\left(13\right)$

D (λ) is defined as:

$d\left(\mathrm{\λ}\right)\stackrel{\mathrm{\Δ}}{=}\min P_{\mathrm{\Σ}}-\mathrm{\λ}(\tilde{C}\left(\right\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\left\}\right)-q)$

$\begin{array}{cc}s.t.& P_R^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0\end{array}---\left(14\right)$

Problem (14) can be decomposed into K subproblem, and a kth subproblem can be expressed as:

$\underset{\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}}{\min }{P}_R^{\[k\]}+P_{S,2}^{\[k\]}+P_{S,1}^{\[k\]}-\mathrm{\λ}\left(\frac{1}{2}{\log }_2\left(\begin{array}{c}{a}^{\[k\]}{P}_{S,1}^{\[k\]}+b^{\[k\]}\sqrt{P_{S,1}^{\[k\]}{P}_R^{\[k\]}}+\\ c^{\[k\]}\sqrt{P_{S,2}^{\[k\]}\left(1+P_{S,1}^{\[k\]}{d}^{\[k\]}\right)}+e^{\[k\]}{P}_R^{\[k\]}+f^{\[k\]}\end{array}\right)-q^{\[k\]}\right)---\left(15\right)$

Wherein: problem (15) be about the convex optimization problem of three variablees, can utilize block coordinate descent (BlockCoordinateDecent.BCD) to obtain optimal solution

After given λ, once try to achieve the solution of problem (15) the subgradient that just can calculate d (λ) is:

$\stackrel{\·}{d}\left(\mathrm{\λ}\right)=q-\tilde{C}\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)---\left(16\right)$

According to the positive negativity of subgradient, dichotomy can be utilized to find optimum λ, i.e. the solution of dual problem (13), thus obtain the solution of former problem (11).Solve problems (11) can ensure that system total power diminishes gradually iteratively, until convergence, finally obtains power assignment value.Fig. 2-4 gives the flow chart of above-mentioned power distribution method.

According to flow chart 2-4, a kind of multicarrier PLC relay system power optimization method ensureing system velocity provided by the invention, comprises the following steps:

Step 1: the t easet ofasubcarriers of system determination choice for use, total sub-carrier number is K; The channel coefficients utilizing pilot frequency system to carry out channel estimating to obtain on each subcarrier k=1,2...K, wherein represent L ₁∈ { S, R} to L ₂∈ the channel coefficients of a kth subcarrier between R, D}, S represents source node, and R represents via node, and D represents destination node, sets total rated design desired value q;

Step 2: initialization iterations: n=0, first makes k=1,2...K, P ^[1]=P ^[2]=...=P ^[K]and C ({ P ^[k])=q, adopt dichotomy to try to achieve initial power to it and distribute (P ^[k]) ^*, k=1,2...K.Order ${\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}={\left(P^{\[k\]}\right)}^{*},$ K=1,2...K, and calculate $P_{\mathrm{\Σ}}^{\left(n\right)}=\underset{k=1}{\overset{K}{\Σ}}\[{\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}\],$ Wherein the system overall transmission power value of n-th iteration, with the transmitting power of the via node of system, source node first stage, a source node second stage kth subcarrier respectively; C ({ P ^[k]) represent the total rate function of system;

Step 3: place, carries out convex approaching to the total rate constraint of system in system total power minimization problem, obtains thus former problem is approximately following convex problem:

$\begin{array}{cc}\underset{\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}}{\min }& \underset{k=1}{\overset{K}{\Σ}}\left(P_R^{\[k\]}+P_{S,2}^{\[k\]}+P_{S,1}^{\[k\]}\right)\end{array}$

$\begin{array}{cc}s.t.& \tilde{C}\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)\≥q\end{array}$

$P_R^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0,k=1,2,...,K$

Wherein,

$\tilde{C}\left(\left\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\right\}\right)\stackrel{\mathrm{\Δ}}{=}\frac{1}{2}\underset{k=1}{\overset{K}{\Σ}}{\log }_2\left(a^{\[k\]}{P}_{S,1}^{\[k\]}+b^{\[k\]}\sqrt{P_{S,1}^{\[k\]}{P}_R^{\[k\]}}+c^{\[k\]}\sqrt{P_{S,2}^{\[k\]}\left(1+P_{S,1}^{\[k\]}{d}^{\[k\]}\right)}+e^{\[k\]}{P}_R^{\[k\]}+f^{\[k\]}\right)$ $a^{\[k\]}={\mathrm{\γ}}_{SD}^{\[k\]}-\frac{x_0^2}{t_0^2}{\mathrm{\γ}}_{SR}^{\[k\]},b^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SR}^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}},c^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SD}^{\[k\]}},d^{\[k\]}={\mathrm{\γ}}_{SR}^{\[k\]},e^{\[k\]}=-\frac{x_0^2}{t_0^2}{\mathrm{\γ}}_{RD}^{\[k\]},f^{\[k\]}=1-\frac{x_0^2}{t_0^2}$ $x_0=\sqrt{{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}}+\sqrt{{\tilde{P}}_{S,2}^{\[k\]}{\mathrm{\γ}}_{SD}^{\[k\]}(1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]})},t_0=1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}+{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]},$ Node L ₁∈ { S, R} to L ₂∈ { the channel normalized gain of a kth subcarrier between R, D} l ₂∈ { the noise power on a kth subcarrier of R, D};

Step 4: the optimal solution utilizing Dual Method to solve to obtain above-mentioned convex Approximation Problem upgrade iterations: n=n+1, order ${\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_R^{\[k\]}\right)}^{(*)},{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{(*)},{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{(*)}$ K=1,2...K, and calculate $P_{\mathrm{\Σ}}^{\left(n\right)}=\underset{k=1}{\overset{K}{\Σ}}\[{\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}\];$

Step 5: judge whether set up, wherein ε ₁represent decision threshold, its value, between 0.001 ~ 0.000001, if set up, repeats step 3-5; Otherwise the solution that the problem of output is last ${\left(P_R^{\[k\]}\right)}^{*}={\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)},{\left(P_{S,1}^{\[k\]}\right)}^{*}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)},$ ${\left(P_{S,2}^{\[k\]}\right)}^{*}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)},$ k＝1,2...K；

Step 6: in multicarrier PLC relay system source node according to set the transmitting power of first and second each subcarriers of stage, relaying according to set the transmitting power of each subcarrier, thus realize the information transmission of PLC system transmitting-receiving two-end.

Dual Method in step 4 recited above, specifically comprises the following steps:

Step 4.1: the system velocity constraint after pairing approximation is introduced Lagrange multiplier λ and obtained part Lagrangian:

And dual problem:

$\begin{array}{cc}\underset{\mathrm{\λ}\≥0}{\max }& d\left(\mathrm{\λ}\right)\end{array}$

D (λ) is dual function, is defined as:

$\begin{array}{cc}s.t.& P_R^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0,k=1,2...K\end{array}$

Wherein, P _∑represent systems radiate gross power;

Step 4.2: according to dichotomy thought, the lower bound λ of the bright multiplier of initialization glug _min=0 and upper bound λ _max=Λ, Λ represent and make d (λ) subgradient be the minimum real number of negative; Make the bright multiplier of glug

Step 4.3: then will the PROBLEM DECOMPOSITION of d (λ) be asked to be K subproblem, wherein a kth subproblem can be expressed as:

Here utilize block coordinate descent (BlockCoordinateDecent, the BCD) overall situation to solve optimal solution that these subproblems obtain K subproblem wherein, a ^[k], b ^[k], c ^[k], d ^[k], e ^[k], f ^[k]as defined in step 3.

Step 4.4: the subgradient calculating dual function if make λ _min=λ, if λ _max=λ;

Step 4.5: judge whether set up, wherein ε ₂represent decision threshold, its value is between 0.001 ~ 0.000001.If set up and then upgrade the bright multiplier of glug then step 4.3 ~ 4.4 are repeated; Otherwise export dual problem optimal solution, thus obtain the optimal solution of above-mentioned convex Approximation Problem

BCD method in step 4.3 recited above, specifically comprises the following steps:

4.3.1 iterations m=0 is made, initialization for any arithmetic number, initialization points is substituted into the target function in step 4.3 obtain initial target functional value

4.3.2 first fixing according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution

4.3.4 secondly fixing according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution

4.3.3 then fix according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution and will substitute into the target function in step 4.3 obtain current target function value

4.3.5 iterations m=m+1 is upgraded, order ${\left(P_R^{\[k\]}\right)}^{\left(m\right)}={\left(P_R^{\[k\]}\right)}^{opt},{\left(P_{S,1}^{\[k\]}\right)}^{\left(m\right)}={\left(P_{S,1}^{\[k\]}\right)}^{opt},$ ${\left(P_{S,2}^{\[k\]}\right)}^{\left(m\right)}={\left(P_{S,2}^{\[k\]}\right)}^{opt},$ Judge whether set up, wherein ε ₃represent decision threshold, its value is between 0.001 ~ 0.000001.If set up, repeat step 4.3.2-4.3.5; Otherwise complete BCD method for solving, export the optimal solution of problem in step 4.3 ${\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(bcd\right)}={\left(P_R^{\[k\]}\right)}^{\left(m\right)},{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(bcd\right)}={\left(P_{S,1}^{\[k\]}\right)}^{\left(m\right)},{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(bcd\right)}={\left(P_{S,2}^{\[k\]}\right)}^{\left(m\right)}$

Fig. 5 is that the present invention is by the simulating, verifying of Matlab to designed scheme.Parameter is specifically set to: bandwidth B is from 2MHz to 32MHz, and total number of sub-carriers K is that 32, q/K is taken as 0.5,1,1.5,2,2.5,3,3.5,4bit/Hz/subcarrier respectively.

Channel transfer functions is according to document [FranciscoJ.Canete, Jos é A.Cort é s, LuisD í ezandJos é T., " AChannelModelProposalforIndoorPowerLineCommunications " IEEECommunicationsMagazine, December2011] produce, noise model is according to document [DirkBenyoucef. " ANewStatisticalModeloftheNoisePowerDensitySpectrumforPow erlineCommunication, " IEEEISPLC26-28march2003pp.136-141] and in model (9) obtain, be specially:

$N_{ES}=N_0+N_1\·e^{-\frac{f}{f_1}}(dBm/Hz)$

Wherein: N _eSfor noise power spectral density, N ₀obedience average is-137.20dBm/Hz, and standard deviation is the normal distribution of 4.14dBm/Hz, N ₁obey between 30.83dBm/Hz and 70.96dBm/Hz and be uniformly distributed, f ₁obeying parameter is the exponential distribution of 0.84MHz, and f is sample point frequency.Data point in Fig. 5 is averaged by 1000 Monte Carlo simulation experiments to obtain.

Fig. 5 gives average subcarrier speed and system total power graph of a relation, wherein ordinate represents the total speed of system, unit is dBW, abscissa represents the speed of average each subcarrier, can be known by figure: along with average subcarrier rate constraint value constantly increases, system total power constantly increases, in addition, with on hypothesis subcarrier, source node and the same subcarrier of via node use the simple optimizing method of equal-wattage to compare, method of the present invention has less system total power, saves communications cost.

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 (3)

1. ensure a multicarrier PLC relay system power optimization method for system velocity, it is characterized in that, comprise the following steps:

Step 1: the t easet ofasubcarriers of system determination choice for use, total sub-carrier number is K; The channel coefficients utilizing pilot frequency system to carry out channel estimating to obtain on each subcarrier k=1,2 ... K, wherein represent L ₁∈ { S, R} to L ₂∈ the channel coefficients of a kth subcarrier between R, D}, S represents source node, and R represents via node, and D represents destination node, sets total rated design desired value q;

Step 2: initialization iterations: n=0, first makes k=1,2 ... K, P ^[1]=P ^[2]=...=P ^[K]and C ({ P ^[k])=q, adopt dichotomy to try to achieve initial power to it and distribute (P ^[k]) ^*, k=1,2 ... K.Order ${\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}={\left(P^{\[k\]}\right)}^{*},$ K=1,2 ... K, and calculate $P_{\mathrm{\Σ}}^{\left(n\right)}=\underset{k=1}{\overset{K}{\Σ}}\[{\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}\],$ Wherein the system overall transmission power value of n-th iteration, with the transmitting power of the via node of system, source node first stage, a source node second stage kth subcarrier respectively; C ({ P ^[k]) represent the total rate function of system;

Step 3: place, carries out convex approaching to the total rate constraint of system in system total power minimization problem, obtains thus former problem is approximately following convex problem:

$\begin{array}{cc}\underset{\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\}}{min}& \underset{k=1}{\overset{K}{\Σ}}(P_R^{\[k\]}+P_{S,2}^{\[k\]}+P_{S,1}^{\[k\]})\end{array}$

$\begin{array}{cc}s.t.& \tilde{C}\left(\right\{P_R^{\[k\]},P_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\left\}\right)\≥q\end{array}$

$P_R^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0,$ k＝1,2,...,K

Wherein,

$\tilde{C}\left(\right\{P_R^{\[k\]}{P}_{S,2}^{\[k\]},P_{S,1}^{\[k\]}\left\}\right)\stackrel{\mathrm{\Δ}}{=}\frac{1}{2}\underset{k=1}{\overset{k}{\mathrm{\Σ}}}{\log }_2\left(a^{\[k\]}{P}_{S,1}^{\[k\]}+b^{\[k\]}\sqrt{P_{S,1}^{\[k\]}{P}_R^{\[k\]}}+c^{\[k\]}\sqrt{P_{S,2}^{\[k\]}(1+P_{S,1}^{\[k\]}{d}^{\[k\]})}+e^{\[k\]}{P}_R^{\[k\]}+f^{\[k\]}\right)$ $a^{\[k\]}={\mathrm{\γ}}_{SD}^{\[k\]}-\frac{x_0^2}{t_0^2}{\mathrm{\γ}}_{SR}^{\[k\]},b^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SR}^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}},c^{\[k\]}=\frac{2x_0}{t_0}\sqrt{{\mathrm{\γ}}_{SD}^{\[k\]}},d^{\[k\]}={\mathrm{\γ}}_{SR}^{\[k\]},e^{\[k\]}=-\frac{x_0^2}{t_0^2}{\mathrm{\γ}}_{RD}^{\[k\]},f^{\[k\]}=1-\frac{x_0^2}{t_0^2}$ $x_0=\sqrt{{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]}}+\sqrt{{\tilde{P}}_{S,2}^{\[k\]}{\mathrm{\γ}}_{SD}^{\[k\]}(1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]})},t_0=1+{\tilde{P}}_{S,1}^{\[k\]}{\mathrm{\γ}}_{SR}^{\[k\]}+{\tilde{P}}_R^{\[k\]}{\mathrm{\γ}}_{RD}^{\[k\]},$ Node L ₁∈ { S, R} to L ₂∈ { the channel normalized gain of a kth subcarrier between R, D} l ₂∈ { the noise power on a kth subcarrier of R, D};

Step 4: the optimal solution utilizing Dual Method to solve to obtain above-mentioned convex Approximation Problem upgrade iterations: n=n+1, order ${\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_R^{\[k\]}\right)}^{(*)},{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{(*)},{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{(*)}$ K=1,2 ... K, and calculate $P_{\mathrm{\Σ}}^{\left(n\right)}=\underset{k=1}{\overset{K}{\Σ}}\[{\left({\tilde{P}}_R^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,1}^{\[k\]}\right)}^{\left(n\right)}+{\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)}\];$

Step 5: judge whether set up, wherein ε ₁represent decision threshold, its value, between 0.001 ~ 0.000001, if set up, repeats step 3-5; Otherwise the solution that the problem of output is last ${\left(P_{S,2}^{\[k\]}\right)}^{*}={\left({\tilde{P}}_{S,2}^{\[k\]}\right)}^{\left(n\right)},$ k＝1,2…K；

Step 6: in multicarrier PLC relay system source node according to set the transmitting power of first and second each subcarriers of stage, relaying according to set the transmitting power of each subcarrier, thus realize the information transmission of PLC system transmitting-receiving two-end.

2. a kind of multicarrier PLC relay system power optimization method ensureing system velocity according to claim 1, is characterized in that the Dual Method in described step 4 specifically comprises following sub-step:

Step 4.1: the system velocity constraint after pairing approximation is introduced Lagrange multiplier λ and obtained part Lagrangian:

And dual problem:

$\begin{array}{cc}\underset{\mathrm{\λ}\≥0}{max}& d\left(\mathrm{\λ}\right)\end{array}$

D (λ) is dual function, is defined as:

$\begin{array}{cc}s.t.& P_R^{\[k\]}\≥0,P_{S,2}^{\[k\]}\≥0,P_{S,1}^{\[k\]}\≥0\end{array},$ k＝1,2…K

Wherein, P _∑represent systems radiate gross power;

Step 4.2: according to dichotomy thought, the lower bound λ of the bright multiplier of initialization glug _min=0 and upper bound λ _max=Λ, Λ represent and make d (λ) subgradient be the minimum real number of negative; Make the bright multiplier of glug

Step 4.3: then will the PROBLEM DECOMPOSITION of d (λ) be asked to be K subproblem, wherein a kth subproblem can be expressed as:

Here utilize block coordinate descent (BlockCoordinateDecent, the BCD) overall situation to solve optimal solution that these subproblems obtain K subproblem wherein, a ^[k], b ^[k], c ^[k], d ^[k], e ^[k], f ^[k]as defined in step 3.

Step 4.4: the subgradient calculating dual function $\stackrel{\&CenterDot;}{d}\left(\mathrm{\&lambda;}\right)=q-\tilde{C}\left(\right\{P_R^{\&lsqb;k\&rsqb;},P_{S,2}^{\&lsqb;k\&rsqb;},P_{S,1}^{\&lsqb;k\&rsqb;}\left\}\right),$ If $\stackrel{\&CenterDot;}{d}\left(\mathrm{\&lambda;}\right)>0,$ Make λ _min=λ, if $\stackrel{\&CenterDot;}{d}\left(\mathrm{\&lambda;}\right)<0,$ λ _max＝λ；

Step 4.5: judge whether set up, wherein ε ₂represent decision threshold, its value is between 0.001 ~ 0.000001.If set up and then upgrade the bright multiplier of glug then step 4.3 ~ 4.4 are repeated; Otherwise export dual problem optimal solution, thus obtain the optimal solution of above-mentioned convex Approximation Problem

3. a kind of multicarrier PLC relay system power optimization method ensureing system velocity according to claim 2, it is characterized in that, the BCD method in described step 4.3, specifically comprises following sub-step:

4.3.1 iterations m=0 is made, initialization for any arithmetic number, initialization points is substituted into the target function in step 4.3 obtain initial target functional value

4.3.2 first fixing according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution

4.3.4 secondly fixing according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution

4.3.3 then fix according to First Order Optimality Condition solve following about optimization problem

Obtain optimal solution and will substitute into the target function in step 4.3 obtain current target function value

4.3.5 iterations m=m+1 is upgraded, order ${\left(P_R^{\&lsqb;k\&rsqb;}\right)}^{\left(m\right)}={\left(P_R^{\&lsqb;k\&rsqb;}\right)}^{opt},{\left(P_{S,1}^{\&lsqb;k\&rsqb;}\right)}^{\left(m\right)}={\left(P_{S,1}^{\&lsqb;k\&rsqb;}\right)}^{opt},$ judge whether set up, wherein ε ₃represent decision threshold, its value is between 0.001 ~ 0.000001.If set up, repeat step 4.3.2-4.3.5; Otherwise complete BCD method for solving, export the optimal solution of problem in step 4.3 ${\left({\tilde{P}}_R^{\&lsqb;k\&rsqb;}\right)}^{\left(bcd\right)}={\left(P_R^{\&lsqb;k\&rsqb;}\right)}^{\left(m\right)},{\left({\tilde{P}}_{S,1}^{\&lsqb;k\&rsqb;}\right)}^{\left(bcd\right)}={\left(P_{S,1}^{\&lsqb;k\&rsqb;}\right)}^{\left(m\right)},{\left({\tilde{P}}_{S,2}^{\&lsqb;k\&rsqb;}\right)}^{\left(bcd\right)}={\left(P_{S,2}^{\&lsqb;k\&rsqb;}\right)}^{\left(m\right)}.$