基本脈衝和連續波CW雷達操作
雷達距離方程
function [snr] = radar_eq(pt, freq, g, sigma, b, nf, loss, range)
% 代L的雷達方程
%
% Inputs:
% pt == 峯值功率 in Watts
% freq == 雷達中心頻率 in Hz
% g == 天線增益 in dB
% sigma == 目標截面積 in meter squared
% b == 帶寬 in Hz
% nf == 噪聲係數 in dB
% loss == 雷達損耗 in dB
% range == 目標距離 in Km
%
% Outputs:
% snr == SNR in dB
%
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); % compute wavelength square in dB
sigmadb = 10*log10(sigma); % convert sigma to dB
four_pi_cub = 10*log10((4.0 * pi)^3); % (4pi)^3 in dB
k_db = 10*log10(1.38e-23); % Boltzman's constant in dB
to_db = 10*log10(290); % noise temp. 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 (2.22)
num = p_peak + g + g + lambda_sqdb + sigmadb;
den = four_pi_cub + k_db + to_db + b_db + nf + loss + range_pwr4_db;
snr = num - den;
return
比較三種不同RCS值下的SNR隨探測距離變化的曲線：
比較三種不同雷達峯值功率值情況下SNR隨探測距離變化的曲線：
% Use this program to reproduce Fig. 2.1 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
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, b, nf, loss, range);
snr2 = radar_eq(pt, freq, g, sigma/10, b, nf, loss, range);
snr3 = radar_eq(pt, freq, g, sigma*10, b, nf, loss, range);
% plot SNR versus range
figure(1)
rangekm = range ./ 1000;
plot(rangekm,snr3,'k',rangekm,snr1,'k -.',rangekm,snr2,'k:','linewidth',1.5)
grid
legend('\sigma = 0 dBsm','\sigma = -10dBsm','\sigma = -20 dBsm')
xlabel ('Detection range - Km');
ylabel ('SNR - dB');
snr1 = radar_eq(pt, freq, g, sigma, b, nf, loss, range);
snr2 = radar_eq(pt*.4, freq, g, sigma, b, nf, loss, range);
snr3 = radar_eq(pt*1.8, freq, g, sigma, b, nf, loss, range);
figure (2)
plot(rangekm,snr3,'k',rangekm,snr1,'k -.',rangekm,snr2,'k:','linewidth',1.5)
grid
legend('P_t = 2.16 MW','P_t = 1.5 MW','P_t = 0.6 MW')
xlabel ('Detection range - Km');
ylabel ('SNR - dB');低PRF雷達方程
function [snr] = lprf_req(pt, g, freq, sigma, np, b, nf, loss, range)
% This program implements Eq. (2.27) of textbook
%
% Inputs:
% pt == 峯值功率 in Watts
% freq == 雷達中心頻率 in Hz
% g == 天線增益 in dB
% sigma == 目標截面積 in meter squared
% b == 帶寬 in Hz
% nf == 噪聲係數 in dB
% np == 脈衝個數
% loss == 雷達損耗 in dB
% range == 目標距離（單值或者向量） in Km
%
% Outputs:
% snr == SNR in dB
%
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); % compute wavelength square in dB
sigmadb = 10*log10(sigma); % convert sigma to dB
four_pi_cub = 10*log10((4.0 * pi)^3); % (4pi)^3 in dB
k_db = 10*log10(1.38e-23); % Boltzman's constant in dB
to_db = 10*log10(290); % noise temp. in dB
b_db = 10*log10(b); % bandwidth in dB
np_db = 10.*log10(np); % number of pulses in dB
range_pwr4_db = 10*log10(range.^4); % vector of target range^4 in dB
% Implement Equation (1.68)
num = p_peak + g + g + lambda_sqdb + sigmadb + np_db;
den = four_pi_cub + k_db + to_db + b_db + nf + loss + range_pwr4_db;
snr = num - den;
return
探測距離與脈衝個數與SNR的關係：
% Use this program to reproduce Fig. 2.2 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
b = 5.0e+6; % radar operating bandwidth in Hz
nf = 3.0; %noise figure in dB
loss = 6.0; % radar losses in dB
np = 1;
range = linspace(25e3,225e3,1000); % range to target from 5 Km 225 Km, 1000 points
snr1 = lprf_req(pt, g, freq, sigma, np, b, nf, loss, range);
snr2 = lprf_req(pt, g, freq, sigma, 5*np, b, nf, loss, range);
snr3 = lprf_req(pt, g, freq, sigma, 10*np, b, nf, loss, range);
% plot SNR versus range
figure(1)
rangekm = range ./ 1000;
plot(rangekm,snr3,'k',rangekm,snr1,'k -.',rangekm,snr2,'k:','linewidth',1.5)
grid
legend('n_p = 10','n_p = 5','n_p = 1')
xlabel ('Detection range - Km');
ylabel ('SNR - dB');
np = linspace(1,500,500);
range = 150e3;
snr1 = lprf_req(pt, g, freq, sigma, np, b, nf, loss, range);
snr2 = lprf_req(pt, g, freq, 10*sigma, np, b, nf, loss, range);
figure (2)
plot(np,snr2,'k',np,snr1,'k -.','linewidth',1.5)
grid
legend('Baseline','\sigma = 0 dBsm')
xlabel ('No. of pulses');
ylabel ('SNR - dB');高PRF雷達方程
function [snr] = hprf_req (pt, Ti, g, freq, sigma, dt, range, nf, loss)
% This program implements Eq. (2.31)of textbook
%
% Inputs:
% pt == 峯值功率 in Watts
% freq == 中心頻率 in Hz
% g == 天線增益 in dB
% sigma == 目標截面積 in meter squared
% Ti == 目標上的時間 in seconds
% nf == 噪聲係數 in dB
% dt == 佔空因子
% loss == 雷達損耗 in dB
% range == 目標距離（單值或者向量） in Km
%
% Outputs:
% snr == SNR in dB
%
c = 3.0e+8; % speed of light
lambda = c / freq; % wavelength
pav = 10*log10(pt*dt); % compute average power in dB
Ti_db = 10*log10(Ti); % time on target in dB
lambda_sqdb = 10*log10(lambda^2); % compute wavelength square in dB
sigmadb = 10*log10(sigma); % convert sigma to dB
four_pi_cub = 10*log10((4.0 * pi)^3); % (4pi)^3 in dB
k_db = 10*log10(1.38e-23); % Boltzman's constant in dB
to_db = 10*log10(290); % noise temp. in dB
range_pwr4_db = 10*log10(range.^4); % vector of target range^4 in dB
% Implement Equation (1.72)
num = pav + Ti_db + g + g + lambda_sqdb + sigmadb;
den = four_pi_cub + k_db + to_db + nf + loss + range_pwr4_db;
snr = num - den;
return佔空因子和探測距離與SNR的關係：
% Use this program to reproduce Fig. 2.3 of text.
close all
clear all
pt = 10e03; % peak power in Watts
freq = 5.6e+9; % radar operating frequency in Hz
g = 20; % antenna gain in dB
sigma = 0.01; % radar cross section in m squared
b = 5.0e+6; % radar operating bandwidth in Hz
nf = 3.0; %noise figure in dB
loss = 8.0; % radar losses in dB
Ti = 2; % time on target in seconds
dt = .05; % 5% duty cycle
range = linspace(10e3,225e3,1000); % range to target from 10 Km 225 Km, 1000 points
snr1 = hprf_req (pt, Ti, g, freq, sigma, .05, range, nf, loss);
snr2 = hprf_req (pt, Ti, g, freq, sigma, .1, range, nf, loss);
snr3 = hprf_req (pt, Ti, g, freq, sigma, .2, range, nf, loss);
% plot SNR versus range
figure(1)
rangekm = range ./ 1000;
plot(rangekm,snr3,'k',rangekm,snr2,'k -.',rangekm,snr1,'k:','linewidth',1.5)
grid
legend('dt = 20%','dt = 10%','dt = 5%')
xlabel ('Detection range - Km');
ylabel ('SNR - dB');監視雷達方程
某個特定的雷達系統必須完成的首要任務是連續掃描空間的特定區域來搜索感興趣的目標。一旦探測建立，由雷達信號和數據處理機提取出諸如距離、角度位置，可能還有目標速度等目標信息。究竟採取何種搜索模式，取決於雷達的設計和天線。
function PAP = power_aperture(snr,tsc,sigma,range,nf,loss,az_angle,el_angle)
% This function implements Eq. (2.38) of textbook
%
% Inputs:
% snr == 靈敏度 in dB
% tsc == 掃描時間 in seconds
% sigma == 目標截面積 in meter squared
% range == 目標距離 in Km
% nf == 噪聲係數 in dB
% loss == 雷達損耗 in dB
% az_angle == 搜索區域方位上的範圍 in degrees
% el_angle == 搜索區域仰角上的範圍 in degrees
%
% Outputs:
% PAP == 功率孔徑積 in dB
%
Tsc = 10*log10(tsc); % convert Tsc into dB
Sigma = 10*log10(sigma); % convert sigma to dB
four_pi = 10*log10(4.0 * pi); % (4pi) in dB
k_db = 10*log10(1.38e-23); % Boltzman's constant in dB
To = 10*log10(290); % noise temp. in dB
range_pwr4_db = 10*log10(range.^4); % target range^4 in dB
omega = (az_angle/57.296) * (el_angle / 57.296); % compute search volume in steraradians
Omega = 10*log10(omega); % search volume in dB
% implement Eq. (1.79)
PAP = snr + four_pi + k_db + To + nf + loss + range_pwr4_db + Omega ...
- Sigma - Tsc;
return給出三種RCS選擇的功率孔徑積和探測距離的關係曲線，以及雷達平均功率與功率孔徑積的關係曲線圖：
% Use this program to reproduce Fig. 2.6 of text.
close all
clear all
tsc = 2.5; % Scan time i s2.5 seconds
sigma = 0.1; % radar cross section in m squared
te = 900.0; % effective noise temperature in Kelvins
snr = 15; % desired SNR in dB
nf = 6.0; %noise figure in dB
loss = 7.0; % radar losses in dB
az_angle = 2; % search volume azimuth extent in degrees
el_angle = 2; %serach volume elevation extent in degrees
range = linspace(20e3,250e3,1000); % range to target from 20 Km 250 Km, 1000 points
pap1 = power_aperture(snr,tsc,sigma/10,range,nf,loss,az_angle,el_angle);
pap2 = power_aperture(snr,tsc,sigma,range,nf,loss,az_angle,el_angle);
pap3 = power_aperture(snr,tsc,sigma*10,range,nf,loss,az_angle,el_angle);
% plot power aperture prodcut versus range
% generate Figure 2.6a
figure(1)
rangekm = range ./ 1000;
plot(rangekm,pap1,'k',rangekm,pap2,'k -.',rangekm,pap3,'k:','linewidth',1.5)
grid
legend('\sigma = -20 dBsm','\sigma = -10dBsm','\sigma = 0 dBsm')
xlabel ('Detection range in Km');
ylabel ('Power aperture product in dB');
% generate Figure 2.6b
lambda = 0.03; % wavelength in meters
G = 45; % antenna gain in dB
ae = linspace(1,25,1000);% aperture size 1 to 25 meter squared, 1000 points
Ae = 10*log10(ae);
range = 250e3; % rnage of interset is 250 Km
pap1 = power_aperture(snr,tsc,sigma/10,range,nf,loss,az_angle,el_angle);
pap2 = power_aperture(snr,tsc,sigma,range,nf,loss,az_angle,el_angle);
pap3 = power_aperture(snr,tsc,sigma*10,range,nf,loss,az_angle,el_angle);
Pav1 = pap1 - Ae;
Pav2 = pap2 - Ae;
Pav3 = pap3 - Ae;
figure(2)
plot(ae,Pav1,'k',ae,Pav2,'k -.',ae,Pav3,'k:','linewidth',1.5)
grid
xlabel('Aperture size in square meters')
ylabel('Pav in dB')
legend('\sigma = -20 dBsm','\sigma = -10dBsm','\sigma = 0 dBsm')帶干擾的雷達方程
任何有意干擾雷達正常工作的電子措施通常稱爲電子對抗ECM。其中包括箔條、雷達誘餌、雷達RCS變更。
自屏蔽干擾器SSJ
燒穿距離
遠距離干擾器SOJ
距離縮減因子
雙基地雷達方程
雷達損耗
發射和接收損耗
發射和接收損耗分別發生在雷達發射機和天線輸入端口之間及天線輸出端口和接收機前端之間，這樣的損耗統稱爲管道損耗。典型的管道損耗是1-2dB。
天線方向圖損耗和掃描損耗
在使用雷達方程時，我們都假設了天線的最大增益，這僅僅在目標位於沿天線視線軸的方向時成立。
大氣損耗
大氣衰減是雷達工作頻率、目標距離和仰角的函數，大氣衰減可以高到幾個dB。
摺疊損耗
積累的返回噪聲脈衝數量大於從目標返回的脈衝數，稱爲摺疊損耗。
處理損耗
- 檢波的近似
- 恆虛警率損耗
- 量化損耗
- 距離門跨越
- 多普勒濾波器跨越
- 其他