www.gusucode.com > MATLAB-TLS系统仿真源码程序 > MATLAB-TLS系统仿真源码程序/TLS.m
%This program is designed to form broadband beam using conventional TLS eigenfilter
%Using ULA
clear all;
clear all;
N=6; %the number of the sensors
L=20; %the number of reference filter laps
d0=0.04; %the spacing the array
c=340; %the speed of sound
f_l=200; %the lowest frequency
f_u=4000; %the highest frequency
step1=10;
f=[f_l:step1:f_u]; %the signal frequency band
fs=2*f_u; %the sampling frequency
Ts=1/fs; %the sampling period
omega=2*pi*f/fs; %the signal anglular frequency
lambda_u=c/f_u; %the wavelength of the highest frequency
p=zeros(1,N); %the position of each sensor
step2=180;
theta=[0:pi/step2:pi]; %the angle
thetaT=pi/2; %the steered signal angle
%d2lambda=; %d to lambda
Theta_p1=70/180*pi;
Theta_p2=110/180*pi;
%Omega_p=
Theta_s1=pi/3;
Theta_s2=2*pi/3;
%Omega_s=
alpha=1;
omegac=1500/4000*pi;
thetac=pi/3;
for(l=1:L)
e(l,:)=exp(-j*(l-1)*omega);
end
for(n=1:N)
d(n)=d0*(n-1);
tau(n,:)=d(n)*cos(theta)*fs/c;
end
%compute Q_p Q_e and Q_eig
M=L*N;
step3=1000;
theta=[Theta_p1:pi/step3:Theta_p2];
theta1=[0:pi/step3:Theta_s1];
theta2=[Theta_s2:pi/step3:pi];
theta3=[0:pi/step3:pi];
omega1=[0:pi/step3:pi];
for(p=1:M)
disp(p);
k=mod(p-1,L);
n=floor((p-1)/L)+1;
a=k;
b=d(n)*fs/c;
gamma=0;
%compute A
A1(p)=trapz(theta,omega((f_u-f_l)/step1+1)*sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta))/pi))...
-trapz(theta,omega(1)*sinc(omega(1)*(a+b*cos(theta))/pi));
% if b==0
% if a==0
% A(p)=cos(gamma)*(Theta_p2-Theta_p1)*(omega((f_u-f_l)/step1+1)-omega(1));
% else
% A(p)=(sin(omega((f_u-f_l)/step1+1)*a+gamma)-sin(omega(1)*a+gamma))/a*(Theta_p2-Theta_p1);
% end
% elseif abs(b)>abs(a)
% thetan=acos(-a/b);
% if thetan>=Theta_p1 & thetan<=Theta_p2
% A(p)=trapz(theta,(sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta)))*b*sqrt(1-a^2/b^2)...
% .*(theta-thetan)+sin(gamma)*(a+b*cos(theta)))...
% ./((a+b*cos(theta))*b*sqrt(1-a^2/b^2).*(theta-thetan)))...
% -trapz(theta,(sin(omega(1)*(a+b*cos(theta)))*b*sqrt(1-a^2/b^2)...
% .*(theta-thetan)+sin(gamma)*(a+b*cos(theta)))...
% ./((a+b*cos(theta))*b*sqrt(1-a^2/b^2).*(theta-thetan)));
% else
% A(p)=trapz(theta,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta)))./(a+b*cos(theta)))...
% -trapz(theta,sin(omega(1)*(a+b*cos(theta)))./(a+b*cos(theta)));
% end
% else
% A(p)=trapz(theta,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta)))./(a+b*cos(theta)))...
% -trapz(theta,sin(omega(1)*(a+b*cos(theta)))./(a+b*cos(theta)));
% end
for(q=1:M)
%disp(q);
l=mod(q-1,L);
m=floor((q-1)/L)+1;
a=k-l;
b=(d(n)-d(m))*fs/c;
gamma=0;
%Qtot_e(p,q)=trapz(theta3,pi*sinc(a+b*cos(theta3)));
%Qtot_e(p,q)=trapz(theta3,pi*sinc(a+b*cos(theta3)));
Qtot_e(p,q)=pi*trapz(omega1,besselj(0,b*omega1).*cos(a*omega1));
%-trapz(theta3,omega(1)*sinc(omega(1)*(a+b*cos(theta3))/pi));
% Qtot_e1(p,q)=trapz(theta3,omega((f_u-f_l)/step1+1)*sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta3))/pi))...
% -trapz(theta3,omega(1)*sinc(omega(1)*(a+b*cos(theta3))/pi));
% syms theta1 theta2;
% g1=subs('sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta))/pi)');
% f1=inline('g1');
% g2=subs('sinc(omega(1)*(a+b*cos(theta))/pi)');
% f2=inline('g2');
% Q_ep(p,q)=quad(f1,Theta_p1,Theta_p2)-quad(f2,Theta_p1,Theta_p2);
% g3=subs('sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta1))/pi)');
% f3=inline('g3');
% g4=subs('sinc(omega(1)*(a+b*cos(theta1))/pi)');
% f4=inline('g4');
% g5=subs('sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta2))/pi)');
% f5=inline('g5');
% g6=subs('sinc(omega(1)*(a+b*cos(theta2))/pi)');
% f6=inline('g6');
% Q_es(p,q)=quad(f3,0,Theta_s1)-quad(f4,0,Theta_s1)+quad(f5,Theta_s2,pi)-quad(f6,Theta_s2,0);
% Q_ep1(p,q)=trapz(theta,omega((f_u-f_l)/step1+1)*sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta))/pi))...
% -trapz(theta,omega(1)*sinc(omega(1)*(a+b*cos(theta))/pi));
% Q_es1(p,q)=trapz(theta1,omega((f_u-f_l)/step1+1)*sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta1))/pi))...
% -trapz(theta1,omega(1)*sinc(omega(1)*(a+b*cos(theta1))/pi))...
% +trapz(theta2,omega((f_u-f_l)/step1+1)*sinc(omega((f_u-f_l)/step1+1)*(a+b*cos(theta2))/pi))...
% -trapz(theta2,omega(1)*sinc(omega(1)*(a+b*cos(theta2))/pi));
if b==0
if a==0
Q_ep(p,q)=cos(gamma)*(Theta_p2-Theta_p1)*(omega((f_u-f_l)/step1+1)-omega(1));
Q_es(p,q)=cos(gamma)*(Theta_s1+pi-Theta_s2)*(omega((f_u-f_l)/step1+1)-omega(1));
else
Q_ep(p,q)=(sin(omega((f_u-f_l)/step1+1)*a+gamma)-sin(omega(1)*a+gamma))/a*(Theta_p2-Theta_p1);
Q_es(p,q)=(sin(omega((f_u-f_l)/step1+1)*a+gamma)-sin(omega(1)*a+gamma))/a*(Theta_s1+pi-Theta_s2);
end
elseif abs(b)>abs(a)
thetan=acos(-a/b);
if thetan>=Theta_p1 & thetan<=Theta_p2
Q_ep(p,q)=trapz(theta,(sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta)))*b*sqrt(1-a^2/b^2)...
.*(theta-thetan)+sin(gamma)*(a+b*cos(theta)))...
./((a+b*cos(theta))*b*sqrt(1-a^2/b^2).*(theta-thetan)))...
-trapz(theta,(sin(omega(1)*(a+b*cos(theta)))*b*sqrt(1-a^2/b^2)...
.*(theta-thetan)+sin(gamma)*(a+b*cos(theta)))...
./((a+b*cos(theta))*b*sqrt(1-a^2/b^2).*(theta-thetan)));
Q_es(p,q)=trapz(theta1,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta1)))./(a+b*cos(theta1)))...
-trapz(theta1,sin(omega(1)*(a+b*cos(theta1)))./(a+b*cos(theta1)))...
+trapz(theta2,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta2)))./(a+b*cos(theta2)))...
-trapz(theta2,sin(omega(1)*(a+b*cos(theta2)))./(a+b*cos(theta2)));
elseif thetan<=Theta_s1 | thetan>=Theta_s2
Q_ep(p,q)=trapz(theta,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta)))./(a+b*cos(theta)))...
-trapz(theta,sin(omega(1)*(a+b*cos(theta)))./(a+b*cos(theta)));
Q_es(p,q)=trapz(theta1,(sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta1)))*b*sqrt(1-a^2/b^2).*(theta1-thetan)+sin(gamma)*(a+b*cos(theta1)))...
./((a+b*cos(theta1))*b*sqrt(1-a^2/b^2).*(theta1-thetan)))...
-trapz(theta1,(sin(omega(1)*(a+b*cos(theta1)))*b*sqrt(1-a^2/b^2).*(theta1-thetan)+sin(gamma)*(a+b*cos(theta1)))...
./((a+b*cos(theta1))*b*sqrt(1-a^2/b^2).*(theta1-thetan)))...
+trapz(theta2,(sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta2)))*b*sqrt(1-a^2/b^2)...
.*(theta2-thetan)+sin(gamma)*(a+b*cos(theta2)))./((a+b*cos(theta2))*b*sqrt(1-a^2/b^2).*(theta2-thetan)))...
-trapz(theta2,(sin(omega(1)*(a+b*cos(theta2)))*b*sqrt(1-a^2/b^2).*(theta2-thetan)+sin(gamma)*(a+b*cos(theta2)))...
./((a+b*cos(theta2))*b*sqrt(1-a^2/b^2).*(theta2-thetan)));
end
Q_ep(p,q)=trapz(theta,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta)))./(a+b*cos(theta)))...
-trapz(theta,sin(omega(1)*(a+b*cos(theta)))./(a+b*cos(theta)));
Q_es(p,q)=trapz(theta1,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta1)))./(a+b*cos(theta1)))...
-trapz(theta1,sin(omega(1)*(a+b*cos(theta1)))./(a+b*cos(theta1)))...
+trapz(theta2,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta2)))./(a+b*cos(theta2)))...
-trapz(theta2,sin(omega(1)*(a+b*cos(theta2)))./(a+b*cos(theta2)));
else
Q_ep(p,q)=trapz(theta,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta)))./(a+b*cos(theta)))...
-trapz(theta,sin(omega(1)*(a+b*cos(theta)))./(a+b*cos(theta)));
Q_es(p,q)=trapz(theta1,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta1)))./(a+b*cos(theta1)))...
-trapz(theta1,sin(omega(1)*(a+b*cos(theta1)))./(a+b*cos(theta1)))...
+trapz(theta2,sin(omega((f_u-f_l)/step1+1)*(a+b*cos(theta2)))./(a+b*cos(theta2)))...
-trapz(theta2,sin(omega(1)*(a+b*cos(theta2)))./(a+b*cos(theta2)));
end
end
end
%compute Q_eig
Q_LS=Q_ep+alpha*Q_es;
d_LS=(Theta_p2-Theta_p1)*(omega((f_u-f_l)/step1+1)-omega(1));
Q_TLS(1:M,1:M)=Q_LS;
Q_TLS(1:M,M+1)=A1';
Q_TLS(M+1,1:M)=A1;
Q_TLS(M+1,M+1)=d_LS;
Qtote(1:M,1:M)=Qtot_e;
Qtote(1:M,M+1)=zeros(M,1);
Qtote(M+1,1:M)=zeros(1,M);
Qtote(M+1,M+1)=1;
% for n=1:N
% C(:,n*L-L+1:n*L)=eye(L);
% end
% b=ones(L,1);
%quadric constraint
[V,D]=eig(Q_TLS,Qtote,'qz');
index=1;
m=D(1,1);
for i=2:M+1
if D(i,i)<m
m=D(i,i);
index=i;
end
end
w=-V(1:M,index+1)/V(M+1,index+1);
JCEF=0;
for(k=1:(f_u-f_l)/step1+1)%omega
%disp(k);
for(i=1:step2+1)%theta
%disp(i);
for(n=1:N)
v(n*L-L+1:n*L,i)=e(:,k)*exp(-j*omega(k)*tau(n,i)); %the array manifold
end
B(k,i)=w'*v(:,i);
if abs(B(k,i))<0.1
B(k,i)=0.1;
end
if i>=71 & i<=111
JCEF=JCEF+abs(B(k ,i)-1)^2;
else
JCEF=JCEF+alpha*abs(B(k,i))^2;
end
end
end
%
theta=[0:180];
[theta,f]=meshgrid(theta,f);
%
figure(1);
mesh(theta,f,20*log10(abs(B)));
axis([0,180,f_l,f_u,-20,0]);
% plot(theta,20*log10(abs(B_d)));
% polardb(abs(B(1,:)));
%figure(2);
%mesh(theta,f,abs(B1));
% mesh(theta,d2lambda,B_amp);
% figure(3);
% polardb(theta(1,:),20*log10(abs(B(151,:))),-40,'b');
% figure(4);
% polardb(theta(1,:),20*log10(abs(B(141,:))),-40,'b');
% figure(5);
% polardb(theta(1,:),20*log10(abs(B(131,:))),-40,'b');
% figure(6);
% polardb(theta(1,:),20*log10(abs(B(121,:))),-40,'b');
% figure(7);
% polardb(theta(1,:),20*log10(abs(B(111,:))),-40,'b');
% figure(8);
% polardb(theta(1,:),20*log10(abs(B(101,:))),-40,'b');
% figure(9);
% polardb(theta(1,:),20*log10(abs(B(91,:))),-40,'b');
% figure(10);
% polardb(theta(1,:),20*log10(abs(B(81,:))),-40,'b');