自適應(yīng)波束形成與Matlab程序代碼注解

1、1.均勻線陣方向圖(1) matlab 程序clc;clear all ;close all ;imag=sqrt(-1);element_num=32; %車元數(shù)為 8d_lamda=1/2; %陣元間距d與波長(zhǎng)lamda的關(guān)系theta=li nspace(-pi/2,pi/2,200);thetaO=O; %來(lái)波方向w=exp(imag*2*pi*dl_lamda*si n(thetaO)*O:eleme nt_nu m-1');for j=1:le ngth(theta)a=exp(imag*2*pi*dd_l amda*si n(theta(j)*0:eleme nt_nu

2、m-1');p(j)=w'*a;endpatter nm ag=abs(p);patter nmagno rm=patter nm ag/max(max(patter nm ag);patterndB=20*log10(patternmag);patter ndBno rm=20*log10(patter nmagno rm);figure(1)plot(theta*180/pi,patternmag);grid on;xlabel( 'theta/radian')ylabel( 'amplitude/dB')title( nu m2str(el

3、eme nt_n um)'陣元均勻線陣方向圖，來(lái)波方向?yàn)閚um2str(theta0*180/pi) '度');hold on;figure(2)plot(theta,patterndBnorm,'r');grid on;xlabel( 'theta/radian')ylabel( 'amplitude/dB')title( nu m2str(eleme nt_n um)'陣元均勻線陣方向圖','來(lái)波方向?yàn)閚um2str(theta0*180/pi) '度');axis(-1.5 1

4、.5 -50 0);(2)仿真結(jié)果A.來(lái)波方向?yàn)?11111 / /y1(11/8陣元均勻線陣萬(wàn)向圖，來(lái)波方向?yàn)?度-80-60-40-20020theta/radian4060801008 7 65 4 3 BeanMupma00不歸一化BOTeanLlpmaI1jrLFl1 111 1jrxi ：*i/JiI1 'IIIi i8陣元均勻線陣方向圖，來(lái)波方向?yàn)?度-1-0.50.51O-51O1520-25300theta/radian1.5歸一化B.來(lái)波方向?yàn)?50-2jf l'II I IL/A Ii iIIJ fV /x y/ jj vrrrI f8陣元均勻線陣萬(wàn)向圖，

5、來(lái)波方向?yàn)?度-1.5-1-0.500.51theta/radian1.528 7 65 4 3 pm a不歸一化IIzI/lII8陣元均勻線陣方向圖，來(lái)波方向?yàn)?度-1-0.50.515 o- 1520-52-0theta/radian1.5C.隨著陣元數(shù)的增加，波束寬度變窄，分辨力提高，仿真圖如下:pm ahI廠廣32陣元均勻線陣萬(wàn)向圖來(lái)波萬(wàn)向?yàn)?度-80-60-40-20020406080100theta/radian亦305 O2 25 O500%非歸一化l ma32陣元均勻線陣方向圖來(lái)波方向?yàn)?度-10.51O 巧101520-52-0.50theta/radian1.535BOTe

6、auLlpma?|!i：iI/VWwif132陣元均勻線陣方向圖來(lái)波方向?yàn)?5度-80-60-40-20020theta/radian4060801003025205o500不歸一化32陣元均勻線陣方向圖來(lái)波方向?yàn)?5度-1-0.50theta/radian0.51-5o520-1.5歸一化2.波束寬度與波達(dá)方向及陣元數(shù)的關(guān)系(1) matlab 程序clc;clear all ;close all ;imag=sqrt(-1);eleme nt_nu m1=16;eleme nt_n um2=128;eleme nt_nu m3=1024;lambda=0.1;d=0.5*lambda;th

7、eta=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)=theta(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,ps

8、i, 'b' ,theta,beta, 'g');grid on;xlabel( 'theta');ylabel( 'width in radians');title('波束寬度與達(dá)波方向及陣元數(shù)目的關(guān)系);legend( 'N=16' , 'N=128' , 'N=1024');(2) 仿真結(jié)果波束寬度與達(dá)波方向及陣元數(shù)目的關(guān)系0.70.60.50.40.1thetaa a n h結(jié)果 N=16N=128N=1024* V-"0.30.23.當(dāng)陣元間距d/2時(shí)，會(huì)

9、出現(xiàn)柵瓣，導(dǎo)致空間模糊(1)仿真結(jié)果1I!'I !a； 訃11 (! 1H I:14/ I JL1/1(* rr i Tk!P '1h1 / 1 氣8陣元均勻線陣萬(wàn)向圖來(lái)波萬(wàn)向?yàn)?度-80-60-40-20020406080100theta/radian8 7 65 4 3 BeanMupma00非歸一化BOTeanLlpma8陣元均勻線陣方向圖來(lái)波方向?yàn)?度-1-0.50.51O-51O15200theta/radian1.5歸一化4. 類似于時(shí)域?yàn)V波，天線方向圖是最優(yōu)權(quán)的傅立葉變換(1)matlab 程序clc;clear all ;close all ;imag=sqrt

10、(-1);eleme nt_num=32;source_ num=1;d_lambda=0.5;theta=li nspace(-pi/2,pi/2,200);thetaO=O;w=exp(imag*2*pi*dambda*s in (thetaO)*O:eleme nt_n um-1');for j=1:length(theta)a=exp(imag*2*pi*dl_l ambda*si n(theta(j)*0:eleme nt_nu m-1'); p(j)=w'*a;endpatter nm ag=abs(p);patter nmagno rm=patter nm

11、 ag/max(max(patter nm ag);patterndB=20*log10(patternmag);patter ndBno rm=20*log10(patter nmagno rm);figure(1)subplot(1,2,1);plot(theta,patter ndBno rm);grid on;xlabel( 'theta/radian' );ylabel( 'amplitude/dB');axis(-2.0 2.0 -50 0);subplot(1,2,2);pfft=fftshift(fft(w,256);pfftmag=abs(pf

12、ft);pfftmag no rm=pfftmag/max(max(pfftmag);pfftdB=20*log10(pfftmag norm);pfftdB norm=20*log10(pfftmag norm);plot(li nspace(-pi/2,pi/2,256),pfftdB norm);grid on;xlabel( 'theta/radian' );ylabel( 'FFT_amplitude/dB');axis(-2.0 2.0 -50 0);(2)仿真結(jié)果-15-15-20Bd-25-35-40-45theta/radiantheta/ra

13、dian|fI,'1r.r'弭1wN ;i>ijjl;1LL-30|Hi也；111-20-25-30-35-40-455. 最大信噪比準(zhǔn)則方向圖和功率譜(1) matlab 程序clc;clear all ;close all ;imag=sqrt(-1);element_num=8; %車元數(shù)為 8d_lambda=0.5; %可距為半波長(zhǎng) theta=-90:0.5:90;描圍thetaO=O; %來(lái)波方位 theta仁20; %干擾方向L=512; %采樣點(diǎn)數(shù)for i=1:Lamp0=10*ra ndn (1);amp1=200*ra ndn (1);amp n=

14、1;s(:,i)=amp0*exp(imag*2*pi*0.5*sin(theta0*pi/180)*0:element_num-1');j(:,i)=amp1*exp(imag*2*pi*0.5*sin(theta1*pi/180)*0:element_num-1');n( :,i)=amp n*exp(ra ndn (eleme nt_nu m,1)+imag*ra ndn (eleme nt_nu m,1);endRs=1/L*s*s'%言號(hào)自相關(guān)矩陣Rnj=1/L*(j*j'+n*n');%干擾+噪聲的自相關(guān)矩陣V,D=eig(Rs,Rnj);

15、%( Rs,Rnj )的廣義特征值和特征向量 D,l=sort(diag(D);%寺征向量排序Wopt=V(:,l(8);%最優(yōu)權(quán)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)=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)

16、;grid on;hold on;plot(theta0,-80:0,'.');plot(theta1,-80:0,'.');xlabel( 'theta/0');ylabel( 'F in dB');title( 'max-SNR 方向圖');axis(-90 90 -80 0);hold on;subplot(1,2,2);plot(theta,P, 'r'); grid on;xlabel( 'theta/0');ylabel('功率 in dB'); titl

17、e( 'max-SNR 功率譜'); grid on;axis(-90 90 -80 0);(2)仿真結(jié)果max-SNR 方向圖max-SNR 功率譜06. ASC旁瓣相消-MSE準(zhǔn)則(1) matlab 程序clc;close all ;clear all ;imag=sqrt(-1);M=32;%輔助天線數(shù)目d_lambda=0.5; %車元間距theta0=-30;%來(lái)波方向theta仁60; %干擾方向L=512; %采樣單元數(shù)s=zeros(1,512);%預(yù)劃分一個(gè)區(qū)域for ii=1:Lamp0=1*ra ndn (1);%言號(hào)的幅度隨機(jī)產(chǎn)生，保證信號(hào)之間是不相關(guān)

18、的amp1=200*ra ndn (1);amp n=1;jam(:,ii)=amp1*exp(imag*2*pi*d_l ambda*si n(theta1*pi/180)*0:M-1')+amp n*(ra ndn( M,1)+imag*ra ndn( M,1);燈擾 + 噪聲+干擾+s(ii)=amp0*exp(imag*2*pi*d_l ambda*si n(theta0*pi/180)+amp1*exp(imag*2*pi*damb da*s in (theta1*pi/180)+amp n*(ra ndn (1,1)+imag*ra ndn (1,1);%接收信號(hào)(信號(hào)噪聲

19、)s0(ii)=amp0*exp(imag*2*pi*dambda*si n(theta0*pi/180);endRx=1/L*jam*jam'r_xd=1/L*jam*s'Wopt=pi nv(Rx)*r_xd;delta=s0-(s-Wopt'*jam);delta 仁abs(mea n(delta92)-(mea n(delta)92);theta=li nspace(-pi/2,pi/2,200);for jj=1:length(theta)a=exp(imag*2*pi*d_lambda*si n( theta(jj)*0:M-1');f(jj)=Wo

20、pt'*a;endF=20*log10(abs(f)/max(max(abs(f);figure(1)plot(theta*180/pi,F);grid on;hold on;plot(theta0,-50:0,'.');plot(theta1,-50:0,'.');xlabel( 'theta/ ° ');ylabel( 'F/dB');title('MSE準(zhǔn)則下的方向圖');axis(-90 90 -50 0);(2)仿真結(jié)果FMSE準(zhǔn)則下的方向圖-10-15-20-30-35-40-45th

21、eta/AIIA AJ3 i . M'r 1 J:1'l*1 F £ <i-257.線性約束最小方差（LCMV準(zhǔn)則(1) matlab 程序clc;clear all ;close all ;imag=sqrt(-1);element_num=8; %車元數(shù)d_lambda=0.5; %車元間距與波長(zhǎng)的關(guān)系theta=-90:0.5:90;滋索圍thetaO=O;%三個(gè)信號(hào)源的來(lái)波方向theta 仁30;theta2=60;L=512; %采樣單元數(shù)for i=1:Lamp0=10*ra ndn (1);amp1=100*ra ndn (1);amp2=10*r

22、a ndn (1);amp n=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/1 80)*0:element_num-1')+ampn*(randn(element_num,1)+imag*randn(element_num,1);endRx=1/L*x*

23、x：steer1=exp(imag*2*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'呀巴三個(gè)方向都作為來(lái)波方向w=i nv(Rx)*C*(i nv(C'*i nv(Rx)*C)

24、*F;for j=1:length(theta)a=exp(imag*2*pi*dl_l ambda*sin(theta(j)*pi/180)*0:element_num-1');f(j)=w'*a;p(j)=1/(a'*i nv(Rx)*a);endF=20*log10(abs(f)/(max(max(abs(f);subplot(1,2,1)plot(theta,F);grid on;hold on;plot(theta0,-20:0,'.');plot(theta1,-20:0,'.');plot(theta2,-20:0,'

25、;.');xlabel( 'theta/ ° ');ylabel( 'F/dB');title('Capon beamforming 方向圖');axis(-90 90 -20 0);P=20*log10(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,'.');xla

26、bel( 'theta/ ° ');ylabel( 'P/dB');title('Capon beamforming 功率譜');axis(-90 90 -20 0);(2)仿真結(jié)果Capon beamforming 方向圖Capon beamforming 功率譜-2-6-12-14-16-18theta/ °P -10i-48. Capon beamforming(1) matlab 程序clc;clear all ;close all ;imag=sqrt(_1);element_num=8; %車元數(shù)d_lambda=

27、0.5; %車元間距與波長(zhǎng)的關(guān)系theta=-90:0.5:90; 滋索圍thetaO=O;%三個(gè)信號(hào)源的來(lái)波方向theta 仁20;theta2=60;L=1000; %采樣單元數(shù)for i=1:Lamp0=10*ra ndn (1);amp1=200*ra ndn (1);amp2=200*ra ndn (1);amp n=3;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

28、_num-1')+amp2*exp(imag*2*pi*d_lambda*sin(theta2*pi/1 80)*0:element_num-1')+ampn*(randn(element_num,1)+imag*randn(element_num,1);endRx=1/L*x*x'R=i nv(Rx);steer=exp(imag*2*pi*dl_l ambda*sin(theta0*pi/180)*0:element_num-1');w=R*steer/(steer'*R*steer);%最優(yōu)權(quán)矢量for j=1:length(theta)a=exp

29、(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);grid on;hold on;plot(theta0,-50:0,'.');plot(theta1,-50:0,'.');plot(theta2,-50:0,'.');xlabel( 'theta/ ° &#

30、39;);ylabel( 'F/dB');title( 'Capon beamforming方向圖');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 功率譜');axis(-90 90 -90 0);(2)仿真結(jié)果Capon beamfo

31、rming 方向圖Capon beamforming 功率譜9.不同方法估計(jì)協(xié)方差矩陣的Capor波束形成(1)matlab 程序clc;clear all ;close all ;imag=sqrt(_1);element_num=8; %車元數(shù)為 8d_lambda=0.5; %可距為半波長(zhǎng) theta=-90:0.5:90;描圍thetaO=O; %來(lái)波方向theta仁50; %干擾方向L=1024; %采樣單元數(shù)for i=1:Lamp0=10*ra ndn ；amp1=50*ra ndn (1);amp n=0.5;s(:,i)=amp0*exp(imag*2*pi*d_lambda

32、*sin(theta0*pi/180)*0:element_num-1');j(:,i)=amp1*exp(imag*2*pi*d_lambda*sin(theta1*pi/180)*0:element_num-1');n(:,i)=amp n*exp(imag*2*pi*ra ndn (1)*0:eleme nt_nu m-1'); endRx=1/L*(s+j+n)*(s+j+n)'滋收信號(hào)自相關(guān)矩陣Rnj=1/L*(j+n)*(j+n)'%(干攏+噪聲的自相關(guān)矩陣e=exp(imag*2*pi*d_lambda*si n( theta0*pi/18

33、0)*0:eleme nt_nu m-1');Wopt_Rx=i nv(Rx)*e/(e'*i nv(Rx)*e);%采用接收信號(hào)的權(quán)矢量Wopt_Rnj=i nv(Rnj)*e/(e'*i nv(Rnj)*e);%采用干攏 + 噪聲信號(hào)的權(quán)矢量for j=1:length(theta)a=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(a

34、bs(f1);F2=20*log10(abs(f2/max(max(abs(f2);figure;plot(theta,F1,theta,F2, 'r');grid on;hold on;plot(theta0,-50:0,'.');plot(theta1,-50:0,'.');xlabel( 'theta/ ° ');ylabel( 'F(1,2)/dB');title('不同方法估計(jì)協(xié)方差矩陣的Capon波束形成);axis(-90 90 -60 0);(2)仿真結(jié)果不同方法估計(jì)協(xié)方差矩陣的C

35、apon波束形成-15-20-25-30-35-45theta/ °"1 .f-、J* 1 1 | j1 !/| to-.-4010.多點(diǎn)約束的Capor波束形成和方向圖(1) matlab 程序clc;clear all ;close all ;imag=sqrt(_1);eleme nt_num=8;d_lambda=0.5;theta=-90:0.3:90;thetaO=O;theta 仁20;theta2=50;L=512;Rx=zeros(eleme nt_nu m,eleme nt_nu m);%產(chǎn)生協(xié)方差矩陣for i=1:Lamp0=10*ra ndn (1

36、);amp1=10*ra ndn (1);amp2=50*ra ndn (1);amp n=0.5*ra ndn (1);%噪聲的幅度隨機(jī)產(chǎn)生，保證噪聲與信號(hào)之間是不相關(guān)的%表示接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*e

37、xp(imag*2*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1')+j(:,i);收信號(hào)endRx=1/L*x*x'R=i nv(Rx); w=amp0*exp(imag*2*pi*d_lambda*sin(theta0*pi/180)*0:element_num-1')+amp1*exp(imag*2*pi*d_la mbda*sin(theta1*pi/180)*0:element_num-1')+amp2*exp(imag*2*pi*d_lambda*sin(theta2*pi/180)* 0:elemen

38、t_num-1');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);P=20*log10(abs(p)/max(max(abs(p);figure;subplot(1,2,1);plot(theta,F);grid on;hold on;plot(theta0,-50:0,'.');plot(theta1

39、,-50:0,'.');plot(theta2,-50:0, '.'); xlabel( 'theta/ ° '); ylabel( 'F/dB');title('Capon beamforming 方向圖');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,&#

40、39;.');xlabel( 'theta/ ° '); ylabel( 'P/dB');title('Capon beamforming 功率譜');(2)仿真結(jié)果Capon beamforming 方向圖Capon beamforming 功率譜11.自適應(yīng)波束形成方向圖(1) matlab 程序clc;clear all ;close all ;imag=sqrt(_1);eleme nt_num=8;c=3e8;f=5e8;lambda=c/f;d_lambda=0.5;theta=-90:0.5:90;thetaO=O;theta 仁45;theta2=60;L=2048;for i=1:Lamp0=10*ra ndn (1);amp1=100*ra ndn (1);amp2=100*ra ndn (1);amp n=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)