前言
本文对雷达基础导论的内容以思维导图的形式呈现,有关仿真部分进行了讲解实现。
一、雷达基础导论
思维导图如下图所示,如有需求请到文章末尾端自取。
二、Matlab 仿真
1、SNR 相对检测距离的仿真
雷达方程:
下面在三种不同数值的 RCS(雷达截面积)和三种不同数值的雷达峰值功率的情况下,对 SNR(信噪比) 相对检测距离的情况进行 Matlab 仿真
①、Matlab 源码
radar_eq.m
function [snr] = radar_eq(pt, freq, g, sigma, te, b, nf, loss, range) % This program implements Eq. (1.56) 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 te_db = 10*log10(te); % 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 (1.56) num = p_peak + g + g + lambda_sqdb + sigmadb; den = four_pi_cub + k_db + te_db + b_db + nf + loss + range_pwr4_db; snr = num - den; return
相关参数说明:
符号 | 描述 | 单位 | 状态 |
pt | 峰值功率 | W | 输入 |
freq | 雷达中心频率 | Hz | 输入 |
g | 天线增益 | dB | 输入 |
sigma | 目标截面积 | m 2 m^2m2 | 输入 |
te | 有效噪声温度 | K | 输入 |
b | 带宽 | Hz | 输入 |
nf | 噪声系数 | dB | 输入 |
loss | 雷达损失 | dB | 输入 |
range | 目标距离(单位或矢量) | m | 输入 |
snr | SNR(单值或矢量,根据输入距离) | dB | 输出 |
函数 “radar.m” 的设计使它对于输入“距离”,可以接受单个数值,或包含很多距离值的矢量
fig1_12.m
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',rangekm,snr1,'k -.',rangekm,snr2,'k:') grid legend('\sigma = 0 dBsm','\sigma = -10dBsm','\sigma = -20 dBsm') xlabel ('Detection range - Km'); ylabel ('SNR - dB'); snr1 = radar_eq(pt, freq, g, sigma, te, b, nf, loss, range); snr2 = radar_eq(pt*.4, freq, g, sigma, te, b, nf, loss, range); snr3 = radar_eq(pt*1.8, 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');
②、仿真
仿真参数默认如下:
峰值功率 Pt=1.5 MW,工作频率 f0=5.6 GHz,天线增益 G=45 dB,有效温度 Te=290 K,雷达损失 L=6 dB,噪声系数 F=3 dB,雷达带宽B=5 MHz,雷达最小和最大检测距离是Rmin=25 km 和 Rmax=165 km,假定目标截面积 σ=0.1 m 2
1)、不同 RCS,SNR 相对检测距离仿真
对三种不同数值的 RCS,SNR 相对检测距离的曲线
注:分贝平方米(dBsm):用雷达散射截面的对数值的十倍来表示,符号是σ dBsm,单位是分贝平方米(dBsm),即σ dBsm=10lgσ。例如,RCS 值 0.1 平方米对应的是 -10 分贝平方米(即 -10dBsm)。
结论:从图中可以看到 RCS(雷达截面积)越大,雷达信噪比越大,且随着距离的增加,雷达信噪比逐渐减小;
2)、不同雷达峰值功率,SNR 相对检测距离仿真
对三种不同数值的雷达峰值功率,SNR 相对检测距离的曲线
结论:从图中可以看到雷达峰值功率越大,雷达信噪比越大,且随着距离的增加,雷达信噪比逐渐减小
2、脉冲宽度相对所要求的 SNR 仿真
雷达检测门限:
下面在三种不同的检测距离数值的情况下,对脉冲宽度相对所要求 SNR(信噪比)的情况进行 Matlab 仿真
①、Matlab 源码
fig1_13.m
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 % Implement Eq.(1.57) den = pt * gain * gain * sigma * lambda^2; num1 = (4*pi)^3 * 1.38e-23 * te * F * loss * range(1)^4 .* snr; num2 = (4*pi)^3 * 1.38e-23 * te * F * loss * range(2)^4 .* snr; num3 = (4*pi)^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,1e6*tau1,'k',snr_db,1e6*tau2,'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');
②、仿真
仿真参数参考上面代码
以下为不同检测距离,脉冲宽度相对所要求的 SNR 仿真
对三种不同的检测距离数值,脉冲宽度相对所要求的 SNR 曲线
结论:从图中可以看到随着雷达 SNR 的增加,脉冲宽度逐渐增大;对应于同一雷达 SNR,距离越远所需要的脉冲宽度越宽
3、功率孔径积相对于距离仿真 及 平均功率相对于孔径大小仿真
搜索雷达方程:
①、Matlab 源码
power_aperture.m
function PAP = power_aperture(snr,tsc,sigma,range,te,nf,loss,az_angle,el_angle) % This program implements Eq. (1.67) 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 Te = 10*log10(te); % 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. (1.67) PAP = snr + four_pi + k_db + Te + nf + loss + range_pwr4_db + Omega ... - Sigma - Tsc; return
相关参数说明:
符号 | 描述 | 单位 | 状态 |
snr | 灵敏度snr | dB | 输入 |
tsc | 扫描时间 | s | 输入 |
sigma | 目标截面积 | m 2 m^2m2 | 输入 |
range | 目标距离(单位或矢量) | m | 输入 |
te | 有效噪声温度 | K | 输入 |
nf | 噪声系数 | dB | 输入 |
loss | 雷达损失 | dB | 输入 |
az_angle | 搜索区域的方位角范围 | ∘ ^\circ∘ | 输入 |
el_angle | 搜索区域的俯仰角范围 | ∘ ^\circ∘ | 输入 |
PAP | 功率孔径积 | dB | 输出 |
fig1_16.m
close all clear all tsc = 2.5; % Scan time i s2.5 seconds sigma = 0.1; % radar cross section in m sqaured 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,te,nf,loss,az_angle,el_angle); pap2 = power_aperture(snr,tsc,sigma,range,te,nf,loss,az_angle,el_angle); pap3 = power_aperture(snr,tsc,sigma*10,range,te,nf,loss,az_angle,el_angle); % plot power aperture prodcut versus range % figure 1.16a figure(1) rangekm = range ./ 1000; plot(rangekm,pap1,'k',rangekm,pap2,'k -.',rangekm,pap3,'k:') grid legend('\sigma = -20 dBsm','\sigma = -10dBsm','\sigma = 0 dBsm') xlabel ('Detection range in Km'); ylabel ('Power aperture product in dB'); % generate Figure 1.16b 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,te,nf,loss,az_angle,el_angle); pap2 = power_aperture(snr,tsc,sigma,range,te,nf,loss,az_angle,el_angle); pap3 = power_aperture(snr,tsc,sigma*10,range,te,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:') grid xlabel('Aperture size in square meters') ylabel('Pav in dB') legend('\sigma = -20 dBsm','\sigma = -10dBsm','\sigma = 0 dBsm')
②、仿真
仿真参数默认如下:
σ \sigmaσ | T s c T_{sc}Tsc | θ e = θ a \theta_e=\theta_aθe=θa | R | T_e | n f ∗ l o s s nf*lossnf∗loss | s n r snrsnr |
0.1 m 2 0.1m^20.1m2 | 2.5 s 2.5s2.5s | 2 ∘ 2^\circ2∘ | 252 k m 252km252km | 900 K 900K900K | 13 d B 13dB13dB | 15 d B 15dB15dB |
1)、不同 RCS,功率孔径积相对于距离仿真
对三种不同的 RCS,功率孔径积相对于检测距离曲线
结论:从图中可以看到随着检测距离的增加,功率孔径积增大;雷达 RCS 越大,功率孔径积也越小
2)、不同 RCS,平均功率相对于孔径大小仿真
对三种不同的 RCS,雷达平均功率相对于孔径大小曲线
结论:从图中可以看到随着雷达孔径大小的增加,雷达平均功率呈现下降趋势;雷达 RCS 越大,雷达孔径越小
4、SNR 增益相对积累脉冲数仿真
注:(SNR)1 是产生给定检测概率所要求的单个脉冲的SNR
①、Matlab 源码
pulse_integration.m
function [snrout] = pulse_integration(pt, freq, g, sigma, te, b, nf, loss, range,np,ci_nci) snr1 = radar_eq(pt, freq, g, sigma, te, b, nf, loss, range) % single pulse SNR snr1=0 if (ci_nci == 1) % coherent integration snrout = snr1 + 10*log10(np); else % non-coherent integration if (ci_nci == 2) snr_nci = 10.^(snr1./10); val1 = (snr_nci.^2) ./ (4.*np.*np); val2 = snr_nci ./ np; val3 = snr_nci ./ (2.*np); SNR_1 = val3 + sqrt(val1 + val2); % Equation 1.87 of text LNCI = (1+SNR_1) ./ SNR_1; % Equation 1.85 of text snrout = snr1 + 10*log10(np) - 10*log10(LNCI); end end return
相关参数说明:
符号 | 描述 | 单位 | 状态 |
pt | 峰值功率 | W | 输入 |
freq | 雷达中心频率 | Hz | 输入 |
g | 天线增益 | dB | 输入 |
sigma | 目标截面积 | m 2 m^2m2 | 输入 |
te | 有效噪声温度 | K | 输入 |
b | 带宽 | Hz | 输入 |
nf | 噪声系数 | dB | 输入 |
loss | 雷达损失 | dB | 输入 |
range | 目标距离(单位或矢量) | m | 输入 |
np | 积累脉冲数 | 无 | 输入 |
ci_nci | 1是CI;2是NCI | 无 | 输入 |
snr | SNR(单值或矢量,根据输入距离) | dB | 输出 |
fig1_21.m
clear all close all np = linspace(1,10000,1000); snrci = pulse_integration(4,94.e9,47,20,290,20e6,7,10,5.01e3,np,1); snrnci = pulse_integration(4,94.e9,47,20,290,20e6,7,10,5.01e3,np,2); semilogx(np,snrci,'k',np,snrnci,'k:') legend('Coherent integration','Non-coherent integration') grid xlabel ('Number of integrated pulses'); ylabel ('SNR - dB');
②、仿真
仿真参数见上面源码
一般情况下 SNR 改善相对脉冲积累数
当使用积累时的 SNR 改善
结论:从图中可以看到随着积累脉冲数的增加,雷达信噪比逐渐增大;且当积累脉冲数相等时,相干积累信噪比大于非相干积累信噪比