%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Figure 6.70
% Lillian Xu 12/18/2000
% updated by K. Bell 1/18/08
% function called: sinc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear all
close all
N = 10;
BWNN = 4/N;
n = (-(N-1)/2:(N-1)/2)';
ud = 0.1;
signalRange = [-ud:1/500:ud];
INRrange = [10 30];
SNRrange = [-10:2:40];
LNRrange = [-20:2:50];
ui1 = -0.30;
ui2 = 0.30;
Vi1 = exp(j*n*pi*ui1);
Vi2 = exp(j*n*pi*ui2);
% MPDR
C1 = exp(j*n*pi*[0]);
f1 = [1];
% directional
u1 = 0.0866;
uc = [0, -u1, u1];
C2 = exp(j*n*pi*uc);
f2 = [1;sin(-(N/2)*pi*u1)./(N*sin(-.5*pi*u1));sin((N/2)*pi*u1)./(N*sin(.5*pi*u1))];
% derivative
coef = 0.8;
C3 = [ones(N,1),j*n,-n.^2];
f3 = [1;0;coef*(1-N^2)/12];
% Taylor
SLL=20;
nBar=2;
Ne = 2;
scale = N*0.5;
A = 1/pi*acosh(10^(SLL/20));
uroot=[1:1:floor((N-1)/2)]/scale; % (N-1)/2 for odd and N/2 - 1 for N even
for m = 1:nBar-1
Vn = nBar*sqrt( (A^2+(m-0.5)^2)/(A^2+(nBar-0.5)^2) );
uroot(m) = Vn/scale;
end
if rem(N,2) == 0 % even
roots = [0 uroot -uroot 1];
else
roots = [0 uroot -uroot];
end
Vr = exp(j*n*pi*roots);
w0 = inv(Vr')*[1;zeros(N-1,1)];
wdBar = w0/norm(w0)^2;
PcWdBar = eye(N) - wdBar*inv(wdBar'*wdBar)*wdBar';
for h1 = 1:N
for h2 = 1:N
Rs(h1,h2) = 2*ud*sinc( (h1-h2)*ud );
end
end
RsBar = PcWdBar*Rs*PcWdBar;
[U,lambda,V] = svd(RsBar);
Cs = V(:,1:Ne); %select 3 eigenvectors
C4 = [wdBar,Cs];
f4 = [1;zeros(Ne,1)];
Gain1 = zeros(length(INRrange),length(SNRrange),length(LNRrange));
Gain2 = zeros(length(INRrange),length(SNRrange),length(LNRrange));
Gain3 = zeros(length(INRrange),length(SNRrange),length(LNRrange));
Gain4 = zeros(length(INRrange),length(SNRrange),length(LNRrange));
k1 = 1;
for INR = 10.^(INRrange/10)
disp(['loop ' int2str(k1) ' of 2 ...'])
k2 = 1;
for SNR = 10.^(SNRrange/10)
k3 = 1;
SINRi = SNR/(1+2*INR);
for LNR = 10.^(LNRrange/10)
for ua = signalRange
Vs = exp(j*n*pi*ua);
Ss = SNR*Vs*Vs';
Sn = eye(N) + INR*Vi1*Vi1'+ INR*Vi2*Vi2';
Sx = Ss + Sn + LNR*eye(N); % Diagonal Loading
% MPDR
W = inv(Sx)*C1*inv(C1'*inv(Sx)*C1)*f1; %consider White Noise only
SINR0 = real((W'*Ss*W)/(W'*Sn*W));
Gain1(k1,k2,k3) = Gain1(k1,k2,k3)+SINR0/SINRi;
% Directional
W = inv(Sx)*C2*inv(C2'*inv(Sx)*C2)*f2; %consider White Noise only
SINR0 = real((W'*Ss*W)/(W'*Sn*W));
Gain2(k1,k2,k3) = Gain2(k1,k2,k3)+SINR0/SINRi;
% Derivative
W = inv(Sx)*C3*inv(C3'*inv(Sx)*C3)*f3; %consider White Noise only
SINR0 = real((W'*Ss*W)/(W'*Sn*W));
Gain3(k1,k2,k3) = Gain3(k1,k2,k3)+SINR0/SINRi;
% Taylor
W = inv(Sx)*C4*inv(C4'*inv(Sx)*C4)*f4; %consider White Noise only
SINR0 = real((W'*Ss*W)/(W'*Sn*W));
Gain4(k1,k2,k3) = Gain4(k1,k2,k3)+SINR0/SINRi;
end % end of ua
k3 = k3 + 1;
end % end of LNR
k2 = k2 + 1;
end % end of SNR
k1 = k1 + 1;
end % end of INR
Gain1 = 10*log10( abs(Gain1)/length(signalRange) ) ;
Gain2 = 10*log10( abs(Gain2)/length(signalRange) ) ;
Gain3 = 10*log10( abs(Gain3)/length(signalRange) ) ;
Gain4 = 10*log10( abs(Gain4)/length(signalRange) ) ;
for k1 = 1:size(Gain1,1)
for k2 = 1:size(Gain1,2)
[A1(k1,k2),I(k1,k2)] = max(Gain1(k1,k2,:));
[A2(k1,k2),I(k1,k2)] = max(Gain2(k1,k2,:));
[A3(k1,k2),I(k1,k2)] = max(Gain3(k1,k2,:));
[A4(k1,k2),I(k1,k2)] = max(Gain4(k1,k2,:));
end
end
figure
plot(SNRrange,A1(1,:),'-',SNRrange,A2(1,:),'--',...
SNRrange,A3(1,:),'-.',SNRrange,A4(1,:),':');
hold on
xlabel('{\it SNR} (dB)')
ylabel('Optimal gain (dB)')
legend('MPDR','DIR,u_c=[0,0.0866,-0.0866],g=[1;B_C;B_C]',...
'DER,C=[1,d(0),d(0)],\alpha=0.8','QP,Taylor(-20dB,{\it n}=3),Ne=2','location','southwest')
%title('performance comparison with optimal LNR,ui=-0.3 & +0.3, INR=10dB(each), N=10')
axis([-10 40 5 25])
grid on
figure
plot(SNRrange,A1(2,:),'-',SNRrange,A2(2,:),'--',...
SNRrange,A3(2,:),'-.',SNRrange,A4(2,:),':');
hold on
xlabel('{\it SNR} (dB)')
ylabel('Optimal gain (dB)')
legend('MPDR','DIR,u_c=[0,0.0866,-0.0866],g=[1;B_C;B_C]',...
'DER,C=[1,d(0),d(0)],\alpha=0.8','QP,Taylor(-20dB,{\it n}=3),Ne=2','location','southwest')
%title('performance comparison with optimal LNR,ui=-0.3 & +0.3, INR=30dB(each), N=10')
axis([-10 40 20 45])
grid on
