第一讲、雷达基本公式（matlab）

理想公式：

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注意G与入这两个是有关联的，这两个因子，不能说越大，R就越大，后面补充里面讲解（波长越短，增益越大）
所以上述表达式子可以为

如果，在实际情况中，雷达接收信号的回波信号会被噪声污染，在所有雷达频率上引入不想要的电压。
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上述式子，广泛的作为雷达方程
F噪声系数、B雷达带宽、L雷达损失、k波尔兹常数、Te是以K表示的有效噪声温度、R距离、sigma雷达截面积、G天线增益、入波长（1/入雷达频率）

下面是上述雷达公式的函数，中间过程通常转换为dB来计算

%radar  function
function [snr] = radar_eq(pt,freq,g,sigma,te,b,nf,loss,range)
%This is a program of radar eq
c=3.0e+8; %speed of light
lambda =c/freq; %wavelength
p_peak=10*log10(pt);  %convert peak power to dB
lambda_sqdb=10*log10(lambda^2);  %computr wavelength square in dB
sigmadb=10*log10(sigma);%convert sigma to dB
four_pi_cub=10*log10((4*pi)^3);  %(4pi)^3 in dB
k_db=10*log10(1.3e-23);%boltzman's constant in dB
te_db=10*log10(te);  %noisetemp. in dB
b_db=10*log10(b);  %bandwidth in dB
range_pwr4_db=10*log10(range.^4);%vector of target range^4 in dB
%implement Equation(1.56)
num=p_peak+g+g+lambda_sqdb+sigmadb;%分子
den=four_pi_cub+k_db+te_db+b_db+nf+loss+range_pwr4_db;%分母
snr=num-den;
return
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下面是以上述表格的数值，观察，取不同的目标截面积值的效果图
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下面输入不同的峰值功率
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% Use this program to reproduce Fig. 1.12 of text.
close all
clear all
pt = 1.5e+6; % peak power in Watts
freq = 5.6e+9; % radar operating frequency in Hz
g = 45.0; % antenna gain in dB
sigma = 0.1; % radar cross section in m squared
te = 290.0; % effective noise temperature in Kelvins
b = 5.0e+6; % radar operating bandwidth in Hz
nf = 3.0; %noise figure in dB
loss = 6.0; % radar losses in dB
range = linspace(25e3,165e3,1000); % range to target from 25 Km 165 Km, 1000 points
snr1 = radar_eq(pt, freq, g, sigma, te, b, nf, loss, range);
snr2 = radar_eq(pt, freq, g, sigma/10, te, b, nf, loss, range);
snr3 = radar_eq(pt, freq, g, sigma*10, te, b, nf, loss, range);
% plot SNR versus range
figure(1)
rangekm  = range ./ 1000;
plot(rangekm,snr3,'k');
hold on;
plot(rangekm,snr1,'k -.');
hold on;
plot(rangekm,snr2,'k:');
grid %开启网格
legend('\sigma = 0 dBsm','\sigma = -10dBsm','\sigma = -20 dBsm')
xlabel ('Detection range - Km');
ylabel ('SNR - dB');
%下面改变不同的功率峰值

snr1 = radar_eq(pt, freq, g, sigma, te, b, nf, loss, range);

snr2 = radar_eq(pt0.4, freq, g, sigma, te, b, nf, loss, range);

snr3 = radar_eq(pt1.8, freq, g, sigma, te, b, nf, loss, range);

figure (2)

plot(rangekm,snr3,'k',rangekm,snr1,'k -.',rangekm,snr2,'k:')

grid

legend('Pt = 2.16 MW','Pt = 1.5 MW','Pt = 0.6 MW')

xlabel ('Detection range - Km');

ylabel ('SNR - dB');
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工程中一般还用到了，根据SNR来确定脉冲宽度
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% Use this program to reproduce Fig. 1.13 of text.
close all
clear all
pt = 1.e+6; % peak power in Watts
freq = 5.6e+9; % radar operating frequency in Hz
g = 40.0; % antenna gain in dB
sigma = 0.1; % radar cross section in m squared
te =300.0; % effective noise temperature in Kelvins
nf = 5.0; %noise figure in dB
loss = 6.0; % radar losses in dB
range = [75e3,100e3,150e3]; % three range values
snr_db = linspace(5,20,200); % SNR values from 5 dB to 20 dB 200 points
snr = 10.^(0.1.*snr_db); % convert snr into base 10
gain = 10^(0.1*g); %convert antenna gain into base 10
loss = 10^(0.1*loss); % convert losses into base 10
F = 10^(0.1*nf); % convert noise figure into base 10
lambda = 3.e8 / freq; % compute wavelength
den = pt * gain * gain * sigma * lambda^2;

num1 = (4pi)^3 * 1.38e-23 * te * F * loss * range(1)^4 . snr;

num2 = (4pi)^3 * 1.38e-23 * te * F * loss * range(2)^4 . snr;

num3 = (4pi)^3 * 1.38e-23 * te * F * loss * range(3)^4 . snr;

tau1 = num1 ./ den ;

tau2 = num2 ./ den;

tau3 = num3 ./ den;

% plot tau versus snr

figure(1)

semilogy(snr_db,1e6tau1,'k',snr_db,1e6tau2,'k -.',snr_db,1e6*tau3,'k:')

grid

legend('R = 75 Km','R = 100 Km','R = 150 Km')

xlabel ('Minimum required SNR - dB');

ylabel ('\tau (pulse width) in \mu sec');
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可以确定脉冲宽度越宽，相同SNR，测量越远

补充

开尔文温度：

开尔文温度和人们习惯使用的摄氏温度相差一个常数273.15，即T=t+273.15

噪声温度

玻尔兹曼常数：1.3806505(24) × 10^-23 J/K
用法：linspace(x1,x2,N)
其中x1、x2、N分别为起始值、终止值、元素个数。若默认N，默认点数为100。
从下图可以看出linspace和传统的生成点的区别，linspace可以指定生成多少个点，而普通的生成点，能指定步长
legend的用法