CN105792258A - Rate and reliability cooperative cross-layer optimization method in wireless sensor network - Google Patents

Abstract

The present invention discloses a rate and reliability cooperative cross-layer optimization method in a wireless sensor network. A non-convex wireless sensor network rate and reliability cooperative cross-layer optimization problem is converted to a protruding problem through adoption of variable substitution and a way to introduce intermediate variable, and a distributed optimization algorithm is designed through adoption of an even separation and subgradient method, so that the converted protruding problem is solved in a distribution way. The rate and reliability cooperative cross-layer optimization method in a wireless sensor network has two important performance indexes consisting of the rate and the reliability in the wireless sensor network and is convenient to convert the provided distributed optimization algorithm to the real enforcement protocol of the wireless sensor network.

Description

The cross-layer optimizing method that wireless sense network medium-rate and reliability are worked in coordination with

Technical field

The present invention relates to wireless communication transmission technique field, be specially in radio sensing network, the method for the speed transmitted by single path and the collaborative cross-layer optimizing of its reliability.

Background technology

Radio sensing network is as being a kind of novel integrated information collection, information processing and information transfer capability in the modernization intelligent network information system of one, it can real-time perception and gather various environmental datas accurately and target information, realize the communication between people and physical world and information is mutual, greatly improve human knowledge and the ability of transformation physical world.Just like a raging fire the carrying out of research of the domestic and international rationale to radio sensing network and key technology at present, and achieve certain achievement in research.Correlational study for the rate control problems in radio sensing network, data transmission credibility problem also achieves certain progress.Rate controlled (also referred to as flow control) is an important technology of resource fairness and effectively distribution in radio sensing network.

Ensure the reliability of data transmission, mainly carry out from two aspects: reduce data packetloss and the probability made mistakes；Once there is loss of data or makeing mistakes, then retransmission data.Increasing scientific research personnel has been put into improving among the research of data transmission credibility.

In recent years, in radio sensing network, the raising of message transmission rate will necessarily reduce the reliability of data transmission, but therefore message transmission rate and data transmission credibility are two basic conflicting optimization aim, there is an inherent tradeoff between the two.So this compromise optimization problem must be studied by we.

Summary of the invention

Present invention aims to the deficiencies in the prior art, it is provided that the cross-layer optimizing method that a kind of radio sensing network medium-rate and reliability are worked in coordination with, the method not only optimizes the speed of data transmission but also makes reliability be guaranteed.

It is an object of the invention to be achieved through the following technical solutions: a kind of radio sensing network medium-rate and the collaborative cross-layer optimizing method of reliability, comprise the following steps:

(1) the cross-layer optimizing problem P that wireless sense network speed and reliability are collaborative is set up₁:

$\underset{r_{l,f},x_f,p_l}{max}{\mathrm{\ω}}_1\underset{f\∈F}{\Σ}{U}_f\left(x_f\right)-(1-{\mathrm{\ω}}_1)\underset{f\∈F}{\Σ}\underset{l\∈L\left(f\right)}{\Σ}{\mathrm{\ω}}_{f}E\left(r_{l,f}\right)$

$\begin{array}{cc}s.t.& \underset{f\∈F\left(l\right)}{\Σ}\frac{x_f}{r_{l,f}}\≤B\log (1+\frac{1}{{\mathrm{\σ}}_l}{p}_l),\∀l\∈L\end{array}$

$x_f^{\min }\≤x_f\≤x_f^{\max },\∀f\∈F$

$\underset{l\∈L_{out}\left(n\right)}{\Σ}{p}_l\≤p_n,\∀n\∈N$

$0\≤r_{l,f}\≤1,\∀l,f\∈F\left(l\right)$

Wherein, x_fRepresent the transfer rate of session stream, U_f(x_f) represent speed utility function, r_l,fRepresenting code check, B represents the bandwidth of link l, σ_lRepresent noise jamming, p_lRepresent the power consumed on link l, p_nRepresent and be transmitted the power that during data, node n consumes, E (r_l,f) represent that session f uses the error probability of link l, it is defined as one about code check r_l,fFunction, in order to weigh transfer rate and the error probability of session stream f, set weighted value w₁, w₁Any one value between desirable [0,1]；In order to keep front and back order-of-magnitude agreement, add w_f。

(2) by the problem P of non-convex₁It is converted into convex problem P₂:

$\underset{x_f^{\′},r_{l,f},p_l}{\max }{\mathrm{\ω}}_1\underset{f\∈F}{\Σ}{U}_f\left(e^{x_f^{\′}}\right)-(1-{\mathrm{\ω}}_1)\underset{f\∈F}{\Σ}\underset{l\∈L\left(f\right)}{\Σ}{\mathrm{\ω}}_{f}E\left(r_{l,f}\right)$

$\begin{array}{cc}s.t.& x_f^{\′\min }\≤x_f^{\′}\≤x_f^{\′max},\∀f\∈F\end{array}$

$x_f^{\′}-log{r}_{l,f}\≤log{c}_{l,f},\∀l\∈L,f\∈F\left(l\right)$

$0\≤r_{l,f}\≤1,\∀l,f\∈F\left(l\right)$

$\underset{f\∈F\left(l\right)}{\Σ}{c}_{l,f}\≤log(1+\frac{1}{{\mathrm{\σ}}_l}{p}_l),\∀l\∈L$

$\underset{l\∈L_{out}\left(n\right)}{\Σ}{p}_l\≤p_n,\∀n\∈N$

Wherein x '_f=log (x_f),c_l,fRepresent the intermediate variable of f session on l link；

(3) adopt Duality Decomposition method and subgradient method to problem P₂Carry out distributed solving.Problem P₂Dual problem P₃For:

maxD(β)

s.t.β≥0

Wherein, β is the antithesis factor.Use Subgradient Algorithm is solved this problem.

Dual problem P₃Object function as follows:

$D\left(\mathrm{\β}\right)=\underset{x,r,c,p\∈\mathrm{\Γ}}{max}L(x,r,c,p,\mathrm{\β})$

$\mathrm{\Γ}=\left\{\begin{array}{c}\underset{f\∈F\left(l\right)}{\Σ}{c}_{l,f}\≤log(1+\frac{1}{{\mathrm{\σ}}_l}{p}_l),\∀l\∈L\\ \underset{l\∈L_{out\left(n\right)}}{\Σ}{p}_l\≤p_n,\∀n\∈N\\ x_f^{\′\min }\≤x_f^{\′}\≤x_f^{\′\max },\∀f\∈F\\ 0\≤r_{l,f}\≤1,\∀l\∈L,f\∈F\left(l\right)\end{array}\right\}$

Therefore, problem P₂Lagrangian as follows:

$\begin{array}{c}L(x,r,c,p,\mathrm{\β})={\mathrm{\ω}}_1\underset{f\∈F}{\Σ}{U}_f\left(e^{x_f^{\′}}\right)-(1-{\mathrm{\ω}}_1)\underset{f\∈F}{\Σ}\underset{l\∈L\left(f\right)}{\Σ}{\mathrm{\ω}}_{f}E\left(r_{l,f}\right)\\ +\underset{l\∈L}{\Σ}\underset{f\∈F\left(l\right)}{\Σ}{\mathrm{\β}}_{l,f}(\log r_{l,f}+\log c_{l,f}-x_f^{\′})\end{array}$

(4) D (β) is decomposed into the three class subproblems that can distributed solve:

Subproblem one:

$\begin{array}{cc}\underset{x_f^{\′}}{\max }& \underset{f\∈F}{\Σ}\{{\mathrm{\ω}}_1{U}_f\left(e^{x_f^{\′}}\right)-\underset{l\∈L\left(f\right)}{\Σ}{\mathrm{\β}}_{l,f}{x}_f^{\′}\}\end{array}$

$\begin{array}{cc}s.t.& x_f^{\′min}\≤x_f^{\′}\≤x_f^{\′max},\∀f\∈F\end{array}$

Subproblem two:

$\begin{array}{c}\underset{r_{l,f}}{\max }-(1-{\mathrm{\ω}}_1)\underset{f\∈F}{\Σ}\underset{l\∈L\left(f\right)}{\Σ}{\mathrm{\ω}}_{f}E\left(r_{l,f}\right)+\underset{l\∈L}{\Σ}\underset{f\∈F\left(l\right)}{\Σ}{\mathrm{\β}}_{l,f}\log r_{l,f}\\ \⇔\underset{r_{l,f}}{\max }\underset{l\∈L}{\Σ}\underset{f\∈F\left(l\right)}{\Σ}\{{\mathrm{\β}}_{l,f}\log r_{l,f}-(1-{\mathrm{\ω}}_1){\mathrm{\ω}}_{f}E\left(r_{l,f}\right)\}\end{array}$

$\begin{array}{cc}s.t.& 0\≤r_{l,f}\≤1,\∀l\∈L,f\∈F\left(l\right)\end{array}$

Subproblem three:

$\begin{array}{c}\underset{c_{l,f,}{p}_l}{\max }\underset{l\∈L}{\Σ}\underset{f\∈F\left(l\right)}{\Σ}\left({\mathrm{\β}}_{l,f}\log c_{l,f}\right)\\ \⇔\underset{c_{l,f},p_l}{\max }\underset{n\∈N}{\Σ}\underset{l\∈L_{out}\left(n\right)}{\Σ}\underset{f\∈F\left(l\right)}{\Σ}{\mathrm{\β}}_{l,f}\log c_{l,f}\end{array}$

$\begin{array}{cc}s.t.& \underset{f\∈F\left(l\right)}{\Σ}{c}_{l,f}\≤B\log (1+\frac{1}{{\mathrm{\σ}}_l}{p}_n),\∀l\∈L\end{array}$

$\underset{l\∈L_{out}\left(n\right)}{\Σ}{p}_l\≤p_n,\∀n\∈N$

Wherein, β_l,fIt it is the antithesis factor.

(5) use distributed method by P₃Carry out distributed solving, specifically include following sub-step:

(5.1) β is initialized_l,f(0), iterations t=1；By β_l,f(0) bring in three antithesis subproblems, obtain c_l,f(0)、p_l(0)、r_l,fAnd x ' (0)_f(0)；

(5.2) Subgradient Algorithm is used to solve P₃, the β of the t time iteration is namely obtained by following formula_l,fI.e. β_l,f(t):

β_l,f(t+1)=[β_l,f(t)-k_β(t)(logc_l,f(t)+logr_l,f(t)-x′_f(t))]⁺

Wherein k_βWhat t () represented is step-length, [z]⁺=max{0, z}；(5.3) the speed x ' of more new session f on session stream_f, maximize:

${\mathrm{\ω}}_1{U}_f\left(e^{x_f^{\′}}\right)-\underset{l\∈L\left(f\right)}{\Σ}{\mathrm{\β}}_{l,f}{x}_f^{\′}$

And x '_f?Within scope, whereinFor the utility function of speed, what L (f) represented is the session f link set flowing through link, sets a weighted value w₁；

(5.4) the session updates code check r on link and link_l,f, maximize:

β_l,flogr_l,f-(1-ω₁)ω_fE(r_l,f)

And r_l,fWithin the scope of [0,1], wherein E (r_l,f) it is the function of error probability, in order to keep front and back order-of-magnitude agreement, thus adding a w_f；

(5.5) on node, intermediate variable c is updated_l,fWith power p_l, maximize:

$\underset{l\∈L_{out}\left(n\right)}{\Σ}\underset{f\∈F\left(l\right)}{\Σ}{\mathrm{\β}}_{l,f}log{c}_{l,f}$

And c_l,fUnder retraining at two, it is respectively as follows:

$\underset{f\∈F\left(l\right)}{\Σ}{c}_{l,f}\≤Blog(1+\frac{1}{{\mathrm{\σ}}_l}{p}_n),\∀l\∈L$

$\underset{l\∈L_{out}\left(n\right)}{\Σ}{p}_l\≤p_n,\∀n\∈N$

(5.6) repeat step (5.1) to step (5.5), until object function convergence, obtain the optimal code rates r of radio sensing network^*, session speed x^*And the power p consumed on link l^*, thus realizing the collaborative cross-layer optimizing of radio sensing network speed and reliability.

The invention has the beneficial effects as follows: the cross-layer optimizing problem that wireless sense network speed and the reliability of a non-convex are worked in coordination with is changed into a convex problem by utilizing the method for variable replacement and introducing intermediate variable by the present invention, then recycling Duality Decomposition and subgradient method, devise distributed optimization algorithm, the convex problem that can distributed solve after changing into.The method has taken into account wireless sense network medium-rate and reliability the two important performance indexes, it is proposed to distributed optimization algorithm be easy to change into the agreement of the actual enforcement of wireless sense network.

Accompanying drawing explanation

Fig. 1 network topological diagram；

Fig. 2 algorithmic statement figure.

Detailed description of the invention

In order to allow the above and other purpose of the present invention, feature and advantage become apparent from, will be described in further detail below.

Assume that network topology is G{N, L} radio sensing network, whereinRepresent the set of nodes,What represent is the set of the link in network,What represent is the set of session stream, and F (l) represents the set of the session stream on link l, and what L (f) represented is the session f link set flowing through link, L_outWhat n () represented is the set of n node outgoing link.

Assuming that all nodes have the energy of abundance, what this network adopted is single path transmission data, it is assumed that the transfer rate of each session stream is x_f, its utility function is U_f(x_f), the boundary of the transfer rate of session stream isWhen data arrive the encoder on link, first it decoded by encoder, extracts useful information therein, then with its code check r_l,fInformation is encoded, code check define justice 0≤r_l,f≤ 1, code check r in addition_l,fIt is defined as: the ratio sending data rate of the information data rate of input coding device and output coder.The speed of session f is

The packet from other node can also be forwarded as relay router owing to the node in network both can send packet as source node, this just requires that the cumulative speed of data stream that node transmits on wireless link l not can exceed that the maximum link capacity of wireless link, usesRepresent maximum link capacity, then have:

$\underset{f\∈F\left(l\right)}{\Σ}{\mathrm{\φ}}_{l,f}=\underset{f\∈F\left(l\right)}{\Σ}\frac{x_f}{r_{l,f}}\≤Blog(1+\frac{1}{{\mathrm{\σ}}_l}{p}_l)$

Wherein B is the bandwidth of link l, σ_lWhat represent is noise jamming, p_lRepresent the power consumed on link l,

$\underset{l\∈L_{out}\left(n\right)}{\Σ}{p}_l\≤p_n$

p_nRepresent and be transmitted the power that during data, node n consumes.

Session f uses link l error probability to be defined as one about code check r_l,fFunction, be represented by E (r_l,f), assume in the present invention this function be one about r_l,fIncreasing function, and this function is convex function.

The error probability ξ of node end-to-end is represented by:

$\mathrm{\ξ}=1-\underset{f\∈F}{\Π}\underset{l\∈L\left(f\right)}{\Π}(1-E(r_{l,f}\left)\right)$

Generally, the error probability of each of the links is very little (i.e. ξ < < 1), thus end to end error probability can be similar to be:

$\mathrm{\&xi;}=\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}E\left(r_{l,f}\right)$

In order to obtain a balance between transfer rate and the error probability of session stream f, set a weighted value w₁, w₁Any one value between desirable [0,1]；In order to keep front and back order-of-magnitude agreement, thus adding a w_f。

In sum, maximization problems P₁Can be expressed as follows:

$\underset{r_{l,f},x_f,p_l}{max}{\mathrm{\&omega;}}_1\underset{f\&Element;F}{\&Sigma;}{U}_f\left(x_f\right)-(1-{\mathrm{\&omega;}}_1)\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)$

$\begin{array}{cc}s.t.& \underset{f\&Element;F\left(l\right)}{\&Sigma;}\frac{x_f}{r_{l,f}}\&le;B\log (1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L\end{array}$

$x_f^{\min }\&le;x_f\&le;x_f^{\max },\&ForAll;f\&Element;F$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

$0\&le;r_{l,f}\&le;1,\&ForAll;l,f\&Element;F\left(l\right)$

In the problems referred to above model, the utility function U of session flow velocity rate_f(x_f) it is concave function, and E (r_l,f) it is convex function

By above-mentioned model, in order to solve the problems referred to above by distributed method, first have to ensure that this problem is a separable convex problem.Ensure that object function is concave function now, but due in restrictive condition:

$\underset{f\&Element;F\left(l\right)}{\&Sigma;}\frac{x_f}{r_{l,f}}\&le;Blog(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L$

The existence of constraint so that the feasible set of this problem is it cannot be guaranteed that be convex set, therefore, also cannot ensure that this problem is a separable convex problem.In this part, we by a series of conversion, will will above show that problem model is converted into a separable convex problem.

Will constraint

$\underset{f\&Element;F\left(l\right)}{\&Sigma;}\frac{x_f}{r_{l,f}}\&le;Blog(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L$

Carry out the conversion being correlated with, order

$\frac{x_f}{r_{l,f}}\&le;c_{l,f}$

Thus by above-mentioned P₁Problem is converted into following problem P₂:

$\underset{x_f^{\&prime;},r_{l,f},p_l}{\max }{\mathrm{\&omega;}}_1\underset{f\&Element;F}{\&Sigma;}{U}_f\left(e^{x_f^{\&prime;}}\right)-(1-{\mathrm{\&omega;}}_1)\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)$

$\begin{array}{cc}s.t.& x_f^{\&prime;\min }\&le;x_f^{\&prime;}\&le;x_f^{\&prime;max},\&ForAll;f\&Element;F\end{array}$

$x_f^{\&prime;}-log{r}_{l,f}\&le;log{c}_{l,f},\&ForAll;l\&Element;L,f\&Element;F\left(l\right)$

$0\&le;r_{l,f}\&le;1,\&ForAll;l,f\&Element;F\left(l\right)$

$\underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;log(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

Wherein x '_f=log (x_f),

Adopt Duality Decomposition method and subgradient method to problem P₂Carry out distributed solving.Problem P₂Dual problem P₃For:

maxD(β)

s.t.β≥0

Wherein, β is the antithesis factor.Use Subgradient Algorithm is solved this problem.

The object function of dual problem is as follows:

$D\left(\mathrm{\&beta;}\right)=\underset{x,r,c,p\&Element;\mathrm{\&Gamma;}}{max}L(x,r,c,p,\mathrm{\&beta;})$

$\mathrm{\&Gamma;}=\left\{\begin{array}{c}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;log(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L\\ \underset{l\&Element;L_{out\left(n\right)}}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N\\ x_f^{\&prime;\min }\&le;x_f^{\&prime;}\&le;x_f^{\&prime;\max },\&ForAll;f\&Element;F\\ 0\&le;r_{l,f}\&le;1,\&ForAll;l\&Element;L,f\&Element;F\left(l\right)\end{array}\right\}$

Therefore, problem P₂Lagrangian as follows:

$\begin{array}{c}L(x,r,c,p,\mathrm{\&beta;})={\mathrm{\&omega;}}_1\underset{f\&Element;F}{\&Sigma;}{U}_f\left(e^{x_f^{\&prime;}}\right)-(1-{\mathrm{\&omega;}}_1)\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)\\ +\underset{l\&Element;L}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}(\log r_{l,f}+\log c_{l,f}-x_f^{\&prime;})\end{array}$

D (β) is decomposed into the three class subproblems that can distributed solve:

Subproblem one:

$\begin{array}{cc}\underset{x_f^{\&prime;}}{\max }& \underset{f\&Element;F}{\&Sigma;}\{{\mathrm{\&omega;}}_1{U}_f\left(e^{x_f^{\&prime;}}\right)-\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}{x}_f^{\&prime;}\}\end{array}$

$\begin{array}{cc}s.t.& x_f^{\&prime;min}\&le;x_f^{\&prime;}\&le;x_f^{\&prime;max},\&ForAll;f\&Element;F\end{array}$

Subproblem two:

$\begin{array}{c}\underset{r_{l,f}}{\max }-(1-{\mathrm{\&omega;}}_1)\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)+\underset{l\&Element;L}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}\log r_{l,f}\\ \&DoubleLeftRightArrow;\underset{r_{l,f}}{\max }\underset{l\&Element;L}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}\{{\mathrm{\&beta;}}_{l,f}\log r_{l,f}-(1-{\mathrm{\&omega;}}_1){\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)\}\end{array}$

$\begin{array}{cc}s.t.& 0\&le;r_{l,f}\&le;1,\&ForAll;l\&Element;L,f\&Element;F\left(l\right)\end{array}$

Subproblem three:

$\begin{array}{c}\underset{c_{l,f,}{p}_l}{\max }\underset{l\&Element;L}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}\left({\mathrm{\&beta;}}_{l,f}\log c_{l,f}\right)\\ \&DoubleLeftRightArrow;\underset{c_{l,f},p_l}{\max }\underset{n\&Element;N}{\&Sigma;}\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}\log c_{l,f}\end{array}$

$\begin{array}{cc}s.t.& \underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;B\log (1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_n),\&ForAll;l\&Element;L\end{array}$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

Wherein, β_l,fIt it is the antithesis factor.

Use distributed method by P₃Carry out distributed solving, specifically include following sub-step:

Step 1: initialize β_l,f(0), iterations t=1；By β_l,f(0) bring in three antithesis subproblems, obtain c_l,f(0)、p_l(0)、r_l,fAnd x ' (0)_f(0)；

Step 2: use Subgradient Algorithm to solve P₃, the β of the t time iteration is namely obtained by following formula_l,fI.e. β_l,f(t):

β_l,f(t+1)=[β_l,f(t)-k_β(t)(logc_l,f(t)+logr_l,f(t)-x′_f(t))]⁺

Wherein k_βWhat t () represented is step-length, [z]⁺=max{0, z}；

Step 3: the speed x ' of more new session f on session stream_f, maximize:

${\mathrm{\&omega;}}_1{U}_f\left(e^{x_f^{\&prime;}}\right)-\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}{x}_f^{\&prime;}$

And x '_f?Within scope, whereinFor the utility function of speed, what L (f) represented is the session f link set flowing through link, sets a weighted value w₁；

Step 4: the session updates code check r on link and link_l,f, maximize:

β_l,flogr_l,f-(1-ω₁)ω_fE(r_l,f)

And r_l,fWithin the scope of [0,1], wherein E (r_l,f) it is the function of error probability, in order to keep front and back order-of-magnitude agreement, thus adding a w_f；

Step 5: update intermediate variable c on node_l,fWith power p_l, maximize:

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}log{c}_{l,f}$

And c_l,fUnder retraining at two, it is respectively as follows:

$\underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;Blog(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_n),\&ForAll;l\&Element;L$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

Step 6: repeat step 1 to step 6, until object function convergence, obtains the optimal code rates r of radio sensing network^*, session speed x^*And the power p consumed on link l^*, thus realizing the collaborative cross-layer optimizing of radio sensing network speed and reliability.

This part is by the convergence of the distributed algorithm proposed by the invention by matlab simulating, verifying.First, adopt centralized algorithm to be solved radio sensing network medium-rate and the collaborative cross-layer optimizing problem of reliability by matlab emulation, obtain globally optimal solution.Then the distributed algorithm that the present invention proposes is adopted, then pass through emulation and solve this problem, and the globally optimal solution that the final result obtained and centralized algorithm obtain compares, thus verifying that can the distributed algorithm based on subgradient Duality Decomposition obtain globally optimal solution.Here only show the convergence result of sensor node total utility.

The function of utility function and error probability can adopt following form:

$U_f\left(e^{x_f^{\&prime;}}\right)=\frac{e^{x_f^{\&prime;(1-\mathrm{\&alpha;})}}-e^{x_f^{\&prime;\min (1-\mathrm{\&alpha;})}}}{e^{x_f^{\&prime;\max (1-\mathrm{\&alpha;})}}-e^{x_f^{\&prime;\min (1-\mathrm{\&alpha;})}}}$

$E\left(r_{l,f}\right)=\frac{1}{2}{e}^{-k(1-r_{l,f})}$

Partial simulation parameter is provided that

w₁=0.5, w_f=0.1, p_n=7 (dBm), β_l,f=0.01, σ_l=-50 (dBm),

α=1.1, k=10, we are provided with iterations t=600 simultaneously.Observe being continuously increased along with iterations by experiment, the change of total utility.

As in figure 2 it is shown, abscissa represents iterations, vertical coordinate represents total utility.Black dotted lines is the centralized value solving out, and black curve is the distributed value solving out, and along with being continuously increased of iterations, total effectiveness is increasing, and finally converges on a stationary value.

Claims (1)

1. the cross-layer optimizing method that a radio sensing network medium-rate and reliability are worked in coordination with, it is characterised in that comprise the following steps:

(1) the cross-layer optimizing problem P that wireless sense network speed and reliability are collaborative is set up₁:

$\begin{array}{cc}\underset{r_{l,f},x_f,p_l}{\max }& {\mathrm{\&omega;}}_1\underset{f\&Element;F}{\&Sigma;}{U}_f\left(x_f\right)-(1-{\mathrm{\&omega;}}_1)\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)\end{array}$

$\begin{array}{cc}s.t.& \underset{f\&Element;F\left(l\right)}{\&Sigma;}\frac{x_f}{r_{l,f}}\&le;B\log (1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L\end{array}$

$x_f^{\min }\&le;x_f\&le;x_f^{\max },\&ForAll;f\&Element;F$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

$0\&le;r_{l,f}\&le;1,\&ForAll;l,f\&Element;F\left(l\right)$

Wherein, x_fRepresent the transfer rate of session stream, U_f(x_f) represent speed utility function, r_l,fRepresenting code check, B represents the bandwidth of link l, σ_lRepresent noise jamming, p_lRepresent the power consumed on link l, p_nRepresent and be transmitted the power that during data, node n consumes, E (r_l,f) represent that session f uses the error probability of link l, it is defined as one about code check r_l,fFunction, in order to weigh transfer rate and the error probability of session stream f, set weighted value w₁, w₁Any one value between desirable [0,1]；In order to keep front and back order-of-magnitude agreement, add w_f。

(2) by the problem P of non-convex₁It is converted into convex problem P₂:

$\begin{array}{cc}\underset{x_f^{\&prime;},r_{l,f},p_l}{\max }& {\mathrm{\&omega;}}_1\underset{f\&Element;F}{\&Sigma;}{U}_f\left(e^{x_f^{\&prime;}}\right)-\left(1-{\mathrm{\&omega;}}_1\right)\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)\end{array}$

$\begin{array}{cc}s.t.& x_f^{\&prime;\min }\&le;x_f^{\&prime;}\&le;x_f^{\&prime;\max },\&ForAll;f\&Element;F\end{array}$

$x_f^{\&prime;}-{\mathrm{logr}}_{l,f}\&le;{\mathrm{logc}}_{l,f},\&ForAll;l\&Element;L,f\&Element;F\left(l\right)$

$0\&le;r_{l,f}\&le;1,\&ForAll;l,f\&Element;F\left(l\right)$

$\underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;\log (1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

Wherein x '_f=log (x_f),c_l,fRepresent the intermediate variable of f session on l link；

(3) adopt Duality Decomposition method and subgradient method to problem P₂Carry out distributed solving.Problem P₂Dual problem P₃For:

maxD(β)

s.t.β≥0

Wherein, β is the antithesis factor.Subgradient Algorithm is used to solve this problem.

Dual problem P₃Object function as follows:

$D\left(\mathrm{\&beta;}\right)=\underset{x,r,c,p\&Element;\mathrm{\&Gamma;}}{max}L(x,r,c,p,\mathrm{\&beta;})$

$\mathrm{\&Gamma;}=\left\{\begin{array}{c}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;log(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_l),\&ForAll;l\&Element;L\\ \underset{l\&Element;L_{out\left(n\right)}}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N\\ x_f^{\&prime;\min }\&le;x_f^{\&prime;}\&le;x_f^{\&prime;\max },\&ForAll;f\&Element;F\\ 0\&le;r_{l,f}\&le;1,\&ForAll;l\&Element;L,f\&Element;F\left(l\right)\end{array}\right\}$

Therefore, problem P₂Lagrangian as follows:

$\begin{array}{c}L\left(x,r,c,p,\mathrm{\&beta;}\right)={\mathrm{\&omega;}}_1\underset{f\&Element;F}{\&Sigma;}{U}_f\left(e^{x_f^{\&prime;}}\right)-\left(1-{\mathrm{\&omega;}}_1\right)\underset{f\&Element;F}{\&Sigma;}\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)\\ +\underset{l\&Element;L}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}\left({\mathrm{logr}}_{l,f}+{\mathrm{logc}}_{l,f}-x_f^{\&prime;}\right)\end{array}$

(4) D (β) is decomposed into the three class subproblems that can distributed solve:

Subproblem one:

$\begin{array}{cc}\underset{x_f^{\&prime;}}{\max }& \underset{f\&Element;F}{\&Sigma;}\{{\mathrm{\&omega;}}_1{U}_f\left(e^{x_f^{\&prime;}}\right)-\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}{x}_f^{\&prime;}\}\end{array}$

$\begin{array}{cc}s.t.& x_f^{\&prime;min}\&le;x_f^{\&prime;}\&le;x_f^{\&prime;max},\&ForAll;f\&Element;F\end{array}$

Subproblem two:

$\begin{array}{c}\underset{r_{l,f}}{\max }-(1-{\mathrm{\&omega;}}_1)\underset{f\&Element;F}{\mathrm{\&Sigma;}}\underset{l\&Element;L\left(f\right)}{\mathrm{\&Sigma;}}{\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)+\underset{l\&Element;L}{\mathrm{\&Sigma;}}\underset{f\&Element;F\left(l\right)}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_{l,f}\log r_{l,f}\\ \&DoubleLeftRightArrow;\underset{r_{l,f}}{\max }\underset{l\&Element;L}{\mathrm{\&Sigma;}}\underset{f\&Element;F\left(l\right)}{\mathrm{\&Sigma;}}\{{\mathrm{\&beta;}}_{l,f}\log r_{l,f}-(1-{\mathrm{\&omega;}}_1){\mathrm{\&omega;}}_{f}E\left(r_{l,f}\right)\}\end{array}$

$\begin{array}{cc}s.t.& 0\&le;r_{l,f}\&le;1,\&ForAll;l\&Element;L,f\&Element;F\left(l\right)\end{array}$

Subproblem three:

$\begin{array}{c}\underset{c_{l,f},p_l}{\max }\underset{l\&Element;L}{\mathrm{\&Sigma;}}\underset{f\&Element;F\left(l\right)}{\mathrm{\&Sigma;}}\left({\mathrm{\&beta;}}_{l,f}\log c_{l,f}\right)\\ \&DoubleLeftRightArrow;\underset{c_{l,f},p_l}{\max }\underset{n\&Element;N}{\mathrm{\&Sigma;}}\underset{l\&Element;L_{\mathrm{out}}\left(n\right)}{\mathrm{\&Sigma;}}\underset{f\&Element;F\left(l\right)}{\mathrm{\&Sigma;}}{\mathrm{\&beta;}}_{l,f}\log c_{l,f}\end{array}$

$\begin{array}{cc}s.t.& \underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;Blog(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_n),\&ForAll;l\&Element;L\end{array}$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

Wherein, β_l,fIt it is the antithesis factor.

(5) use distributed method by P₃Carry out distributed solving, specifically include following sub-step:

(5.1) β is initialized_l,f(0), iterations t=1；By β_l,f(0) bring in three antithesis subproblems, obtain c_l,f(0)、p_l(0)、r_l,fAnd x ' (0)_f(0)；

(5.2) Subgradient Algorithm is used to solve P₃, the β of the t time iteration is namely obtained by following formula_l,fI.e. β_l,f(t):

β_l,f(t+1)=[β_l,f(t)-k_β(t)(logc_l,f(t)+logr_l,f(t)-x′_f(t))]⁺

Wherein k_βWhat t () represented is step-length, [z]⁺=max{0, z}；

(5.3) the speed x ' of more new session f on session stream_f, maximize:

${\mathrm{\&omega;}}_1{U}_f\left(e^{x_f^{\&prime;}}\right)-\underset{l\&Element;L\left(f\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}{x}_f^{\&prime;}$

And x '_f?Within scope, whereinFor the utility function of speed, what L (f) represented is the session f link set flowing through link, sets a weighted value w₁；

(5.4) the session updates code check r on link and link_l,f, maximize:

β_l,flogr_l,f-(1-ω₁)ω_fE(r_l,f)

And r_l,fWithin the scope of [0,1], wherein E (r_l,f) it is the function of error probability, in order to keep front and back order-of-magnitude agreement, thus adding a w_f；

(5_.5) on node, intermediate variable c is updated_l,fWith power p_l, maximize:

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}\underset{f\&Element;F\left(l\right)}{\&Sigma;}{\mathrm{\&beta;}}_{l,f}{\mathrm{logc}}_{l,f}$

And c_l,fUnder retraining at two, it is respectively as follows:

$\underset{f\&Element;F\left(l\right)}{\&Sigma;}{c}_{l,f}\&le;Blog(1+\frac{1}{{\mathrm{\&sigma;}}_l}{p}_n),\&ForAll;l\&Element;L$

$\underset{l\&Element;L_{out}\left(n\right)}{\&Sigma;}{p}_l\&le;p_n,\&ForAll;n\&Element;N$

(5.6) repeat step (5.1) to step (5.5), until object function convergence, obtain the optimal code rates r of radio sensing network^*, session speed x^*And the power p consumed on link l^*, thus realizing the collaborative cross-layer optimizing of radio sensing network speed and reliability.