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work.m
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work.m
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%clc, clear all
a1 = 0.01:0.01:0.4; %Size of Scatterers (sm)
lya1 = 0.2; %Wavelength (sm)
f = 30./lya1; %Frequency (GHz)
X1 = 2.*pi.*a1./lya1;
t1 = 20; %Temperature in degrees Celsius
lyas1 = 1.4662.*exp(-0.0634.*t1)+0.000136.*t1.*t1-0.027296.*t1+1.8735116; %лямбда эстое
e011 = 5.5; %эпсилон
es11 = 0.00081.*t1.*t1-0.40885.*t1+88.2; %эпсилон эстое
e111 = e011+((es11-e011)./(1+((lyas1./lya1).*(lyas1./lya1)))); %эпсилон первое
e211 = ((es11-e011).*(lyas1./lya1))./(1+((lyas1./lya1).*(lyas1./lya1))); %эпсилон второе
m111 = sqrt((e111+sqrt(e111.*e111+e211.*e211))./2);
m211 = sqrt((-e111+sqrt(e111.*e111+e211.*e211))./2);
m1 = m111-1i.*m211;
Y1 = X1.*m1;
k1 = 2.*pi./lya1;
for kk1 = 1:length(X1)
XX1 = X1(kk1); % берётся значение к-го элемента массива Х, с ним идёт цикл по Nmax
Nmax1 = round(XX1+4.*(XX1.^(1./3))+2);
massPsix1(1) = (sin(XX1)./XX1)-cos(XX1);
massPsix1(2) = (3./XX1).*((sin(XX1)./XX1)-cos(XX1))-sin(XX1);
massHex1(1) = (cos(XX1)./XX1)+sin(XX1);
massHex1(2) = (3./XX1).*((cos(XX1)./XX1)+sin(XX1))-cos(XX1);
massPsiSx1(1) = sin(XX1)-(1/XX1).*((sin(XX1)./XX1)-cos(XX1));
massPsiSx1(2) = (sin(XX1)./XX1)-cos(XX1)-(2./XX1).*((3./XX1).*((sin(XX1)./XX1)-cos(XX1))-sin(XX1));
massHeSx1(1) = cos(XX1)-(1/XX1).*((cos(XX1)./XX1)+sin(XX1));
massHeSx1(2) = (cos(XX1)./XX1)+sin(XX1)-(2./XX1).*((3./XX1).*((cos(XX1)./XX1)+sin(XX1))-cos(XX1));
for n1 = 2:Nmax1
massPsix1(n1+1) = ((2.*n1+1)./XX1).*massPsix1(n1)-massPsix1(n1-1);
massHex1(n1+1) = ((2.*n1+1)./XX1).*massHex1(n1)-massHex1(n1-1);
massPsiSx1(n1+1) = massPsix1(n1)-((n1+1)./XX1).*massPsix1(n1+1);
massHeSx1(n1+1) = massHex1(n1)-((n1+1)./XX1).*massHex1(n1+1);
massPsix1_mat(1,kk1) = massPsix1(1);
massPsix1_mat(n1,kk1) = massPsix1(n1);
massHex1_mat(1,kk1) = massHex1(1);
massHex1_mat(n1,kk1) = massHex1(n1);
massPsiSx1_mat(1,kk1) = massPsiSx1(1);
massPsiSx1_mat(n1,kk1) = massPsiSx1(n1);
massHeSx1_mat(1,kk1) = massHeSx1(1);
massHeSx1_mat(n1,kk1) = massHeSx1(n1);
end
end
for kk1 = 1:length(Y1)
YY1 = Y1(kk1); % берётся значение к-го элемента массива Х, с ним идёт цикл по Nmax
XX1 = X1(kk1);
Nmax1 = round(XX1+4.*(XX1.^(1./3))+2);
massPsiy1(1) = (sin(YY1)./YY1)-cos(YY1);
massPsiy1(2) = (3./YY1).*((sin(YY1)./YY1)-cos(YY1))-sin(YY1);
massHey1(1) = (cos(YY1)./YY1)+sin(YY1);
massHey1(2) = (3./YY1).*((cos(YY1)./YY1)+sin(YY1))-cos(YY1);
massPsiSy1(1) = sin(YY1)-(1./YY1).*((sin(YY1)./YY1)-cos(YY1));
massPsiSy1(2) = (sin(YY1)./YY1)-cos(YY1)-(2./YY1).*((3./YY1).*((sin(YY1)./YY1)-cos(YY1))-sin(YY1));
massHeSy1(1) = cos(YY1)-(1./YY1).*((cos(YY1)./YY1)+sin(YY1));
massHeSy1(2) = (cos(YY1)./YY1)+sin(YY1)-(2./YY1).*((3/YY1).*((cos(YY1)./YY1)+sin(YY1))-cos(YY1));
for n1 = 2:Nmax1
massPsiy1(n1+1) = ((2.*n1+1)./YY1).*massPsiy1(n1)-massPsiy1(n1-1);
massHey1(n1+1) = ((2.*n1+1)./YY1)*massHey1(n1)-massHey1(n1-1);
massPsiSy1(n1+1) = massPsiy1(n1)-((n1+1)./YY1)*massPsiy1(n1+1);
massHeSy1(n1+1) = massHey1(n1)-((n1+1)./YY1)*massHey1(n1+1);
massPsiy1_mat(1,kk1) = massPsiy1(1);
massPsiy1_mat(n1,kk1) = massPsiy1(n1);
massHey1_mat(1,kk1) = massHey1(1);
massHey1_mat(n1,kk1) = massHey1(n1);
massPsiSy1_mat(1,kk1) = massPsiSy1(1);
massPsiSy1_mat(n1,kk1) = massPsiSy1(n1);
massHeSy1_mat(1,kk1) = massHeSy1(1);
massHeSy1_mat(n1,kk1) = massHeSy1(n1);
end
end
MAT_DZTX1 = massPsix1_mat + 1i.*massHex1_mat;
MAT_DZTSX1 = massPsiSx1_mat + 1i.*massHeSx1_mat;
MAT_DZTY1 = massPsiy1_mat + 1i.*massHey1_mat;
MAT_DZTSY1 = massPsiSy1_mat + 1i.*massHeSy1_mat;
MAT_An1 = (massPsix1_mat.*massPsiSy1_mat-m1.*massPsiy1_mat.*massPsiSx1_mat)./(MAT_DZTX1.*massPsiSy1_mat-m1.*massPsiy1_mat.*MAT_DZTSX1);
MAT_Bn1 = (m1.*massPsix1_mat.*massPsiSy1_mat-massPsiy1_mat.*massPsiSx1_mat)./(m1.*MAT_DZTX1.*massPsiSy1_mat-massPsiy1_mat.*MAT_DZTSX1);
MAT_An1(isnan(MAT_An1))=0;
MAT_Bn1(isnan(MAT_Bn1))=0;
h = zeros(1,6);
h(1,1) = 0.5;
h(1,2) = h(1,1)/2;
for i = 3:length(h)
h(1,i) = h(1,i-1)/2;
end
theta_1 = 0:h(1,6)*(pi/180):(pi/2); %h(1,6) самое точное ошибка 0.015(1.5%)
for kk = 1:length(theta_1)
theta1 = theta_1(kk); % берётся значение к-го элемента массива theta, с ним идёт цикл по Nmax
massPi1(1) = 1;
massTau1(1) = cos(theta1);
massPi1(2) = 3.*cos(theta1);
massTau1(2) = 6.*cos(theta1).*cos(theta1)-3;
for n1 = 3:Nmax1
massPi1(n1) = ((1./(n1-1)).*(2.*n1-1)).*cos(theta1).*massPi1(n1-1)-(n1./(n1-1)).*massPi1(n1-2);
massTau1(n1) = n1.*cos(theta1).*massPi1(n1)-(n1+1).*massPi1(n1-1);
massPi1_mat(1,kk) = massPi1(1);
massPi1_mat(2,kk) = massPi1(2);
massPi1_mat(n1,kk) = massPi1(n1);
massTau1_mat(1,kk) = massTau1(1);
massTau1_mat(2,kk) = massTau1(2);
massTau1_mat(n1,kk) = massTau1(n1);
end
end
for j = 1:length(a1)
massPi1_mat_s(:,:,j) = massPi1_mat(:,:);
massTau1_mat_s(:,:,j) = massTau1_mat(:,:);
end
for j = 1:length(theta_1)
MAT_An1_s(:,j,:) = MAT_An1(:,:);
MAT_Bn1_s(:,j,:) = MAT_Bn1(:,:);
end
matAP_BT = MAT_An1_s.*massPi1_mat_s + MAT_Bn1_s.*massTau1_mat_s;
matAT_BP = MAT_An1_s.*massTau1_mat_s + MAT_Bn1_s.*massPi1_mat_s;
for j = 1:Nmax1
matN(j,:) = (2.*j+1)./(j.*(j+1));
end
for j = 1:length(a1)
for jj = 1:length(theta_1)
matN_L(:,jj,j) = matN(:);
end
end
matUSf1 = matAP_BT.*matN_L;
matUSf2 = matAT_BP.*matN_L;
ff1 = squeeze(sum((1i./k1).*matUSf1(:,:,:)));
ff2 = -squeeze(sum((1i./k1).*matUSf2(:,:,:)));
ff1_mod = abs(ff1); ff2_mod = abs(ff2);
white1 = ff1_mod.^2 + ff2_mod.^2;
ff2_conj = conj(ff2);
black1 = real(ff1.*ff2_conj);
S_1 = (3/4).*white1 + (1/2).*black1;
I1 = 0:10:100;
%I1 = 10;
for j=1:length(I1)
S__1(:,:,j) = S_1(:,:)';
end
for j=1:length(a1)
I1_a(j,:) = I1(:);
end
for j=1:length(I1)
a1_I(:,j) = a1(:);
end
%w1 = 5.674.*(10.^-5).*(I1_a.^0.324).*((2.*a1_I).^-1.75).*exp(-98.5.*((2.*a1_I).^2.25).*(I1_a.^-0.522)); %distribution of Best
%w1 = 7.3656.*(10^-5).*(I1_a.^0.411).*((2.*a1_I).^-1.71).*exp(-116.97.*((2.*a1_I).^2.29).*(I1_a.^-0.456)); %distribution of Lous-Parsons
%w1 = 0.16.*exp(-41.*(2.*a1_I).*(I1_a.^-0.21)); %distribution of Marshal-Palmer
w1 = 1.25.*(I1_a.^-0.139).*exp(-((113.*a1_I)./(I1_a.^0.175))); %distribution of Polyakovoy-Shifrin
for j = 1:length(theta_1)
w1_2(:,j,:) = w1(:,:);
end
func_und_int = S__1.*w1_2;%alpha/theta/I
%fff1 = squeeze(sum(func_und_int)).*0.01; %взят интеграл по а1 %+
fff = trapz(a1,func_und_int,1);
fg = squeeze(fff);
%______________________________________________________________
ksi = 0.001:0.001:1;
for j = 1:length(ksi)
ffff(:,j,:) = fg(:,:);
end
fffff = squeeze(ffff);
% константы:
g1 = 10; % g1 = 1-10 deg
tettat0 = g1.*(pi/180);
alphaT = 4.*log(2)./(tettat0.^2);
g2 = 10; % g2 = 1-10 deg
tettar0 = g2.*(pi/180);
alphaR = 4.*log(2)./(tettar0.^2);
kh = 1.5823; % 0.2: 1.5823; 0.36: 1.2101; 0.8: 0.3895;
alph = 0.6494; % 0.2: 0.6494; 0.36: 0.7052; 0.8: 0.8817;
GAMMA = kh.*(I1.^(alph));
L = 10;% 1 km = 10^5 sm; L = 1-10;
% 2D сетка координат
[K,T,GAMMAA] = meshgrid(ksi,theta_1,GAMMA);% [..GAMMAA]=..GAMMA
% расчет подынтегральной функции:
F = fffff.*((10^5).*pi.*L.*(T./(K.^2))).*exp(-(T.*T).*alphaT).*exp(-(T.*T).*alphaR.*(((1-K)./K).^2)).*exp(-(T.*T).*((0.1.*log(10).*L.*GAMMAA)./2).*(((1-K)./K)));
% метод трапеций
i1st = trapz(theta_1,F,1);
i_tr = squeeze(squeeze(trapz(ksi,i1st)));
%loglog(I1,i_tr,'*'); %x,s,o,*,d,.,h,:,--,b--o,
%plot(I1,i_tr,'x'); %x,s,o,*,d,.,h,:,--,b--o,
%xlabel('Инстенсивность дождя, мм/ч');
%ylabel('Дисперсия');
%title('Засивимость дисперсии от интенсивности, разные распределения');
text(11,1.1,'Длина трассы(L) 10 км, полуширины по 10 град, длина волны 0.2 см');
%grid on
%legend('длина волны 0.2 см','длина волны 0.36 см','длина волны 0.8 см');
%legend('Бест','Лоус-Парсонс','Маршал-Пальмер', 'Полякова-Шифрин');
hold on