ESPRIT算法

%%%%%%非相干信号，声压阵，clc;

close all;

clear all;

M=10; %阵元数

m=[0:M-1]';

N=30; %采样点数

n=0:N-1;

f=1000; %频率

fs=10*f; %采样频率

c=1500; %声速

lamd=c/f; %波长

d=lamd/2; %阵元间距

u1=80*pi/180; %目标1方位

u2=88*pi/180; %目标2方位

snr1=0;

snr2=10;

s1=exp(j*(2*pi*f*n/fs+2*pi*rand(1,N))); s2=exp(j*(2*pi*f*n/fs+2*pi*rand(1,N))); s=[s1;s2];

a1=exp(j*2*pi*f*m*d*cos(u1)/c);

a2=exp(j*2*pi*f*m*d*cos(u2)/c);

a=[a1 a2];

%S=a*s; %无噪声S=awgn(a*s,snr1,'measured','db'); %有噪声

R=S*S'/N;

[V,D]=eig(R);

Vm=V(:,1:8);

IR=inv(R);

Wmvdr=IR*a1/(a1'*IR*a1);

step=1;

Ang=0:step:180;

for kk=1:length(Ang)

a=exp(i*(2*m*pi*f*d*cos(Ang(kk)*pi/180)/c));

Pc(kk)=a'*R*a;

PP(kk)=1/(a'*IR*a); %MVDR方位谱

Pm(kk)=1/(a'*Vm*Vm'*a); %MUSIC方位谱end

figure(1);

h1=plot(Ang,10*log10(abs(Pc)/max(abs(Pc))),'g'); hold on;

h2=plot(Ang,10*log10(abs(PP)/max(abs(PP))),'r.-'); hold on;

h3=plot(Ang,10*log10(abs(Pm)/max(abs(Pm)))); legend([h1 h2 h3],'CBF','MVDR','MUSIC');

grid on;

%%%ESPRIT操作

X1=S(1:M-1,:);

X2=S(2:M,:);

X=[X1;X2];

R=X*X'/N;

[V,D]=eig(R);

Us=[V(:,2*(M-1)-1) V(:,2*(M-1))];

Us1=Us(1:M-1,:);

Us2=Us(M:2*(M-1),:);

FAI=inv(Us1'*Us1)*Us1'*Us2;

[V1,D1]=eig(FAI);

sita1=acos(-i*lamd*log(D1(1,1))/(2*pi*d))*180/pi; sita2=acos(-i*lamd*log(D1(2,2))/(2*pi*d))*180/pi;