CN103024763B - Method for relay-free remote communication of distributed wireless sensor network - Google Patents

Abstract

The invention discloses a method for relay-free remote communication of a distributed wireless sensor network in order to lower difficulty in relay-free remote communication between the distributed wireless sensor network and a remote control center in the field of distributed wireless sensor network communication. The method includes: firstly, determining the number and positions of sensor nodes in the distributed wireless sensor network; secondly, selecting part of the sensor nodes to serve as sparse antenna array elements to form a sparse antenna array, and determining the positions and excitation of the sparse antenna array elements by means of related algorithms; and finally, enabling the sparse antenna array elements to emit wave beams, and combining the wave beams to form a high-gain wave beam, so that relay-free remote communication between the distributed wireless sensor network and the remote control center is realized. Relay-free remote communication between the distributed wireless sensor network and the remote control center is realized by means of wave beaming combination by the aid of the sparse antenna array, redundant array elements of the antenna array are reduced, and the difficulty in relay-free remote communication between the distributed wireless sensor network and the remote control center is lowered.

Description

The method of the non-relay telecommunication of a kind of Distributed Wireless Sensor Networks

Technical field

The invention belongs to the Distributed Wireless Sensor Networks communications field, be specifically related to the method for the non-relay telecommunication of a kind of Distributed Wireless Sensor Networks.

Background technology

Distributed Wireless Sensor Networks is a kind of ad hoc deployed wireless networks be made up of a large amount of sensor node.Distributed Wireless Sensor Networks realizes the communication of Distributed Wireless Sensor Networks network and remote control center with the communication of sensor node and remote control center.Due to sensor node finite energy each in Distributed Wireless Sensor Networks, each sensor node communicates with remote control center in multi-hop relay mode under normal circumstances.But in some applications, each sensor node can not adopt the mode of multi-hop relay to carry out expanding transmission distance, or the via node power of multi-hop relay can not support transmission range enough far away, which limits the communication of sensor node and remote control center, thus limit the communication of Distributed Wireless Sensor Networks and remote control center.In this case, Distributed Wireless Sensor Networks communicates with remote control center in non-relay mode, namely Distributed Wireless Sensor Networks realizes the communication with remote control center with beam synthesizing method, concrete grammar is: in radio sensing network, sensor node forms antenna array as antenna array array element in a distributed manner, the wave beam that each antenna array array element is launched is carried out the wave beam that Beam synthesis forms high-gain by this antenna array, and Distributed Wireless Sensor Networks utilizes this high-gain wave beam to realize the communication with remote control center.But, in Distributed Wireless Sensor Networks, sensor node quantity is many, locus Arbitrary distribution, this makes to be that the antenna array that antenna array array element forms exists bulk redundancy array element with sensor node, and antenna array array operation amount is large, feeding network is complicated, Beam synthesis is difficult.Which has limited the realization of Distributed Wireless Sensor Networks and the non-relay communication of remote control center.

Summary of the invention

In order to reduce the difficulty realizing Distributed Wireless Sensor Networks and the non-relay communication of remote control center.The present invention proposes the method for the non-relay telecommunication of a kind of Distributed Wireless Sensor Networks.Concrete thought of the present invention is: first, determines sensor node quantity and position in Distributed Wireless Sensor Networks; Then, from all the sensors node, select part of nodes as thinned array array element composition thinned array, utilize related algorithm determination thinned array element position and excitation; Finally, thinned array array element launching beam and carry out Beam synthesis and form the wave beam of high-gain, realizes Distributed Wireless Sensor Networks and the non-relay communication of remote control center.Concrete steps of the present invention are as follows:

Step one: determine Distributed Wireless Sensor Networks sensor node quantity and position

A large amount of sensor nodes is had, by the quantity representing sensor node in Distributed Wireless Sensor Networks.For representing the position of sensor node, first selecting a reference node, then calculating the position of other sensor node relative to reference node.With represent the individual sensor node is relative to the position of reference node.

Step 2: determine thinned array element position and excitation

Operative sensor node is selected as thinned array array element, with these array element composition thinned array from all the sensors node.For determining thinned array element position and excitation, carry out array element optimization, concrete grammar is:

A () describes the Antenna Array Pattern of individual array element

Using all sensors node as antenna array array element composition antenna array, namely individual sensor node is as antenna array array element composition antenna array, and this Antenna Array Pattern function is

（1）

Wherein, horizontal azimuth, for the directional diagram of array-element antenna, to simplify the analysis, make ; ? the excitation of individual antenna array array element, excitation density, excitation phase, it is imaginary unit; Coefficient , for signal wavelength

B () utilizes thinned array directional diagram to approach desirable Antenna Array Pattern

From select in individual sensor node individual sensor node is as thinned array array element composition thinned array, and wherein, thinned array element position is used represent.This thinned array directional diagram is utilized to approach desirable Antenna Array Pattern .Approximation ratio following formula is stated:

（2）

Wherein, ? the excitation of individual thinned array array element, the excitation density of this excitation, it is the excitation phase of this excitation; for fidelity, weigh the mean square error of thinned array directional diagram and desirable Antenna Array Pattern.

The discrete form of formula 2 is expressed as:

（3）

Wherein, represent horizontal azimuth the secondary sampled value, represent sampling total degree.

The equivalent matrix form of formula 3 is:

（4）

Wherein, it is desirable Antenna Array Pattern vector;

being weighing vector, is also array element excitation vector, its each element

Observing matrix

（5）

Error vector , wherein each element be average being zero variance is complex Gaussian random variables.Wherein, variance with fidelity be directly proportional, namely .

C () determines weighing vector

Utilize MAP estimation determination weighing vector , detailed process is:

C1. weighing vector priori probability density function be

（6）

Wherein, determine weighing vector the parameter vector of prior distribution, parameter determine the parameter of prior distribution.Parameter vector probability density function be:

（7）

Wherein, the probability density function of Gamma distribution, , gamma distributed constant, .

C2. variance priori probability density function be:

（8）

Wherein, the probability density function of Gamma distribution, , gamma distributed constant, .

C3. weighing vector , parameter vector and variance posterior probability density function:

（9）

Wherein, it is weighing vector posterior probability density function, from the known weighing vector of this posterior probability density function posterior distrbutionp be Gaussian Profile, the mean vector of this Gaussian Profile, the covariance matrix of this Gaussian Profile, diagonal matrix ; , wherein,

, be rank unit matrix.

C4. weighing vector is determined

Determine weighing vector mAP estimation: in step c3, known weighing vector posterior distrbutionp be Gaussian Profile, therefore weighing vector mAP estimation be weighing vector the mean vector of posteriority Gaussian Profile , i.e. weighing vector mAP estimation

（10）

Because mean vector it is variance and covariance matrix function, covariance matrix it is diagonal matrix function, diagonal matrix by parameter composition, so mean vector it is variance and parameter function.So, weighing vector mAP estimation also be variance and parameter function, so determining weighing vector mAP estimation first to determine parameter before and variance .Utilize maximal possibility estimation determination parameter and variance :

wherein, .

Definition likelihood function ,

Make likelihood function right partial derivative be zero, namely

Obtain parameter

（11）

Wherein, it is mean vector in individual element, it is covariance matrix in individual diagonal entry.

In like manner, likelihood function is made right partial derivative be zero, namely

Obtain variance

（12）

Wherein, .

Notice in (11) formula, (12) formula, parameter be with function, variance it is mean vector

With function, known it is mean vector element, it is covariance matrix element, therefore parameter and variance it is all mean vector and covariance matrix function.Notice again, mean vector it is variance and covariance matrix function, covariance matrix it is variance and diagonal matrix function, diagonal matrix by parameter composition, therefore mean vector and covariance matrix it is all parameter and variance function.Known from the above mentioned, mean vector , covariance matrix , parameter and variance iteration can be carried out to determine mean vector convergency value.Again because weighing vector mAP estimation , so iteration can be carried out to determine the MAP estimation of weighing vector convergency value, iterative process is:

When time stop iteration, error amount, mark represent iterations.After iteration stopping, determine weighing vector

（13）

Wherein, with obtain in a front iteration.Finally weighing vector can be determined according to (13) formula .

D () determines thinned array element position and excitation

According to weighing vector determine thinned array element position and excitation, weighing vector middle nonzero element is exactly the excitation of thinned array array element, weight vectors the position of the sensor node that middle nonzero element is corresponding is exactly the position of thinned array array element.

Step 3: realize Distributed Wireless Sensor Networks and the non-relay communication of remote control center

According to thinned array element position and excitation, each thinned array array element launching beam and carry out the wave beam that Beam synthesis forms high-gain simultaneously, utilizes this high-gain wave beam to realize Distributed Wireless Sensor Networks and the non-relay communication of remote control center.

Beneficial effect of the present invention is to utilize thinned array to achieve Distributed Wireless Sensor Networks and the non-relay communication of remote control center in Beam synthesis mode, decrease the redundancy array element of antenna array, reduce the difficulty realizing Distributed Wireless Sensor Networks and the non-relay communication of remote control center.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention.

Fig. 2 is the flow chart determining thinned array element position and excitation.

Embodiment

As shown in Figure 1, concrete implementation step is as follows for implementing procedure figure of the present invention:

Step 1: according in esse Distributed Wireless Sensor Networks determination sensor node quantity , a selected reference node, calculates the position of other node relative to reference node .

Step 2: select from all the sensors node operative sensor node as thinned array array element composition thinned array, namely from select in individual sensor node ( ) individual sensor node is as thinned array array element composition thinned array, the positional representation of thinned array array element is .For determining thinned array element position and excitation, carry out array element optimization, as shown in Figure 2, specific implementation process is this process flow diagram:

2.1 determine desirable Antenna Array Pattern vector, fidelity, observing matrix and error vector

Desirable Antenna Array Pattern is determined according to actual requirement and fidelity , from desirable Antenna Array Pattern equal intervals is taked individual sampled point, obtain desirable Antenna Array Pattern vector, detailed process is: horizontal azimuth with interval from change to , obtain horizontal azimuth vector

Correspondingly obtain desirable Antenna Array Pattern vector:

According to sensor node position with horizontal azimuth vector , determine observing matrix

Error vector , wherein each element be average being zero variance is complex Gaussian random variables.Variance with fidelity be directly proportional, namely .

2.2 determine weighing vector priori probability density function

Because weighing vector priori probability density function in have parameter vector , so determining weighing vector priori probability density function before, first determine parameter vector probability density function.Parameter vector probability density function be:

Wherein, the probability density function of Gamma distribution, , gamma distributed constant, order , .

Weighing vector priori probability density function be

2.3 determine variance priori probability density function:

Wherein, the probability density function of Gamma distribution, , gamma distributed constant, order , .

2.4 determine weighing vector , parameter vector and variance posterior probability density function:

Wherein, it is weighing vector posterior probability density function, from the known weighing vector of this posterior probability density function posterior distrbutionp be Gaussian Profile, the mean vector of this Gaussian Profile, the covariance matrix of this Gaussian Profile, diagonal matrix ; , wherein,

, be rank unit matrix.

2.5 determine weighing vector

Determine weighing vector mAP estimation: in step 2.4, known weighing vector posterior distrbutionp be Gaussian Profile, therefore weighing vector mAP estimation be weighing vector the mean vector of posteriority Gaussian Profile , i.e. weighing vector mAP estimation

Because mean vector it is variance and covariance matrix function, covariance matrix it is diagonal matrix function, diagonal matrix again by parameter composition, so mean vector it is variance and parameter function.So, weighing vector mAP estimation also be variance and parameter function, so determining weighing vector mAP estimation first to determine parameter before and variance .Utilize maximal possibility estimation determination parameter and variance :

Determine likelihood function .Because make , , therefore likelihood function .Make likelihood function right partial derivative be zero, namely

Obtain parameter

In like manner, likelihood function is made right partial derivative be zero, namely

Obtain variance

Weighing vector mAP estimation , covariance matrix , parameter and variance carry out iteration determination weighing vector mAP estimation convergency value, iterative process is:

When time stop iteration, mark represent iterations.After iteration stopping, determine weighing vector

2.6 determine thinned array element position and excitation

According to weighing vector determine thinned array element position and excitation, weighing vector middle nonzero element is exactly the excitation of thinned array array element, weight vectors the position of the sensor node that middle nonzero element is corresponding is exactly the position of thinned array array element.

Step 3: after the excitation of thinned array array element and position are determined, each thinned array array element launching beam and carry out the wave beam that Beam synthesis forms high-gain simultaneously, utilizes this high-gain wave beam to realize Distributed Wireless Sensor Networks and the non-relay communication of remote control center.

Claims (1)

1. a method for the non-relay telecommunication of Distributed Wireless Sensor Networks, is characterized in that the concrete steps of the method are:

Step one: determine Distributed Wireless Sensor Networks sensor node quantity and position, specifically:

There is a large amount of sensor nodes in Distributed Wireless Sensor Networks, represent the quantity of sensor node with N; For representing the position of sensor node, first selecting a reference node, then calculating the position of other sensor node relative to reference node; Use d _n, n=1,2 ..., N represents the position of the n-th sensor node relative to reference node;

Step 2: determine thinned array element position and excitation, specifically:

Operative sensor node is selected as thinned array array element, with these array element composition thinned array from all the sensors node; For determining thinned array element position and excitation, carry out array element optimization, concrete grammar is:

A () describes the Antenna Array Pattern of N number of array element

Using all sensors node as antenna array array element composition antenna array, namely N number of sensor node is as antenna array array element composition antenna array, and this Antenna Array Pattern function is

$F\left(\mathrm{\θ}\right)=F_e\left(\mathrm{\θ}\right)\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{I}_n\exp \left(j{\mathrm{\β}}_n\right)\exp \left[\mathrm{jk}{d}_n\cos \left(\mathrm{\θ}\right)\right]---\left(1\right)$

Wherein, θ is horizontal azimuth, F _e(θ) be the directional diagram of array-element antenna, to simplify the analysis, make F _e(θ)=1;

I _nexp (j β _n) be the excitation of the n-th antenna array array element, I _nexcitation density, β _nbe excitation phase, j is imaginary unit; Coefficient k=2 π/λ, λ are signal wavelength

B () utilizes thinned array directional diagram to approach desirable Antenna Array Pattern

From N number of sensor node, select P sensor node as thinned array array element composition thinned array, wherein, thinned array element position z _p, p=1,2 ..., P represents; This thinned array directional diagram is utilized to approach desirable Antenna Array Pattern F _ref(θ); Approximation ratio following formula is stated:

${\&Integral;}_{-\mathrm{\&pi;}}^{\mathrm{\&pi;}}{[F_{\mathrm{ref}}\left(\mathrm{\&theta;}\right)-\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{I}_p\exp \left(j{\mathrm{\&beta;}}_p\right)\exp [\mathrm{jk}{z}_p\cos \left(\mathrm{\&theta;}\right)\left]\right]}^2\mathrm{d\&theta;}<\mathrm{\&epsiv;}---\left(2\right)$

Wherein, I _pexp (j β _p) be the excitation of p thinned array array element, I _pthe excitation density of this excitation, β _pit is the excitation phase of this excitation; ε is fidelity, weighs the mean square error of thinned array directional diagram and desirable Antenna Array Pattern;

The discrete form of formula 2 is expressed as:

$\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{[F_{\mathrm{ref}}\left({\mathrm{\&theta;}}_m\right)-\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{I}_p\exp \left(j{\mathrm{\&beta;}}_p\right)\exp [\mathrm{jk}{z}_p\cos \left({\mathrm{\&theta;}}_m\right)\left]\right]}^2<\mathrm{\&epsiv;}---\left(3\right)$

Wherein, θ _mrepresent horizontal azimuth the m time sampled value, M represents sampling total degree;

The equivalent matrix form of formula 3 is:

F _ref-Φw＝D (4)

Wherein, F _ref=[F _ref(θ ₁), F _ref(θ ₂) ..., F _ref(θ _m)] ^tit is desirable Antenna Array Pattern vector;

W=[w ₁, w ₂..., w _n] ^tbeing weighing vector, is also array element excitation vector, its each element

Observing matrix

Error vector D=[Δ ₁..., Δ _m], wherein each element Δ _m, m=1,2 ..., M is complex Gaussian random variables, and the average of this complex Gaussian random variables is zero, and variance is σ ²; Wherein, variances sigma ²be directly proportional to fidelity ε, i.e. σ ²∝ ε;

C () determines weighing vector w

Utilize MAP estimation determination weighing vector w, detailed process is:

C1. the priori probability density function of weighing vector w is

$p\left(w\right|a)=\frac{{\mathrm{\&Pi;}}_{n=1}^N\sqrt{a_n}\exp (-\frac{a_n{w}_n^2}{2})}{{\left(2\mathrm{\&pi;}\right)}^{N/2}}---\left(6\right)$

Wherein, a=[a ₁, a ₂..., a _n] ^tthe parameter vector determining weighing vector w prior distribution, parameter a _ndetermine w _nthe parameter of prior distribution; The probability density function of parameter vector a is:

$p\left(a\right)=\underset{n=1}{\overset{N}{\mathrm{\&Pi;}}}G\left(a_n\right|{\mathrm{\&alpha;}}_1,{\mathrm{\&alpha;}}_2)---\left(7\right)$

Wherein, the probability density function of Gamma distribution, α ₁, α ₂gamma distributed constant, $\mathrm{\&Gamma;}\left({\mathrm{\&alpha;}}_1\right)={\&Integral;}_0^{\&infin;}{t}^{{\mathrm{\&alpha;}}_1-1}{e}^{-t}\mathrm{dt};$

C2. variances sigma ²priori probability density function be:

$p\left(\frac{1}{{\mathrm{\&sigma;}}^2}\right)=G\left(\frac{1}{{\mathrm{\&sigma;}}^2}\right|{\mathrm{\&alpha;}}_3,{\mathrm{\&alpha;}}_4)---\left(8\right)$

Wherein, the probability density function of Gamma distribution, α ₃, α ₄gamma distributed constant, $\mathrm{\&Gamma;}\left({\mathrm{\&alpha;}}_3\right)={\&Integral;}_0^{\&infin;}{t}^{{\mathrm{\&alpha;}}_3-1}{e}^{-t}\mathrm{dt};$

C3. weighing vector w, parameter vector a and variances sigma ²posterior probability density function:

p(w,a,σ ²|F _ref)＝p(w|F _ref,a,σ ²)p(a,σ ²|F _ref) (9)

Wherein, $p\left(w\right|F_{\mathrm{ref}}a,{\mathrm{\&sigma;}}^2)={\left(2\mathrm{\&pi;}\right)}^{-N/2}{\left|\mathrm{\&Sigma;}\right|}^{-1/2}\exp \{-\frac{1}{2}{(w-\mathrm{\&mu;})}^T{\mathrm{\&Sigma;}}^{-1}(w-\mathrm{\&mu;})\}$ Being the posterior probability density function of weighing vector w, is Gaussian Profile from the Posterior distrbutionp of the known weighing vector w of this posterior probability density function, μ=σ ^-2Σ Φ ^tf _refthe mean vector of this Gaussian Profile, Σ=(σ ^-2Φ ^tΦ+A) ^-1the covariance matrix of this Gaussian Profile, diagonal matrix A=diag (a ₁, a ₂..., a _n); P (a, σ ²| F _ref) ∝ p (F _ref| a, σ ²) p (a) p (σ ²), wherein, $p\left(F_{\mathrm{ref}}\right|a,{\mathrm{\&sigma;}}^2)={\left(2\mathrm{\&pi;}\right)}^{-N/2}{|{\mathrm{\&sigma;}}^{2}I+\mathrm{\&Phi;}{A}^{-1}{\mathrm{\&Phi;}}^T|}^{-1/2}\exp \{-\frac{1}{2}{F_{\mathrm{ref}}}^T{({\mathrm{\&sigma;}}^{2}I+\mathrm{\&Phi;}{A}^{-1}{\mathrm{\&Phi;}}^T)}^{-1}{F}_{\mathrm{ref}}\},$ I is M rank unit matrix;

C4. weighing vector w is determined

Determine the MAP estimation of weighing vector w: in step c3, the Posterior distrbutionp of known weighing vector w is Gaussian Profile, therefore the MAP estimation of weighing vector w is the mean vector μ of weighing vector w posteriority Gaussian Profile, the i.e. MAP estimation of weighing vector w

w _map＝μ (10)

Because mean vector μ is variances sigma ²with the function of covariance matrix Σ, covariance matrix Σ is the function of diagonal matrix A, and diagonal matrix A is by parameter a _n, n=1,2 ..., N forms, so mean vector μ is variances sigma ²with parameter a _n, n=1,2 ..., the function of N; So, the MAP estimation w of weighing vector w _mapalso be variances sigma ²with parameter a _n, n=1,2 ..., the function of N, so determining the MAP estimation w of weighing vector w _mapfirst to determine parameter a before _n, n=1,2 ... N and variances sigma ²; Utilize maximal possibility estimation determination parameter a _n, n=1,2 ... N and variances sigma ²:

$\begin{array}{c}\underset{a,{\mathrm{\&sigma;}}^2}{\arg \max }p(a,{\mathrm{\&sigma;}}^2|F_{\mathrm{ref}})=\underset{a,{\mathrm{\&sigma;}}^2}{\arg \max }\left[p\left(F_{\mathrm{ref}}\right|a,{\mathrm{\&sigma;}}^2)p\left(a\right)p\left({\mathrm{\&sigma;}}^2\right)\right]\\ =\underset{a,{\mathrm{\&sigma;}}^2}{\arg \max }\log \left[p\left(F_{\mathrm{ref}}\right|\log a,\log {\mathrm{\&sigma;}}^2)p\left(\log a\right)p\left(\log {\mathrm{\&sigma;}}^2\right)\right]\\ =\underset{a,{\mathrm{\&sigma;}}^2}{\arg \max }\{-\frac{1}{2}[N\log 2\mathrm{\&pi;}+\log \left|C\right|+F_{\mathrm{ref}}^T{C}^{-1}{F}_{\mathrm{ref}}]+\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_1\log a_n-{\mathrm{\&alpha;}}_2{a}_n)+{\mathrm{\&alpha;}}_3\log {\mathrm{\&sigma;}}^{-2}-{\mathrm{\&alpha;}}_4{\mathrm{\&sigma;}}^{-2}\}\end{array}$ Wherein, C=σ ²i+ Φ A ^-1Φ ^t;

Definition likelihood function $H=-\frac{1}{2}\left[\log \right|C|+F_{\mathrm{ref}}^T{C}^{-1}{F}_{\mathrm{ref}}]+\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_1\log a_n-{\mathrm{\&alpha;}}_2{a}_n)+{\mathrm{\&alpha;}}_3\log {\mathrm{\&sigma;}}^{-2}-{\mathrm{\&alpha;}}_4{\mathrm{\&sigma;}}^{-2},$

Make likelihood function Η to log a _npartial derivative be zero, namely

$\frac{\&PartialD;H}{\&PartialD;\log a_n}=\frac{1}{2}[1-a_n({\mathrm{\&mu;}}_n^2+{\mathrm{\&Sigma;}}_{\mathrm{nn}})]+{\mathrm{\&alpha;}}_1-{\mathrm{\&alpha;}}_2{a}_n=0$

Obtain parameter

$a_n=\frac{1+2{\mathrm{\&alpha;}}_1}{{\mathrm{\&mu;}}_n^2+{\mathrm{\&Sigma;}}_{\mathrm{nn}}+2{\mathrm{\&alpha;}}_2}---\left(11\right)$

Wherein, μ _nthe n-th element in mean vector μ, Σ _nnit is the n-th diagonal entry in covariance matrix Σ;

In like manner, make likelihood function Η to log σ ^-2partial derivative be zero, namely

$\frac{\&PartialD;H}{\&PartialD;\log {\mathrm{\&sigma;}}^{-2}}=\frac{1}{2}[N{\mathrm{\&sigma;}}^2-{\left|\right|F_{\mathrm{ref}}-\mathrm{\&Phi;\&mu;}\left|\right|}^2-{\mathrm{\&sigma;}}^2\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_n]+{\mathrm{\&alpha;}}_3-{\mathrm{\&alpha;}}_4{\mathrm{\&sigma;}}^{-2}=0$

Obtain variance

${\mathrm{\&sigma;}}^2=\frac{{\left|\right|F_{\mathrm{ref}}-\mathrm{\&Phi;\&mu;}\left|\right|}^2+2{\mathrm{\&alpha;}}_3}{N-\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_n+2{\mathrm{\&alpha;}}_4}---\left(12\right)$

Wherein, γ _n=1-a _nΣ _nn;

Notice in (11) formula, (12) formula, parameter a _nμ _nand Σ _nnfunction, variances sigma ²mean vector μ and Σ _nnfunction, known μ _nthe element of mean vector μ, Σ _nnthe element of covariance matrix Σ, therefore parameter a _nand variances sigma ²it is all the function of mean vector μ and covariance matrix Σ; Notice again, mean vector μ is variances sigma ²with the function of covariance matrix Σ, covariance matrix Σ is variances sigma ²with the function of diagonal matrix A, diagonal matrix A is by parameter a _n, n=1,2 ..., N forms, therefore mean vector μ and covariance matrix Σ is parameter a _nand variances sigma ²function; From the above mentioned, mean vector μ, covariance matrix Σ, parameter a _nand variances sigma ²iteration can be carried out to determine the convergency value of mean vector μ; Again because the MAP estimation w of weighing vector w _map=μ, so can carry out iteration to determine the MAP estimation w of weighing vector w _mapconvergency value, iterative process is:

$w_{\mathrm{map}}^{i+1}={\mathrm{\&mu;}}^{i+1}={\mathrm{\&sigma;}}_i^{-2}{\mathrm{\&Sigma;}}^i{\mathrm{\&Phi;}}^T{F}_{\mathrm{ref}}$

${\mathrm{\&Sigma;}}^{i+1}={({\mathrm{\&sigma;}}_i^{-2}{\mathrm{\&Phi;}}^T\mathrm{\&Phi;}+A_i)}^{-1}$

$a_{n,i+1}=\frac{1+2{\mathrm{\&alpha;}}_1}{{\mathrm{\&mu;}}_{n,i}^2+{\mathrm{\&Sigma;}}_{\mathrm{nn}}^i+2{\mathrm{\&alpha;}}_2}$

${\mathrm{\&sigma;}}_{i+1}^2=\frac{{\left|\right|F_{\mathrm{ref}}-\mathrm{\&Phi;}{\mathrm{\&mu;}}^i\left|\right|}^2+2{\mathrm{\&alpha;}}_3}{N-\underset{n=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&gamma;}}_{n,i}+2{\mathrm{\&alpha;}}_4}$

When time stop iteration, δ is error amount, mark i represent iterations; After iteration stopping, determine weighing vector

$w=w_{\mathrm{map}}^{i+1}={\mathrm{\&mu;}}^{i+1}={\mathrm{\&sigma;}}_i^{-2}{\mathrm{\&Sigma;}}^i{\mathrm{\&Phi;}}^T{F}_{\mathrm{ref}}---\left(13\right)$

Wherein, and Σ ⁱobtain in a front iteration; Weighing vector w can be finally determined according to (13) formula;

D () determines thinned array element position and excitation

Determine thinned array element position and excitation according to weighing vector w, in weighing vector w, nonzero element is exactly the excitation of thinned array array element, and in weight vectors w, the position of the sensor node that nonzero element is corresponding is exactly the position of thinned array array element;

Step 3: realize Distributed Wireless Sensor Networks and the non-relay communication of remote control center, specifically:

According to thinned array element position and excitation, each thinned array array element launching beam and carry out the wave beam that Beam synthesis forms high-gain simultaneously, utilizes this high-gain wave beam to realize Distributed Wireless Sensor Networks and the non-relay communication of remote control center.