CN105550783A - Radar networking deployment optimization method - Google Patents

Abstract

The invention discloses a radar networking deployment optimization method. A radar network consists of N pieces of same-frequency or same-frequency-band different-frequency radar. An optimum deployment scheme is selected, so that an obtained alert region G can approach to the required alert region A<g>, and the detection probability can reach a requirement P<dg>; meanwhile, an obtained key detection region C can also approach to a required key detection airspace A<c> to a great degree, and the detection probability can reach the detection requirement P<dc>; the higher the radar electromagnetic compatibility degree phi<total>, the better; and the problem belongs to a multi-objective optimization problem. The radar electromagnetic compatibility and the space covering coefficient are used as radar optimization objectives; and an optimization algorithm is combined for performing optimization deployment on a radar network formed by same-frequency radar, same-frequency-band different-frequency radar, mixed same-frequency and same-frequency-band different-frequency radar and multi-frequency-band radar. The method has the advantages that the radar space covering degree and the radar electromagnetic compatibility are considered, so that the radar networking has good compatibility work capability and good work effects in the complicated electromagnetic environment.

Description

Radar network composite disposition optimization method

Technical field

The present invention relates to radar network composite disposition optimization method, belong to Radar Signal Processing Technology field.

Background technology

Radar network composite is an important trends of world radar development, under the situation of modern science and technology war, the form of war is from platform centric warfare (FCW) to network-centric warfare (NCW) transition, and along with the development of electronic technology, radar electronic warfare war is more and more fiery, developing into early warning system, communication network, command net and the catch net prevention and control operation Network system for mark, is the prerequisite condition winning future high-tech war.Radar network composite can bring huge military benefit, causes the extensive attention of countries in the world, and obtains very large development, all has application widely at home and abroad.

Radar stands in great numbers afield, when especially radar frequency spectrums of operation is crowded, can produces serious electromagnetic compatibility problem simultaneously, at this time need to be optimized deployment to radar when close and same frequency radar works.Existing method generally only considers that radar is to the covering of zone of responsibility, be main target of optimization by coverage coefficient and overlap coefficient, mainly from covering the target area Main way, main height layer, redundant digit is maximum, volume is maximum and the coverage coefficient of radar to target maximum two aspects in single portion are optimized deployment for this method.The method also had considers the detection probability of radar, optimizing radar network composite, giving single portion radar detection probability and radar network combined detection probability model, realizing Optimization deployment by the relation of analytical model and radar site by improving radar detection probability.But said method all have ignored the electromagnetic compatibility problem existed between radar, especially when spectrum congestion.

Summary of the invention

The object of the present invention is to provide a kind of radar network composite disposition optimization method, using the electromagnetic compatibility between radar and space coverage coefficient as radar optimization aim, in conjunction with optimized algorithm to radar frequently, non-with radar frequently, with frequently and same frequency range is non-to mix mutually with radar frequently and radar fence that the radar of multiband forms is optimized the method for deployment with frequency range.

Object of the present invention is achieved by the following technical programs:

A kind of radar network composite disposition optimization method, radar fence is by N portion with frequently or with frequency range is non-forming with frequency radar, and step is as follows:

Step 1: set up spatial domain Modulus Model:

(1) dispose the geographic position of each portion radar, to obtain maximum spatial domain detectivity f, its mathematical model is as follows:

$f=\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j\&lsqb;(1-\mathrm{\&lambda;})\frac{G_j}{A_g}+\mathrm{\&lambda;}\frac{C_j}{A_c}\&rsqb;,$

λ, w _j∈ [0,1] and

$G_j=\underset{i=1}{\overset{N}{\&cup;}}{A}_{ij}\&cap;A_g$

Wherein, G _jfor the warning region obtained at jth height layer, A _ijbe the search coverage of i-th radar at jth height layer; M is highl stratification number; λ is the significance level of the Party A's target in territory, focus detecting area, and its value, in [0,1] scope, is determined according to actual requirement; w _j(j=1,2 ..., M) and for radar fence is to the degree of attentiveness of each height layer, for dissimilar Party B's target, this weighting coefficient is determined by the flying height of Party B's target; Choose one group of w _j(j=1,2 ..., M), make radar fence effectively resist low latitude, hedgehopping target; C _jfor the territory, focus detecting area obtained at jth height layer, detection probability is:

$P=1-\underset{i=1}{\overset{N}{\&Pi;}}(1-P_i)$

Wherein: P _iit is the detection probability of i-th radar; N is radar network number;

(2) make for security area coverage coefficient, attach most importance to area coverage fraction, carrying out simplification to the formula of maximum spatial domain detectivity f can obtain:

$f=\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j\&lsqb;(1-\mathrm{\&lambda;})C_{gj}+{\mathrm{\&lambda;C}}_{ej}\&rsqb;,$

λ, w _j∈ [0,1] and

Step 2: set up electromagnetic compatibility Degree Model:

1. identical working frequency range is non-with electromagnetic compatibility model time frequently

Time noiseless, the maximum operating range of radar is:

$R_{max}={\left(\frac{{\mathrm{PG}}^2{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{S}_{min}L}\right)}^{1/4}$

In formula, P is the emissive power of radar, and G is radar antenna gain, and λ is radar emission electromagnetic wavelength, and σ is Target scatter section area, S _minfor radar minimum detectable signal, L is radar emission and receives the energy loss in electromagnetic wave process;

The dB unit expression formula of L is:

L _(dB)＝L′ _(dB)+L _r(dB)+L _P(dB)

In formula, L ' is atmospheric absorption loss, sleet loss, two radars the various loss such as radome loss, feeder line loss and, unit dB; L _ppolarization loss, i.e. the loss of the difference introducing of two polarization radar modes, modern radar adopts linear polarization mostly, if two polarization radar modes are identical, polarization loss gets 0dB, otherwise gets 20dB; L _r(=32.5+20lgf+20lgR) is electromagnetic wave space propagation loss, and unit is dB; F is frequency, and unit is MHz; R is propagation distance, unit K m;

N portion radar works simultaneously, and there is co-channel interference; The impact on unwanted emission machine emission spectrum rejection coefficient FDR that the selectivity curve that the interference that radar n receives other radars is subject to receiver produces:

$FDR\left(\mathrm{\&Delta;}f\right)=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H(f+\mathrm{\&Delta;}f){|}^{2}df}dB$

Wherein, P (f) is the power spectrum density of undesired signal equivalence medium-frequency IF; The frequency response that H (f) is receiver; Δ f=ft – fr, wherein, ft is the real-time frequency of interference source; Fr is the tuned frequency of receiver;

FDR can be divided into two, and tuning suppression OTR and frequency detuning suppress OFR, and frequency detuning suppression OFR is the extra suppression because interference source and receiver off resonance produce;

FDR(Δf)＝OTR+OFR(Δf)dB

Wherein:

$OTR=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H\left(f\right){|}^{2}df}dB;OFR\left(\mathrm{\&Delta;}f\right)=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H\left(f\right){|}^{2}df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H(f+\mathrm{\&Delta;}f){|}^{2}df}dB$

N-th radar receives the interference P of other radars _rnbe expressed as:

$P_{rn}=\frac{P_{n1}}{{\mathrm{FDR}}_{n1}}+\frac{P_{n2}}{{\mathrm{FDR}}_{n2}}+...+\frac{P_{n(n-1)}}{{\mathrm{FDR}}_{n(n-1)}}+\frac{P_{n(n+1)}}{{\mathrm{FDR}}_{n(n+1)}}+...+\frac{P_{nN}}{{\mathrm{FDR}}_{nN}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}$

In formula, P _ifor the emissive power of adjacent interference radar i, G _ifor the antenna gain of adjacent interference radar i, G ' _nfor being disturbed the antenna receiving gain of radar n, γ _nfor radar i undesired signal is to the polarization coefficient of radar n receiving antenna, R _infor radar i and the spacing being disturbed radar n, L _infor the electromagnetic wave of radar i transmitting is by the energy loss in radar n receiving course; FDR _nibe the frequency dependence rejection coefficient of i-th radar jamming to radar n, being general value here, is not dB value; λ _tiit is the wavelength of i-th interference radar; If two radars are with frequently, then FDR coefficient is 1;

The echo signal power P that radar n receives _rsfor:

$P_{rs}=\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R}_n^4{L}_n}$

In formula, R _nfor the distance of radar n and target, λ _tnfor the wavelength of radar n;

Be disturbed under condition, radar is wanted find target, the echo signal power P received _rswith the jamming power P received _rjmust meet the following conditions:

$\frac{P_{rj}}{P_{rs}}=\frac{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R}_n^4{L}_n}}\&le;K_n$

In formula, K _nit is the blanket factor of the n-th radar;

Work as P _rj/ S _{(n) min}≤ K _ntime, the maximum operating range of radar is unaffected; Work as P _rj/ S _{(n) min}> K _ntime, the maximum radar range R ' under disturbing can be obtained _nmax:

$R_{n\max }^{\&prime;}={\left(\frac{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{L}_n}}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{K}_n\right)}^{1/4}$

It is normalized, with the R ' when being disturbed _nmaxwith interference-free under R _nmaxratio μ _nas the electromagnetic compatibility degree of radar n; Obtain:

${\mathrm{\&mu;}}_n=\left\{\begin{array}{cc}1,& P_{rj}/S_{\left(n\right)\min }\&le;K_n\\ \frac{R_{n\max }^{\&prime;}}{R_{n\max }}={\left(\frac{\frac{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{L}_n}}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{K}_n}{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{S}_{n\min }{L}_n}}\right)}^{1/4}={\left(\frac{S_{n\min }{K}_n}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}\right)}^{1/4},& P_{rj}/S_{\left(n\right)\min }>K_n\end{array}\right.$

2. disturbed radar can be aligned

When being aimed at by radar antenna, receiver front end there will be overload phenomenon, and electromagnetic compatibility degree is very poor, can think electromagnetic compatibility degree μ=0;

If disturbed radar two is in the sweep limit of interference radar one or two radar, then consider that radar a pair radar two is to punctual situation; Suppose radar one, the distance of radar two is R ₁₂, be centre of sphere R with radar one ₁₂for radius makes a sphere, radar two is made to drop on sphere, with the horizontal scan angle of radar one with pitching scanning angle θ ₁its scan area is showed; Around radar two, radar one is aimed at the limit surface product representation of radar two out;

Probability of interference p ₂₁for:

$\frac{U\&cap;V}{U}=p_{21}$

Wherein W is the limit aligning area of wave beam sometime, and enclosed along radar two position translation one by W, all scopes obtained are V; U is radar scanning scope;

The area equivalent of curved surface U is: curved surface V is an ellipse, and its equivalent area is: $4R_{12}^2\&CenterDot;{\mathrm{sin\&alpha;}}_1\&CenterDot;{\mathrm{sin\&beta;}}_1\&ap;4R_{12}^2\&CenterDot;{\mathrm{\&alpha;}}_1.{\mathrm{\&beta;}}_1$ If v '=4 α ₁β ₁, obtain:

$\frac{U}{U^{\&prime;}}=\frac{V}{V^{\&prime;}}\&DoubleRightArrow;\frac{U}{V}=\frac{U^{\&prime;}}{V^{\&prime;}}\&DoubleRightArrow;\frac{U\&cap;V}{U}=\frac{U^{\&prime;}\&cap;V^{\&prime;}}{U^{\&prime;}}=p_{21}$

Therefore, p ₂₁end value and radar one, distance between radar two have nothing to do;

Be provided with M radar can aim at radar n; Radar i is to the aligning probability of radar n:

$\frac{U^{\&prime;}\&cap;{V_i}^{\&prime;}}{U^{\&prime;}}=p_{ni}$

The probability that radar n is not aligned for:

${\stackrel{\&OverBar;}{p}}_n=1-\underset{i=1}{\overset{M}{\&Sigma;}}{p}_{ni}$

So its electromagnetic compatibility degree μ ' _n:

${\mathrm{\&mu;}}_n^{\&prime;}=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{p}}_n,& P_{rj}/S_{\left(n\right)\min }\&le;K_n\\ {\stackrel{\&OverBar;}{p}}_n\frac{R_{n\max }^{\&prime;}}{R_{n\max }}={\stackrel{\&OverBar;}{p}}_n{\left(\frac{S_{n\min }{K}_n}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}\right)}^{1/4},& P_{rj}/S_{\left(n\right)\min }>K_n\end{array}\right.$

3. radar is disturbed can mutually to aim at disturbed radar

When the main lobe wave beam of two radars can be aimed at mutually time, both needed to avoid also needing to avoid aiming at other antennas to the aligning of other antennas;

Two radars are mutually aimed at and are needed level orientation and pitching orientation all to aim at, and its probability is:

$p_{\mathrm{\&upsi;}}=\frac{{\mathrm{\&beta;}}_1}{{\mathrm{\&theta;}}_1}\&times;\frac{{\mathrm{\&beta;}}_2}{{\mathrm{\&theta;}}_2}$

In formula, P _hfor level orientation aims at probability; α ₁, α ₂for the antenna beamwidth of radar one and radar two; for the angle in radar one, radar two antenna horizontal scanning region; P _υfor pitching alignment of orientation probability; β ₁, β ₂radar one and radar two pitching beam angle; θ ₁, θ ₂for the sweep limit of the angle of pitch;

The aligning Probability p of radar one and radar two ' ₁₂be exactly the probability of alignment of orientation aims at probability product with pitching, that is:

p′ ₁₂＝p _h×p _υ

Then, suppose that beam radar m can aim between two with L beam radar, the mutual misalignment probability of available radar m and other radars for:

${\stackrel{\&OverBar;}{p}}_m=1-\underset{j=1}{\overset{J}{\&Sigma;}}(p_{mj}+p_{jm}-p_{mj}^{\&prime;})$

Wherein, p _mjbe the aligning probability of radar j to radar m, can be drawn by probability model; p _jmthe aligning probability of radar m to radar j; P ' _mjit is the mutual aligning probability of radar m, j;

So its electromagnetic compatibility degree μ " _m:

${\mathrm{\&mu;}}_m^{\&prime;\&prime;}=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{p}}_m,& P_{rj}/S_{\left(m\right)\min }\&le;K_m\\ {\stackrel{\&OverBar;}{p}}_m\frac{R_{m\max }^{\&prime;}}{R_{m\max }}={\stackrel{\&OverBar;}{p}}_m{\left(\frac{S_{m\min }{K}_m}{\underset{i=1}{\overset{T}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_m^{\&prime;}{\mathrm{\&lambda;}}^2{\mathrm{\&gamma;}}_m}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{im}^2{L}_{im}}}\right)}^{1/4},& P_{rj}/S_{\left(m\right)\min }>K_m\end{array}\right.$

4. similar frequency bands radar composition system between electromagnetic compatibility model

The radar of all same frequencys is formed a system, predict the electromagnetic compatibility degree of whole radar system; Suppose always to have N portion radar, K radar can aim at other radars, wherein has M radar to aim between two, then total electromagnetic compatibility degree is:

In formula, η _iit is the significant coefficient of i-th radar;

5. the electromagnetic compatibility model of all frequency range radar systems

Radar system with frequency range has Y, and the electromagnetic compatibility degree of so all same frequency radar systems is:

Step 3: application particle cluster algorithm:

1. construct initialization population, namely the number of particle, initial position and initial speed are set

First X is used _ispace representation n ties up the current location of the particle i of search volume; Use V _irepresent the flying speed of current particle; Use P _irepresent the desired positions that current particle experiences;

$\left\{\begin{array}{c}{X}_i=(x_{i1},x_{i2},...,x_{in})\\ V_i=(v_{i1},v_{i2},...,v_{in})\\ P_i=(p_{i1},p_{i2},...,p_{in})\end{array}\right.$

Wherein, n represents dimension; I represents i-th particle and current particle;

2. using electromagnetic compatibility degree Φ and coverage coefficient as maximized target fitness function, then the current desired positions of particle i is:

Wherein, t represents the t time iteration;

If population is S in colony, compares the desired positions of all particle experience in colony, global optimum position P can be obtained _g(t), that is:

P _g(t)∈{P ₀(t),P ₁(t),...,P _S(t)}|f(P _g(t))＝max{f(P ₀(t)),f(P ₁(t)),...,f(P _S(t))}

3. according to speed and the position of the current and global optimum's position calculation renewal obtained before:

v _ij(t+1)＝w·v _ij(t)+c ₁r _1j(t)·(P _ij(t)-x _ij(t))+c ₂r _2j(t)·(P _gj(t)-x _ij(t))

x _ij(t+1)＝x _ij(t)+v _ij(t+1)

Wherein, x _ij(t), v _ijt () represents that particle i jth ties up position and the movement velocity in t generation; W is inertial coefficient, is worth between 0 ~ 1; c ₁, c ₂for acceleration constant, be worth between 0 ~ 2; r _1j, r _1jbe respectively two separate random numbers, be worth between 0 ~ 1; P _gjt () represents jth dimension optimal location particle;

4. judge whether to reach iterations, otherwise continue to repeat 2. 3.;

5. optimal location is exported.

Object of the present invention can also be realized further by following technical measures:

Aforementioned radar network composite disposition optimization method, when calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, FDR coefficient, with frequently, is set to 1, calculates by following formula by all radars:

$P_{rn}=\frac{P_{n1}}{{\mathrm{FDR}}_{n1}}+\frac{P_{n2}}{{\mathrm{FDR}}_{n2}}+...+\frac{P_{n(n-1)}}{{\mathrm{FDR}}_{n(n-1)}}+\frac{P_{n(n+1)}}{{\mathrm{FDR}}_{n(n+1)}}+...+\frac{P_{nN}}{{\mathrm{FDR}}_{nN}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}$

Aforementioned radar network composite disposition optimization method, when calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, all radars are non-with frequently with frequency range, then press workflow management radar electromagnetic compatibility degree after first calculating FDR coefficient.

Aforementioned radar network composite disposition optimization method, when calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, all radars are non-with frequently with frequency mixing with frequency range, non-with frequently calculating FDR coefficient with frequency range, with frequently FDR coefficient is set to 1 after by workflow management radar electromagnetic compatibility degree.

Aforementioned radar network composite disposition optimization method, when calculating radar electromagnetic compatibility degree, if there is the radar system of Y frequency range, calculate the electromagnetic compatibility degree of each system according to same frequency range, and then be calculated as follows total electromagnetic compatibility degree of radar system of Y frequency range:

Compared with prior art, the invention has the beneficial effects as follows: using the electromagnetic compatibility between radar and space coverage coefficient as radar optimization aim, in conjunction with optimized algorithm to radar frequently, non-with radar frequently, with frequently and same frequency range is non-to mix mutually with radar frequently and radar fence that the radar of multiband forms is optimized deployment with frequency range.The present invention takes into account the spatial coverage of radar and the electromagnetic compatibility of radar, makes radar network composite under complex electromagnetic environment, have good compatible operations ability and good working effect.

Accompanying drawing explanation

Fig. 1 is aligning scope simulation figure of the present invention.

Embodiment

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

A radar fence is made up of with frequency radar with frequency or with frequency range is non-N portion, selects a kind of optimum deployment scheme, makes the warning region G of gained energy close to required warning region A _gand detection probability reaches requirement P _dg, make territory, the focus detecting area C of gained also can detect spatial domain A close to required emphasis largely simultaneously _cand detection probability reaches detection requires P _dc, and, the electromagnetic compatibility degree Φ of radar _alwaysmore high better.This problem belongs to multi-objective optimization question, and its step is as follows:

Step 1: set up spatial domain Modulus Model:

(1) dispose the geographic position of each portion radar, to obtain maximum spatial domain detectivity f, its mathematical model is as follows:

$f=\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j\&lsqb;(1-\mathrm{\&lambda;})\frac{G_j}{A_g}+\mathrm{\&lambda;}\frac{C_j}{A_c}\&rsqb;,$

λ, w _j∈ [0,1] and

$G_j=\underset{i=1}{\overset{N}{\&cup;}}{A}_{ij}\&cap;A_g$

Wherein, G _jfor the warning region obtained at jth height layer, A _ijbe the search coverage of i-th radar at jth height layer; M is highl stratification number; λ is the significance level of the Party A's target in territory, focus detecting area, and its value, in [0,1] scope, is determined according to actual requirement; w _j(j=1,2 ..., M) and for radar fence is to the degree of attentiveness of each height layer, for dissimilar Party B's target, this weighting coefficient is determined by the flying height of Party B's target; Choose one group of w _j(j=1,2 ..., M), make radar fence effectively resist low latitude, hedgehopping target; C _jfor the territory, focus detecting area obtained at jth height layer, detection probability is:

$P=1-\underset{i=1}{\overset{N}{\&Pi;}}(1-P_i)$

Wherein: P _iit is the detection probability of i-th radar; N is radar network number;

(2) make for security area coverage coefficient, attach most importance to area coverage fraction, carrying out simplification to the formula of maximum spatial domain detectivity f can obtain:

$f=\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j\&lsqb;(1-\mathrm{\&lambda;})C_{gj}+{\mathrm{\&lambda;C}}_{ej}\&rsqb;,$

λ, w _j∈ [0,1] and

Step 2: set up electromagnetic compatibility Degree Model:

1. identical working frequency range is non-with electromagnetic compatibility model time frequently

Time noiseless, the maximum operating range of radar is:

$R_{max}={\left(\frac{{\mathrm{PG}}^2{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{S}_{min}L}\right)}^{1/4}$

In formula, P is the emissive power of radar, and G is radar antenna gain, and λ is radar emission electromagnetic wavelength, and σ is Target scatter section area, S _minfor radar minimum detectable signal, L is radar emission and receives the energy loss in electromagnetic wave process;

The dB unit expression formula of L is:

L _(dB)＝L′ _(dB)+L _r(dB)+L _P(dB)

In formula, L ' is atmospheric absorption loss, sleet loss, two radars the various loss such as radome loss, feeder line loss and, unit dB; L _ppolarization loss, i.e. the loss of the difference introducing of two polarization radar modes, modern radar adopts linear polarization mostly, if two polarization radar modes are identical, polarization loss gets 0dB, otherwise gets 20dB; L _r(=32.5+20lgf+20lgR) is electromagnetic wave space propagation loss, and unit is dB; F is frequency, and unit is MHz; R is propagation distance, unit K m;

N portion radar works simultaneously, and there is co-channel interference; The impact on unwanted emission machine emission spectrum rejection coefficient FDR that the selectivity curve that the interference that radar n receives other radars is subject to receiver produces, this coefficient (FDR) can by international standard " frequency and distance interval ", and standard No. is that the suggestion of ITU-RSM.337-6 draws:

$FDR\left(\mathrm{\&Delta;}f\right)=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H(f+\mathrm{\&Delta;}f){|}^{2}df}dB$

Wherein, P (f) is the power spectrum density of undesired signal equivalence medium-frequency IF; The frequency response that H (f) is receiver; Δ f=ft – fr, wherein, ft is the real-time frequency of interference source; Fr is the tuned frequency of receiver;

FDR can be divided into two, and tuning suppression OTR and frequency detuning suppress OFR, and frequency detuning suppression OFR is the extra suppression because interference source and receiver off resonance produce;

FDR(Δf)＝OTR+OFR(Δf)dB

Wherein:

$OTR=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H\left(f\right){|}^{2}df}dB;OFR\left(\mathrm{\&Delta;}f\right)=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H\left(f\right){|}^{2}df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H(f+\mathrm{\&Delta;}f){|}^{2}df}dB$

N-th radar receives the interference P of other radars _rnbe expressed as:

$P_{rn}=\frac{P_{n1}}{{\mathrm{FDR}}_{n1}}+\frac{P_{n2}}{{\mathrm{FDR}}_{n2}}+...+\frac{P_{n(n-1)}}{{\mathrm{FDR}}_{n(n-1)}}+\frac{P_{n(n+1)}}{{\mathrm{FDR}}_{n(n+1)}}+...+\frac{P_{nN}}{{\mathrm{FDR}}_{nN}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}$

In formula, P _ifor the emissive power of adjacent interference radar i, G _ifor the antenna gain of adjacent interference radar i, G ' _nfor being disturbed the antenna receiving gain of radar n, γ _nfor radar i undesired signal is to the polarization coefficient of radar n receiving antenna, R _infor radar i and the spacing being disturbed radar n, L _infor the electromagnetic wave of radar i transmitting is by the energy loss in radar n receiving course; FDR _nibe the frequency dependence rejection coefficient of i-th radar jamming to radar n, being general value here, is not dB value; λ _tiit is the wavelength of i-th interference radar; If two radars are with frequently, then FDR coefficient is 1;

The echo signal power P that radar n receives _rsfor:

$P_{rs}=\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R}_n^4{L}_n}$

In formula, R _nfor the distance of radar n and target, λ _tnfor the wavelength of radar n;

Be disturbed under condition, radar is wanted find target, the echo signal power P received _rswith the jamming power P received _rjmust meet the following conditions:

$\frac{P_{rj}}{P_{rs}}=\frac{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R}_n^4{L}_n}}\&le;K_n$

In formula, K _nit is the blanket factor of the n-th radar;

Work as P _rj/ S _{(n) min}≤ K _ntime, the maximum operating range of radar is unaffected; Work as P _rj/ S _{(n) min}> K _ntime, the maximum radar range R ' under disturbing can be obtained _nmax:

$R_{n\max }^{\&prime;}={\left(\frac{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{L}_n}}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{K}_n\right)}^{1/4}$

It is normalized, with the R ' when being disturbed _nmaxwith interference-free under R _nmaxratio μ _nas the electromagnetic compatibility degree of radar n; Obtain:

${\mathrm{\&mu;}}_n=\left\{\begin{array}{cc}1,& P_{rj}/S_{\left(n\right)\min }\&le;K_n\\ \frac{R_{n\max }^{\&prime;}}{R_{n\max }}={\left(\frac{\frac{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{L}_n}}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{K}_n}{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{S}_{n\min }{L}_n}}\right)}^{1/4}={\left(\frac{S_{n\min }{K}_n}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}\right)}^{1/4},& P_{rj}/S_{\left(n\right)\min }>K_n\end{array}\right.$

2. disturbed radar can be aligned

When being aimed at by radar antenna, receiver front end there will be overload phenomenon, and electromagnetic compatibility degree is very poor, can think electromagnetic compatibility degree μ=0;

If disturbed radar two, in the sweep limit of interference radar one or two radar, will consider that radar a pair radar two is to punctual situation.Suppose radar one, the distance of radar two is R ₁₂, be centre of sphere R with radar one ₁₂for radius makes a sphere, radar two is made to drop on sphere, with the horizontal scan angle of radar one with pitching scanning angle θ ₁its scan area is showed.Same method will aim at the limit surface product representation of radar two out as shown in Figure 1.

In figure, stain place is radar two position 1, and minimum circle is the limit aligning area W2 of wave beam sometime, the limit is aimed at area W2 along radar two position 1 translation one circle, all scope V3 obtained; Circle maximum in figure is radar scanning scope U4.

Probability of interference p ₂₁for:

$\frac{U\&cap;V}{U}=p_{21}$

The area equivalent of curved surface U is: curved surface V is an ellipse, and its equivalent area is: $4R_{12}^2\&CenterDot;{\mathrm{sin\&alpha;}}_1\&CenterDot;{\mathrm{sin\&beta;}}_1\&ap;4R_{12}^2\&CenterDot;{\mathrm{\&alpha;}}_1\&CenterDot;{\mathrm{\&beta;}}_1$ If v '=4 α ₁β ₁, obtain:

$\frac{U}{U^{\&prime;}}=\frac{V}{V^{\&prime;}}\&DoubleRightArrow;\frac{U}{V}=\frac{U^{\&prime;}}{V^{\&prime;}}\&DoubleRightArrow;\frac{U\&cap;V}{U}=\frac{U^{\&prime;}\&cap;V^{\&prime;}}{U^{\&prime;}}=p_{21}$

Therefore, p ₂₁end value and radar one, distance between radar two have nothing to do;

Be provided with M radar can aim at radar n; Radar i is to the aligning probability of radar n:

$\frac{U^{\&prime;}\&cap;{V_i}^{\&prime;}}{U^{\&prime;}}=p_{ni}$

The probability that radar n is not aligned for:

${\stackrel{\&OverBar;}{p}}_n=1-\underset{i=1}{\overset{M}{\&Sigma;}}{p}_{ni}$

So its electromagnetic compatibility degree μ ' _n:

${\mathrm{\&mu;}}_n^{\&prime;}=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{p}}_n,& P_{rj}/S_{\left(n\right)\min }\&le;K_n\\ {\stackrel{\&OverBar;}{p}}_n\frac{R_{n\max }^{\&prime;}}{R_{n\max }}={\stackrel{\&OverBar;}{p}}_n{\left(\frac{S_{n\min }{K}_n}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}\right)}^{1/4},& P_{rj}/S_{\left(n\right)\min }>K_n\end{array}\right.$

3. radar is disturbed can mutually to aim at disturbed radar

When the main lobe wave beam of two radars can be aimed at mutually time, both needed to avoid also needing to avoid aiming at other antennas to the aligning of other antennas;

Two radars are mutually aimed at and are needed level orientation and pitching orientation all to aim at, and its probability is:

$p_{\mathrm{\&upsi;}}=\frac{{\mathrm{\&beta;}}_1}{{\mathrm{\&theta;}}_1}\&times;\frac{{\mathrm{\&beta;}}_2}{{\mathrm{\&theta;}}_2}$

In formula, P _hfor level orientation aims at probability; α ₁, α ₂for the antenna beamwidth of radar one and radar two; for the angle in radar one, radar two antenna horizontal scanning region; P _υfor pitching alignment of orientation probability; β ₁, β ₂radar one and radar two pitching beam angle; θ ₁, θ ₂for the sweep limit of the angle of pitch;

The aligning Probability p of radar one and radar two ' ₁₂be exactly the probability of alignment of orientation aims at probability product with pitching, that is:

p′ ₁₂＝p _h×p _υ

Then, suppose that beam radar m can aim between two with L beam radar, the mutual misalignment probability of available radar m and other radars for:

${\stackrel{\&OverBar;}{p}}_m=1-\underset{j=1}{\overset{J}{\&Sigma;}}(p_{mj}+p_{jm}-p_{mj}^{\&prime;})$

Wherein, p _mjbe the aligning probability of radar j to radar m, can be drawn by probability model; p _jmthe aligning probability of radar m to radar j; P ' _mjit is the mutual aligning probability of radar m, j;

So its electromagnetic compatibility degree μ " _m:

${\mathrm{\&mu;}}_m^{\&prime;\&prime;}=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{p}}_m,& P_{rj}/S_{\left(m\right)\min }\&le;K_m\\ {\stackrel{\&OverBar;}{p}}_m\frac{R_{m\max }^{\&prime;}}{R_{m\max }}={\stackrel{\&OverBar;}{p}}_m{\left(\frac{S_{m\min }{K}_m}{\underset{i=1}{\overset{T}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_m^{\&prime;}{\mathrm{\&lambda;}}^2{\mathrm{\&gamma;}}_m}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{im}^2{L}_{im}}}\right)}^{1/4},& P_{rj}/S_{\left(m\right)\min }>K_m\end{array}\right.$

4. similar frequency bands radar composition system between electromagnetic compatibility model

The radar of all same frequencys is formed a system, predict the electromagnetic compatibility degree of whole radar system; Suppose always to have N portion radar, K radar can aim at other radars, wherein has M radar to aim between two, then total electromagnetic compatibility degree is:

In formula, η _iit is the significant coefficient of i-th radar;

5. the electromagnetic compatibility model of all frequency range radar systems

Radar system with frequency range has Y, and the electromagnetic compatibility degree of so all same frequency radar systems is:

Step 3: application particle cluster algorithm:

1. construct initialization population, namely the number of particle, initial position and initial speed are set

First X is used _ispace representation n ties up the current location of the particle i of search volume; Use V _irepresent the flying speed of current particle; Use P _irepresent the desired positions that current particle experiences;

$\left\{\begin{array}{c}{X}_i=(x_{i1},x_{i2},...,x_{in})\\ V_i=(v_{i1},v_{i2},...,v_{in})\\ P_i=(p_{i1},p_{i2},...,p_{in})\end{array}\right.$

Wherein, n represents dimension; I represents i-th particle and current particle;

2. using electromagnetic compatibility degree Φ and coverage coefficient as maximized target fitness function, then the current desired positions of particle i is:

Wherein, t represents the t time iteration;

If population is S in colony, compares the desired positions of all particle experience in colony, global optimum position P can be obtained _g(t), that is:

P _g(t)∈{P ₀(t),P ₁(t),...,P _S(t)}|f(P _g(t))＝max{f(P ₀(t)),f(P ₁(t)),...,f(P _S(t))}

3. according to speed and the position of the current and global optimum's position calculation renewal obtained before:

v _ij(t+1)＝w·v _ij(t)+c ₁r _1j(t)·(P _ij(t)-x _ij(t))+c ₂r _2j(t)·(P _gj(t)-x _ij(t))

x _ij(t+1)＝x _ij(t)+v _ij(t+1)

Wherein, x _ij(t), v _ijt () represents that particle i jth ties up position and the movement velocity in t generation; W is inertial coefficient, is worth between 0-1; c ₁, c ₂for acceleration constant, be worth between 0-2; r _1j, r _1jbe respectively two separate random numbers, be worth between 0-1; P _gjt () represents jth dimension optimal location particle;

4. judge whether to reach iterations, otherwise continue to repeat 2. 3.;

5. optimal location is exported.

This radar network composite disposition optimization method, when calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, FDR coefficient, with frequently, is set to 1, calculates by following formula by all radars:

$P_{rn}=\frac{P_{n1}}{{\mathrm{FDR}}_{n1}}+\frac{P_{n2}}{{\mathrm{FDR}}_{n2}}+...+\frac{P_{n(n-1)}}{{\mathrm{FDR}}_{n(n-1)}}+\frac{P_{n(n+1)}}{{\mathrm{FDR}}_{n(n+1)}}+...+\frac{P_{nN}}{{\mathrm{FDR}}_{nN}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}$

When calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, all radars are non-with frequently with frequency range, then press workflow management radar electromagnetic compatibility degree after first calculating FDR coefficient.

When calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, all radars with frequency range non-with frequently with frequently mix, non-with frequently calculating FDR coefficient with frequency range, with frequency FDR coefficient is set to 1 after by workflow management radar electromagnetic compatibility degree.

When calculating radar electromagnetic compatibility degree, if there is the radar system of Y frequency range, calculate the electromagnetic compatibility degree of each system according to same frequency range, and then be calculated as follows total electromagnetic compatibility degree of radar system of Y frequency range:

In addition to the implementation, the present invention can also have other embodiments, and all employings are equal to the technical scheme of replacement or equivalent transformation formation, all drop in the protection domain of application claims.

Claims (5)

1. a radar network composite disposition optimization method, radar fence is by N portion with frequently or with frequency range is non-forming with frequency radar, and it is characterized in that, step is as follows:

Step 1: set up spatial domain Modulus Model:

(1) dispose the geographic position of each portion radar, to obtain maximum spatial domain detectivity f, its mathematical model is as follows:

$f=\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j\&lsqb;(1-\mathrm{\&lambda;})\frac{G_j}{A_g}+\mathrm{\&lambda;}\frac{C_j}{A_c}\&rsqb;,$

λ, w _j∈ [0,1] and $\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j=1$

$G_j=\underset{i=1}{\overset{N}{\&cup;}}{A}_{ij}\&cap;A_g$

Wherein, G _jfor the warning region obtained at jth height layer, A _ijbe the search coverage of i-th radar at jth height layer; M is highl stratification number; λ is the significance level of the Party A's target in territory, focus detecting area, and its value, in [0,1] scope, is determined according to actual requirement; w _j(j=1,2 ..., M) and for radar fence is to the degree of attentiveness of each height layer, for dissimilar Party B's target, this weighting coefficient is determined by the flying height of Party B's target; Choose one group of w _j(j=1,2 ..., M), make radar fence effectively resist low latitude, hedgehopping target; C _jfor the territory, focus detecting area obtained at jth height layer, detection probability is:

$P=1-\underset{i=1}{\overset{N}{\&Pi;}}(1-P_i)$

Wherein: P _iit is the detection probability of i-th radar; N is radar network number;

(2) make for security area coverage coefficient, attach most importance to area coverage fraction, carrying out simplification to the formula of maximum spatial domain detectivity f can obtain:

$f=\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j\&lsqb;(1-\mathrm{\&lambda;})C_{gj}+{\mathrm{\&lambda;C}}_{ej}\&rsqb;,$

λ, w _j∈ [0,1] and $\underset{j=1}{\overset{M}{\&Sigma;}}{w}_j=1$

Step 2: set up electromagnetic compatibility Degree Model:

1. identical working frequency range is non-with electromagnetic compatibility model time frequently

Time noiseless, the maximum operating range of radar is:

$R_{max}={\left(\frac{{\mathrm{PG}}^2{\mathrm{\&lambda;}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{S}_{min}L}\right)}^{1/4}$

In formula, P is the emissive power of radar, and G is radar antenna gain, and λ is radar emission electromagnetic wavelength, and σ is Target scatter section area, S _minfor radar minimum detectable signal, L is radar emission and receives the energy loss in electromagnetic wave process;

The dB unit expression formula of L is:

L _(dB)＝L' _(dB)+L _r(dB)+L _P(dB)

In formula, L' be atmospheric absorption loss, sleet loss, two radars the various loss such as radome loss, feeder line loss and, unit dB; L _ppolarization loss, i.e. the loss of the difference introducing of two polarization radar modes, modern radar adopts linear polarization mostly, if two polarization radar modes are identical, polarization loss gets 0dB, otherwise gets 20dB; L _r(=32.5+20lgf+20lgR) is electromagnetic wave space propagation loss, and unit is dB; F is frequency, and unit is MHz; R is propagation distance, unit K m;

N portion radar works simultaneously, and there is co-channel interference; The impact on unwanted emission machine emission spectrum rejection coefficient FDR that the selectivity curve that the interference that radar n receives other radars is subject to receiver produces:

$FDR\left(\mathrm{\&Delta;}f\right)=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H(f+\mathrm{\&Delta;}f){|}^{2}df}dB$

Wherein, P (f) is the power spectrum density of undesired signal equivalence medium-frequency IF; The frequency response that H (f) is receiver; Δ f=ft – fr, wherein, ft is the real-time frequency of interference source; Fr is the tuned frequency of receiver;

FDR can be divided into two, and tuning suppression OTR and frequency detuning suppress OFR, and frequency detuning suppression OFR is the extra suppression because interference source and receiver off resonance produce;

FDR(Δf)＝OTR+OFR(Δf)dB

Wherein:

$OTR=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H\left(f\right){|}^{2}df}dB;OFR\left(\mathrm{\&Delta;}f\right)=10log\frac{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H\left(f\right){|}^{2}df}{\underset{0}{\overset{\mathrm{\&infin;}}{\&Integral;}}P\left(f\right)|H(f+\mathrm{\&Delta;}f){|}^{2}df}dB$

N-th radar receives the interference P of other radars _rnbe expressed as:

$P_{rn}=\frac{P_{n1}}{{\mathrm{FDR}}_{n1}}+\frac{P_{n2}}{{\mathrm{FDR}}_{n2}}+...+\frac{P_{n(n-1)}}{{\mathrm{FDR}}_{n(n-1)}}+\frac{P_{n(n+1)}}{{\mathrm{FDR}}_{n(n+1)}}+...+\frac{P_{nN}}{{\mathrm{FDR}}_{nN}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}$

In formula, P _ifor the emissive power of adjacent interference radar i, G _ifor the antenna gain of adjacent interference radar i, G' _nfor being disturbed the antenna receiving gain of radar n, γ _nfor radar i undesired signal is to the polarization coefficient of radar n receiving antenna, R _infor radar i and the spacing being disturbed radar n, L _infor the electromagnetic wave of radar i transmitting is by the energy loss in radar n receiving course; FDR _nibe the frequency dependence rejection coefficient of i-th radar jamming to radar n, being general value here, is not dB value; λ _tiit is the wavelength of i-th interference radar; If two radars are with frequently, then FDR coefficient is 1;

The echo signal power P that radar n receives _rsfor:

$P_{rs}=\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R}_n^4{L}_n}$

In formula, R _nfor the distance of radar n and target, λ _tnfor the wavelength of radar n;

Be disturbed under condition, radar is wanted find target, the echo signal power P received _rswith the jamming power P received _rjmust meet the following conditions:

$\frac{P_{rj}}{P_{rs}}=\frac{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{R}_n^4{L}_n}}\&le;K_n$

In formula, K _nit is the blanket factor of the n-th radar;

Work as P _rj/ S _{(n) min}≤ K _ntime, the maximum operating range of radar is unaffected; Work as P _rj/ S _{(n) min}> K _ntime, the maximum radar range R' under disturbing can be obtained _nmax:

$R_{n\max }^{\&prime;}={\left(\frac{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{L}_n}}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{K}_n\right)}^{1/4}$

It is normalized, with R' when being disturbed _nmaxwith interference-free under R _nmaxratio μ _nas the electromagnetic compatibility degree of radar n; Obtain:

${\mathrm{\&mu;}}_n=\left\{\begin{array}{cc}1,& P_{rj}/S_{\left(n\right)\min }\&le;K_n\\ \frac{R_{n\max }^{\&prime;}}{R_{n\max }}={\left(\frac{\frac{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{L}_n}}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}{K}_n}{\frac{P_n{G}_n^2{{\mathrm{\&lambda;}}_{rn}}^2\mathrm{\&sigma;}}{{\left(4\mathrm{\&pi;}\right)}^3{S}_{n\min }{L}_n}}\right)}^{1/4}={\left(\frac{S_{n\min }{K}_n}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}\right)}^{1/4},& P_{rj}/S_{\left(n\right)\min }>K_n\end{array}\right.$

2. disturbed radar can be aligned

When being aimed at by radar antenna, receiver front end there will be overload phenomenon, and electromagnetic compatibility degree is very poor, can think electromagnetic compatibility degree μ=0;

If disturbed radar two is in the sweep limit of interference radar one or two radar, then consider that radar a pair radar two is to punctual situation; Suppose radar one, the distance of radar two is R ₁₂, be centre of sphere R with radar one ₁₂for radius makes a sphere, radar two is made to drop on sphere, with the horizontal scan angle of radar one with pitching scanning angle θ ₁its scan area is showed; Around radar two, radar one is aimed at the limit surface product representation of radar two out;

Probability of interference p ₂₁for:

$\frac{U\&cap;V}{U}=p_{21}$

Wherein W is the limit aligning area of wave beam sometime, and enclosed along radar two position translation one by W, all scopes obtained are V; U is radar scanning scope;

The area equivalent of curved surface U is: curved surface V is an ellipse, and its equivalent area is: $4R_{12}^2\&CenterDot;{\mathrm{sin\&alpha;}}_1\&CenterDot;{\mathrm{sin\&beta;}}_1\&ap;4R_{12}^2\&CenterDot;{\mathrm{\&alpha;}}_1\&CenterDot;{\mathrm{\&beta;}}_1$ If v'=4 α ₁β ₁, obtain:

$\frac{U}{U^{\&prime;}}=\frac{V}{V^{\&prime;}}\&DoubleRightArrow;\frac{U}{V}=\frac{U^{\&prime;}}{V^{\&prime;}}\&DoubleRightArrow;\frac{U\&cap;V}{U}=\frac{U^{\&prime;}\&cap;V^{\&prime;}}{U^{\&prime;}}=p_{21}$

Therefore, p ₂₁end value and radar one, distance between radar two have nothing to do;

Be provided with M radar can aim at radar n; Radar i is to the aligning probability of radar n:

$\frac{U^{\&prime;}\&cap;{V_i}^{\&prime;}}{U^{\&prime;}}=p_{ni}$

The probability that radar n is not aligned for:

${\stackrel{\&OverBar;}{p}}_n=1-\underset{i=1}{\overset{M}{\&Sigma;}}{p}_{ni}$

So its electromagnetic compatibility degree μ ' _n:

${\mathrm{\&mu;}}_n^{\&prime;}=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{p}}_n,& P_{rj}/S_{\left(n\right)\min }\&le;K_n\\ {\stackrel{\&OverBar;}{p}}_n\frac{R_{n\max }^{\&prime;}}{R_{n\max }}={\stackrel{\&OverBar;}{p}}_n{\left(\frac{S_{n\min }{K}_n}{\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}}\right)}^{1/4},& P_{rj}/S_{\left(n\right)\min }>K_n\end{array}\right.$

3. radar is disturbed can mutually to aim at disturbed radar

When the main lobe wave beam of two radars can be aimed at mutually time, both needed to avoid also needing to avoid aiming at other antennas to the aligning of other antennas;

Two radars are mutually aimed at and are needed level orientation and pitching orientation all to aim at, and its probability is:

$p_{\mathrm{\&upsi;}}=\frac{{\mathrm{\&beta;}}_1}{{\mathrm{\&theta;}}_1}\&times;\frac{{\mathrm{\&beta;}}_2}{{\mathrm{\&theta;}}_2}$

In formula, P _hfor level orientation aims at probability; α ₁, α ₂for the antenna beamwidth of radar one and radar two; for the angle in radar one, radar two antenna horizontal scanning region; P _υfor pitching alignment of orientation probability; β ₁, β ₂radar one and radar two pitching beam angle; θ ₁, θ ₂for the sweep limit of the angle of pitch;

The aligning Probability p of radar one and radar two ' ₁₂be exactly the probability of alignment of orientation aims at probability product with pitching, that is:

p' ₁₂＝p _h×p _υ

Then, suppose that beam radar m can aim between two with L beam radar, the mutual misalignment probability of available radar m and other radars for:

${\stackrel{\&OverBar;}{p}}_m=1-\underset{j=1}{\overset{J}{\&Sigma;}}(p_{mj}+p_{jm}-p_{mj}^{\&prime;})$

Wherein, p _mjbe the aligning probability of radar j to radar m, can be drawn by probability model; p _jmthe aligning probability of radar m to radar j; P' _mjit is the mutual aligning probability of radar m, j;

So its electromagnetic compatibility degree μ " _m:

${\mathrm{\&mu;}}_m^{\&prime;\&prime;}=\left\{\begin{array}{cc}{\stackrel{\&OverBar;}{p}}_m,& P_{rj}/S_{\left(m\right)\min }\&le;K_m\\ {\stackrel{\&OverBar;}{p}}_m\frac{R_{m\max }^{\&prime;}}{R_{m\max }}={\stackrel{\&OverBar;}{p}}_m{\left(\frac{S_{m\min }{K}_m}{\underset{i=1}{\overset{T}{\&Sigma;}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_m^{\&prime;}{\mathrm{\&lambda;}}^2{\mathrm{\&gamma;}}_m}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{im}^2{L}_{im}}}\right)}^{1/4},& P_{rj}/S_{\left(m\right)\min }>K_m\end{array}\right.$

4. similar frequency bands radar composition system between electromagnetic compatibility model

The radar of all same frequencys is formed a system, predict the electromagnetic compatibility degree of whole radar system; Suppose always to have N portion radar, K radar can aim at other radars, wherein has M radar to aim between two, then total electromagnetic compatibility degree is:

In formula, η _iit is the significant coefficient of i-th radar;

5. the electromagnetic compatibility model of all frequency range radar systems

Radar system with frequency range has Y, and the electromagnetic compatibility degree of so all same frequency radar systems is:

Step 3: application particle cluster algorithm:

1. construct initialization population, namely the number of particle, initial position and initial speed are set

First X is used _ispace representation n ties up the current location of the particle i of search volume; Use V _irepresent the flying speed of current particle; Use P _irepresent the desired positions that current particle experiences;

$\left\{\begin{array}{c}{X}_i=(x_{i1},x_{i2},...,x_{in})\\ V_i=(v_{i1},v_{i2},...,v_{in})\\ P_i=(p_{i1},p_{i2},...,p_{in})\end{array}\right.$

Wherein, n represents dimension; I represents i-th particle and current particle;

2. using electromagnetic compatibility degree Φ and coverage coefficient as maximized target fitness function, then the current desired positions of particle i is:

Wherein, t represents the t time iteration;

If population is S in colony, compares the desired positions of all particle experience in colony, global optimum position P can be obtained _g(t),

That is:

P _g(t)∈{P ₀(t),P ₁(t),...,P _S(t)}|f(P _g(t))＝max{f(P ₀(t)),f(P ₁(t)),...,f(P _S(t))}

3. according to speed and the position of the current and global optimum's position calculation renewal obtained before:

v _ij(t+1)＝w·v _ij(t)+c ₁r _1j(t)·(P _ij(t)-x _ij(t))+c ₂r _2j(t)·(P _gj(t)-x _ij(t))

x _ij(t+1)＝x _ij(t)+v _ij(t+1)

Wherein, x _ij(t), v _ijt () represents that particle i jth ties up position and the movement velocity in t generation; W is inertial coefficient, is worth between 0 ~ 1; c ₁, c ₂for acceleration constant, be worth between 0 ~ 2; r _1j, r _1jbe respectively two separate random numbers, be worth between 0 ~ 1; P _gjt () represents jth dimension optimal location particle;

4. judge whether to reach iterations, otherwise continue to repeat 2. 3.;

5. optimal location is exported.

2. radar network composite disposition optimization method as claimed in claim 1, is characterized in that, when calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, FDR coefficient, with frequently, is set to 1, calculates by following formula by all radars:

$P_{rn}=\frac{P_{n1}}{{\mathrm{FDR}}_{n1}}+\frac{P_{n2}}{{\mathrm{FDR}}_{n2}}+...+\frac{P_{n(n-1)}}{{\mathrm{FDR}}_{n(n-1)}}+\frac{P_{n(n+1)}}{{\mathrm{FDR}}_{n(n+1)}}+...+\frac{P_{nN}}{{\mathrm{FDR}}_{nN}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\mathrm{\&Sigma;}}}\frac{1}{{\mathrm{FDR}}_{ni}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}=\underset{i=1,i\&NotEqual;n}{\overset{N}{\&Sigma;}}\frac{P_i{G}_i{G}_n^{\&prime;}{{\mathrm{\&lambda;}}_{ti}}^2{\mathrm{\&gamma;}}_n}{{\left(4\mathrm{\&pi;}\right)}^2{R}_{in}^2{L}_{in}}$

3. radar network composite disposition optimization method as claimed in claim 1, it is characterized in that, when calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, all radars are non-with frequently with frequency range, then press workflow management radar electromagnetic compatibility degree after first calculating FDR coefficient.

4. radar network composite disposition optimization method as claimed in claim 1, it is characterized in that, when calculating radar electromagnetic compatibility degree, if only have a frequency range radar system and Y=1, all radars are non-with frequently with frequency mixing with frequency range, non-with frequently calculating FDR coefficient with frequency range, with frequently FDR coefficient is set to 1 after by workflow management radar electromagnetic compatibility degree.

5. radar network composite disposition optimization method as claimed in claim 1, it is characterized in that, when calculating radar electromagnetic compatibility degree, if there is the radar system of Y frequency range, calculate the electromagnetic compatibility degree of each system according to same frequency range, and then be calculated as follows total electromagnetic compatibility degree of radar system of Y frequency range: