自适应波束形成与Matlab程序代码注解

1、1.均匀线阵方向图(1) matlab 程序clc;clearall ;closeall ;imag=sqrt(-1);element_num=32;%阵元数为8d_lamda=1/2;%车元间距d与波长lamda的关系theta=linspace(-pi/2,pi/2,200);theta0=0;%来波方向w=exp(imag*2*pi*d_lamda*sin(theta0)*0:element_num-1);for j=1:length(theta)a=exp(imag*2*pi*d_lamda*sin(theta(j)*0:element_num-1);p(j)=w*a;end patt

2、ernmag=abs(p);patternmagnorm=patternmag/max(max(patternmag);patterndB=20*log10(patternmag);patterndBnorm=20*log10(patternmagnorm);figure(1)plot(theta*180/pi,patternmag);grid on ;xlabel(theta/radian)ylabel(amplitude/dB)title(num2str(element_num)阵num2str(theta0*180/pi)度);hold on ; figure(2) plot(theta

3、,patterndBnorm,r );grid on ; xlabel(theta/radian)ylabel(amplitude/dB)title(num2str(element_num)阵num2str(theta0*180/pi)度);axis(-1.5 1.5 -50 0);元均匀线阵方向图，来波方向为元均匀线阵方向图，来波方向为(2)仿真结果A.来波方向为 0不归一化归一化B.来波方向为 45不归一化8阵元均匀线阵方向图，来波方向为 0 度0-5-10-15-206B5u 4pm a321I 1I111111Ij1r i1J Iw /V V1*.j1f1 /8 阵元均匀线阵方向图，来

4、波方向为 0 度00.511.52theta/radian0-2-1.5-1-0.5j11iX.|1| |i j1I111.5-25-30-35-40-45-50-1.5-1-0.500.51theta/radian归一化C.随着阵元数的增加，波束宽度变窄，分辨力提局，仿真图如下:2阵元均匀线阵方向图来波方向为 0 度 353025B20d u m15 a1050-100-80-60-40-20020406080100theta/radian非归一化32 阵元均匀线阵方向图来波方向为。度 0-5-10-15-20-25-30-35-40-45-50-1.5-1-0.500.511.5theta

5、/radian归一化32 阵元均匀线阵方向图来波方向为 45 度不归一化归一化2.波束宽度与波达方向及阵元数的关系(1) matlab 程序clc;clearall ;closeall ;imag=sqrt(-1);element_num1=16;element_num2=128;element_num3=1024;lambda=0.1;d=0.5*lambda;theta=0:0.5:90;for j=1:length(theta)fai(j)=theta(j)*pi/180-asin(sin(theta(j)*pi/180)-lambda/(element_num1*d);psi(j)=t

6、heta(j)*pi/180-asin(sin(theta(j)*pi/180)-lambda/(element_num2*d);beta(j)=theta(j)*pi/180-asin(sin(theta(j)*pi/180)-lambda/(element_num3*d);endfigureplot(theta,fai,r ,theta,psi, b ,theta,beta, g);grid on;xlabel( theta );ylabel( width in radians);title(波束宽度与达波方向及阵元数目的关系);legend( N=16 , N=128, N=1024);

7、(2)仿真结果0.70.6-N=16-N=128N=1024一-h波束宽度与达波方向及阵元数目的关系909060605050士口3.当阵元间距d 九/ 2时，会出现栅瓣，导致空间模糊(1)仿真结果非归一化归一化4.类似于时域滤波，天线方向图是最优权的傅立叶变换(1) matlab 程序clc;clearall ;closeall ;imag=sqrt(-1);element_num=32;source_num=1;d_lambda=0.5;theta=linspace(-pi/2,pi/2,200);theta0=0;w=exp(imag*2*pi*d_lambda*sin(theta0)*0

8、:element_num-1);for j=1:length(theta)a=exp(imag*2*pi*d_lambda*sin(theta(j)*0:element_num-1);p(j)=w*a;endpatternmag=abs(p);patternmagnorm=patternmag/max(max(patternmag);patterndB=20*log10(patternmag);patterndBnorm=20*log10(patternmagnorm);figure(1)subplot(1,2,1);plot(theta,patterndBnorm);grid on ;xla

9、bel(theta/radian);ylabel(amplitude/dB);axis(-2.0 2.0 -50 0);subplot(1,2,2);pfft=fftshift(fft(w,256);pfftmag=abs(pfft);pfftmagnorm=pfftmag/max(max(pfftmag);pfftdB=20*log10(pfftmagnorm);pfftdBnorm=20*log10(pfftmagnorm);plot(linspace(-pi/2,pi/2,256),pfftdBnorm);grid on ;xlabel( theta/radian );ylabel( F

10、FT_amplitude/dB );axis(-2.0 2.0 -50 0);(2)仿真结果pmBedtheta/radianBdFPmaTF5.最大信噪比准那么方向图和功率谱closeimag=sqrt(-1);element_num=8;d_lambda=0.5;theta=-90:0.5:90;theta0=0;%来波方位theta1=20;%干扰方向L=512;%采样点数for i=1:Lamp0=10*randn(1);amp1=200*randn(1);ampn=1;s(:,i)=amp0*exp(imag*2*pi*0.5*sin(theta0*pi/180)*0:element

11、_num-1);j(:,i)=amp1*exp(imag*2*pi*0.5*sin(theta1*pi/180)*0:element_num-1);n(:,i)=ampn*exp(randn(element_num,1)+imag*randn(element_num,1); endRs=1/L*s*s;Rnj=1/L*(j*j+n*n);V,D=eig(Rs,Rnj);D,I=sort(diag(D);Wopt=V(:,I(8);for j=1:length(theta)a=exp(imag*2*pi*d_lambda*sin(theta(j)*pi/180)*0:element_num-1)

12、;axis(-90 90 -80 0);(1)matlab程序clc;clearall ;all ;%阵元数为8%可距为半波长%扫描范围%言号自相关矩阵%汗扰+噪声的自相关矩阵% (Rs,Rnj)的广义特征值和特征向量%寺征向量排序%最优权矢量f(j)=Wopt*a;p(j)=a*Rs*a+a*Rnj*a;endF=20*log10(abs(f)/max(max(abs(f);P=20*log10(abs(p)/max(max(abs(p);subplot(1,2,1) plot(theta,F); gridon ;holdon ;plot(theta0,-80:0, plot(theta1,

13、-80:0,xlabel( ylabel( title(theta/0F in dBmax-SNR)；););方向图);hold on; subplot(1,2,2); plot(theta,P, r); grid on; xlabel( theta/0 ); ylabel(功率in dB );title( max-SNR功率谱); grid on;axis(-90 90 -80 0);(2)仿真结果6. ASC旁瓣相消-MSE准那么matlab 程序clc;closeall ;clearall ;imag=sqrt(-1);M=32;%|甫助天线数目d_lambda=0.5;%车元间距the

14、ta0=-30;%来波方向theta1=60;%干扰方向L=512; %采样单元数s=zeros(1,512);% 划分一个区域for ii=1:Lamp0=1*randn(1);%言号的幅度随机产生，保证信号之间是不相关的amp1=200*randn(1);ampn=1;jam(:,ii)=amp1*exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:M-1)+ampn*(randn(M,1)+imag*randn(M,1);涉扰 +噪声s(ii)=amp0*exp(imag*2*pi*d_lambda*sin(theta0*pi/180)+amp1*ex

15、p(imag*2*pi*d_lambda*sin(theta1*pi/180)+ampn*(randn(1,1)+imag*randn(1,1);%接收信号(信号+干扰+噪声)s0(ii)=amp0*exp(imag*2*pi*d_lambda*sin(theta0*pi/180);endRx=1/L*jam*jam;r_xd=1/L*jam*s;Wopt=pinv(Rx)*r_xd;delta=s0-(s-Wopt*jam);delta1=abs(mean(delta.A2)-(mean(delta).A2);theta=linspace(-pi/2,pi/2,200);for jj=1:l

16、ength(theta)a=exp(imag*2*pi*d_lambda*sin(theta(jj)*0:M-1);f(jj)=Wopt*a;endF=20*log10(abs(f)/max(max(abs(f);figure(1)plot(theta*180/pi,F);gridon ;holdon ;plot(theta0,-50:0,.);plot(theta1,-50:0,.);xlabel(theta/ );ylabel(F/dB);title( MSE准那么下的方向图);axis(-90 90 -50 0);(2)仿真结果-501V i；H I土i f J Ul YiL1J1ibM

17、SE准那么下的方向图-5-10-15-20-30-35-40-45-80-60-40-20020406080theta/Bd-25F7. 线性约束最小方差(LCMV 淮那么 matlab 程序clc;clearall;closeall;imag=sqrt(-1);element_num=8;%车元数d_lambda=0.5;%阵元间距与波长的关系theta=-90:0.5:90;涮索范围theta0=0;%三个信号源的来波方向theta1=30;theta2=60;L=512; %采样单元数for i=1:Lamp0=10*randn(1);amp1=100*randn(1);amp2=10*

18、randn(1);ampn=10;x(:,i)=amp0*exp(imag*2*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1)+amp1*exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:element_num-1)+amp2*exp(imag*2*pi*d_lambda*sin(theta2*pi/180)*0:element_num-1)+ampn*(randn(element_num,1)+imag*randn(element_num,1);endRx=1/L*x*x;steer1=exp(imag*2

19、*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1);steer2=exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:element_num-1);steer3=exp(imag*2*pi*d_lambda*sin(theta2*pi/180)*0:element_num-1);C=steer1 steer2 steer3;F=1 0 1;%J巴三个方向都作为来波方向w=inv(Rx)*C*(inv(C*inv(Rx)*C)*F;for j=1:length(theta)a=exp(imag*2*pi*d_lam

20、bda*sin(theta(j)*pi/180)*0:element_num-1);f(j)=w*a;p(j)=1/(a*inv(Rx)*a);endF=20*log10(abs(f)/(max(max(abs(f);subplot(1,2,1)plot(theta,F);gridon ;holdon ;plot(theta0,-20:0,. );plot(theta1,-20:0,.);plot(theta2,-20:0,.);xlabel(theta/ );ylabel(F/dB);title( Capon beamforming方向图);axis(-90 90 -20 0);P=20*l

21、og10(abs(p)/(max(max(abs(p);subplot(1,2,2)plot(theta,P);grid on;hold on;plot(theta0,-20:0,.);plot(theta1,-20:0,.);plot(theta2,-20:0,.);xlabel(theta/ );ylabel(P/dB);title( Capon beamforming功率谱);axis(-90 90 -20 0);(2)仿真结果-201-hCapon beamforming功率谱-2-4-6-8-12-14-16-1840d-10P6080-80-60-40-20020theta/ 8.

22、 Capon beamforming(1) matlab 程序clc;clearall ;closeall ;imag=sqrt(-1);element_num=8;%车元数d_lambda=0.5;%阵元间距与波长的关系theta=-90:0.5:90;涮索范围theta0=0;%三个信号源的来波方向theta1=20;theta2=60;L=1000;%样单元数for i=1:Lamp0=10*randn(1);amp1=200*randn(1);amp2=200*randn(1);ampn=3;x(:,i)=amp0*exp(imag*2*pi*d_lambda*sin(theta0*p

23、i/180)*0:element_num-1)+amp1*exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:element_num-1)+amp2*exp(imag*2*pi*d_lambda*sin(theta2*pi/180)*0:element_num-1)+ampn*(randn(element_num,1)+imag*randn(element_num,1);endRx=1/L*x*x;R=inv(Rx);steer=exp(imag*2*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1);w=R*st

24、eer/(steer*R*steer);%!i优权矢量for j=1:length(theta)a=exp(imag*2*pi*d_lambda*sin(theta(j)*pi/180)*0:element_num-1);f(j)=w*a;p(j)=1/(a*R*a);endF=20*log10(abs(f)/(max(max(abs(f);subplot(1,2,1)plot(theta,F);gridon ;holdon ;plot(theta0,-50:0,.);plot(theta1,-50:0,.);plot(theta2,-50:0,.);xlabel( theta/ );ylab

25、el( F/dB);title( Capon beamforming方向图); axis(-90 90 -50 0);P=20*log10(abs(p)/(max(max(abs(p);subplot(1,2,2)plot(theta,P);grid on;hold on;xlabel( theta/ );ylabel( P/dB);title( Capon beamforming功率谱); axis(-90 90 -90 0);(2)仿真结果P9. 不同方法估计协方差矩阵的 Caper束形成(1) matlab 程序clc; clearall ;closeall ;imag=sqrt(-1)

26、; element_num=8;啷车元数为8 d_lambda=0.5;%可距为半波长theta=-90:0.5:90;%3才苗范围theta0=0;%来波方向theta1=50;%干扰方向L=1024;% 样 单 元 数fori=1:Lamp0=10*randn(1);amp1=50*randn(1);ampn=0.5;s(:,i)=amp0*exp(imag*2*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1);j(:,i)=amp1*exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:element_num

27、-1);n(:,i)=ampn*exp(imag*2*pi*randn(1)*0:element_num-1); end Rx=1/L*(s+j+n)*(s+j+n);板 收信号自相关矩阵Rnj=1/L*(j+n)*(j+n);%狩拢+噪声的自相关矩阵e=exp(imag*2*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1);Wopt_Rx=inv(Rx)*e/(e*inv(Rx)*e);哄用接收信号的权矢量Wopt_Rnj=inv(Rnj)*e/(e*inv(Rnj)*e);%采用干拢+噪声信号的权矢量forj=1:length(theta)a=

28、exp(imag*2*pi*d_lambda*sin(theta(j)*pi/180)*0:element_num-1);f1(j)=Wopt_Rx*a;f2(j)=Wopt_Rnj*a;endF1=20*log10(abs(f1)/max(max(abs(f1);F2=20*log10(abs(f2/max(max(abs(f2); figure; plot(theta,F1,theta,F2, r);gridon ;holdon ;plot(theta0,-50:0,.);plot(theta1,-50:0,.);xlabel( theta/ ); ylabel( F(1,2)/dB);t

29、itle(不同方法估计协方差矩阵的Capon波束形成);axis(-90 90 -60 0);(2)仿真结果不同方法估计协方差矩阵的Capon波束形成10. 多点约束的 Caper束形成和方向图(1) matlab 程序clc;clearall ;closeall ;imag=sqrt(-1);element_num=8;d_lambda=0.5;theta=-90:0.3:90;theta0=0;theta1=20;theta2=50;L=512;Rx=zeros(element_num,element_num);%生协方差矩阵for i=1:Lamp0=10*randn(1);amp1=1

30、0*randn(1);amp2=50*randn(1);ampn=0.5*randn(1);%M声的幅度随机产生，保证噪声与信号之间是不相关的j(:,i)=amp1*exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:element_num-1)+amp2*exp(imag*2*pi*d_lambda*sin(theta2*pi/180)*0:element_num-1)+ampn*exp(imag*2*pi*randn(1)*0:element_num-1);x(:,i)=amp0*exp(imag*2*pi*d_lambda*sin(theta0*pi/

31、180)*0:element_num-1)+j(:,i);%表示接收信号endRx=1/L*x*x;R=inv(Rx);w=amp0*exp(imag*2*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1)+amp1*exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:element_num-1)+amp2*exp(imag*2*pi*d_lambda*sin(theta2*pi/180)*0:element_num-1);for j=1:length(theta)a=exp(imag*2*pi*d_lambda*

32、sin(theta(j)*pi/180)*0:element_num-1);f(j)=w*a;p(j)=1/(a*R*a);endF=20*log10(abs(f)/max(max(abs(f);P=20*log10(abs(p)/max(max(abs(p);figure;subplot(1,2,1);plot(theta,F);gridon ;holdon ;plot(theta0,-50:0,.);plot(theta1,-50:0,.);plot(theta2,-50:0,.);xlabel(theta/ );ylabel(F/dB);title( Capon beamforming方

33、向图);axis(-90 90 -50 0);subplot(1,2,2);plot(theta,P);hold on;grid on;plot(theta0,-90:0,.);plot(theta1,-90:0,.);plot(theta2,-90:0,.);xlabel(theta/ );ylabel(P/dB);title( Capon beamforming功率谱);(2)仿真结果0Capon beamforming方图-5B 1-10PF *-15rh-20B -25f | |JF-30+-351h-40-45B-50F-8-6-40-22040680-10111-201-30-40

34、1勺BP-501-60:-701-801-90itheta/Capon beamforming功率谱0-100-8-6-4-20206080100theta/ 11. 白适应波束形成方向图(1) matlab 程序clc;clearall;closeall;imag=sqrt(-1);element_num=8;c=3e8;f=5e8;lambda=c/f;d_lambda=0.5;theta=-90:0.5:90;theta0=0;theta1=45;theta2=60;L=2048;for i=1:Lamp0=10*randn(1);amp1=100*randn(1);amp2=100*randn(1);ampn=10;x(:,i)=amp0*exp(imag*2*pi*d_lambda