--- /dev/null
+
+function W=SeDuMiBeampatternDesign(X,Y,F,C,NULLDIR,SELFNOISEdB,BW,SLLdB,N_theta,N_phi)
+ lambda=C/F;
+
+ nulldir_theta=NULLDIR(:,1);
+ nulldir_phi=NULLDIR(:,2);
+
+ if size(X,2) > size(X,1)
+ X=X';
+ end
+ if size(X,2) ~= 1
+ X=X(:,1);
+ end
+ if size(Y,2) > size(Y,1)
+ Y=Y';
+ end
+ if size(Y,2) ~= 1
+ Y=Y(:,1);
+ end
+
+ M = length(X)
+ N_nulls=length(nulldir_theta);
+
+ R=0;
+ V_nulls = zeros(M,N_nulls);
+ for n_null=1:N_nulls
+ %V_nulls(:,n_null) =
+ v = exp(1i*2*pi/lambda*(sin(nulldir_theta(n_null)).*cos(nulldir_phi(n_null))*X + sin(nulldir_theta(n_null)).*sin(nulldir_phi(n_null))*Y));
+ %v = exp(1i*pi*sin(nulldir_theta)*[1:M]');
+
+ R = R + 10^(45/10)*(v*v');
+ end
+ R = R + 10^(SELFNOISEdB/10)*eye(M);
+ L=chol(R);
+
+ epsilon=10^(SLLdB/10)
+ N_slobedirs_theta=N_theta;
+ N_slobedirs_phi=N_phi;
+
+ slobedir_theta = linspace(BW, 90/180*pi, N_theta);
+ if N_phi==1
+ slobedir_phi = [0,pi];
+ else
+ slobedir_phi = linspace(0, 2*pi*(N_slobedirs_phi-1)/N_slobedirs_phi, N_slobedirs_phi);
+ end
+
+ [slobedir_theta,slobedir_phi]=meshgrid(slobedir_theta, slobedir_phi);
+ slobedir_theta=slobedir_theta(:); slobedir_phi=slobedir_phi(:);
+
+ N_slobes=length(slobedir_theta)
+
+
+ as = ones(M,1);
+
+
+b = [-1;zeros(M+1,1)];
+A1 = [0,0;1,0;zeros(M,1),conj(as)];
+c1 = [sqrt(epsilon);1];
+A2 = [-1,zeros(1,M);0,zeros(1,M);zeros(M,1),-L.'];
+c2 = zeros(M+1,1);
+
+A = [A1,A2];
+c = [c1;c2];
+
+ for n_slobe=1:N_slobes
+ v = exp(-1i*2*pi/lambda*(sin(slobedir_theta(n_slobe)).*cos(slobedir_phi(n_slobe))*X + sin(slobedir_theta(n_slobe)).*sin(slobedir_phi(n_slobe))*Y));
+ Aj = [0,0;-1,0;zeros(M,1),-conj(v)];
+ cj = zeros(2,1);
+
+ A = [A, Aj];
+ c = [c;cj];
+ end
+
+K.f = 2;
+K.q = [M+1,2*ones(1,N_slobes)];
+K.ycomplex=3:size(A,1);
+K.xcomplex=1:size(A,2);
+
+%pars.eps=1E-16;
+[x,y,info]=sedumi(A,b,c,K);
+ W=y(3:end);
+ c1
+ y(1:2)
+ c1 - A1.'*y
\ No newline at end of file
--- /dev/null
+M = 16;
+R = eye(M);
+N_time=256;
+vi = exp(1i*pi*sind(50)*[1:M]');
+vi = 10^(45/20)*repmat(vi, 1, N_time);
+noise=randn(M,N_time);
+sigplusnoise = vi + noise;
+R = sigplusnoise*sigplusnoise'/N_time;
+R = vi*vi' + 10^(-45/10)*eye(M);
+
+
+L = chol(R)';
+SLLdB = -30;
+SLL = 10^(SLLdB/10);
+SLL = 1E-3;
+
+N_theta = 512;
+theta_min = 12/180*pi; theta_max = 90/180*pi;
+theta_vals = linspace(theta_min, theta_max, N_theta);
+theta_vals = [-fliplr(theta_vals),theta_vals];
+N_theta = length(theta_vals);
+V = zeros(2*M,N_theta);
+for m=1:M
+ V(m,:) = real(exp(-1i*pi*sin(theta_vals)*m));
+end
+for m=M+1:2*M
+ V(m,:) = imag(exp(-1i*pi*sin(theta_vals)*(m-M)));
+end
+
+epsilon = SLL;
+as = [ones(M,1); zeros(M,1)];
+
+b = [-1;zeros(2*M+1,1)];
+
+A1 = [0,0;1,0;zeros(2*M,1),conj(as)];
+c1 = [sqrt(epsilon);1];
+
+A1b = [0,0;1,0;zeros(2*M,1),conj(as)];
+c1b = [0;0];
+
+A2 = [-1,zeros(1,M);0,zeros(1,2*M);zeros(2*M,1),-L];
+c2 = zeros(M+1,1);
+
+A = [A1,A2];
+c = [c1;c2];
+for n_theta=1:N_theta
+ Aj = [0,0;-1,0;zeros(M,1),-conj(V(:,n_theta))];
+ cj = zeros(2,1);
+
+ A = [A, real(Aj];
+ c = [c;cj];
+end
+
+%A = [A,A1];
+%c = [c;c1];
+K.f = 4;
+K.q = [M+1,2*ones(1,N_theta)];
+%K.ycomplex=3:size(A,1);
+[x,y,info]=sedumi(A,b,c,K);
+
+Nfft=1024;
+xaxisvalues = asind([0:Nfft-1]/Nfft);
--- /dev/null
+clear all;
+close all;
+
+M = 16;
+R = eye(M);
+N_time=256;
+vi = exp(1i*pi*sind(50)*[1:M]');
+vi = 10^(45/20)*repmat(vi, 1, N_time);
+noise=randn(M,N_time);
+sigplusnoise = vi + noise;
+R = sigplusnoise*sigplusnoise'/N_time;
+R = vi*vi' + 10^(-45/10)*eye(M);
+
+N_intangle = 512;
+intangle_min = -90/180*pi; intangle_max = 90/180*pi;
+intangle_vals = linspace(intangle_min, intangle_max, N_intangle);
+Vint = zeros(M,N_intangle);
+for m=1:M
+ Vint(m,:) = exp(-1i*pi*sin(intangle_vals)*m);
+end
+
+%R = Vint*Vint' + 10^(-45/10)*eye(M);
+
+L = chol(R);
+SLLdB = -30;
+SLL = 10^(SLLdB/10);
+SLL = 1E-3;
+
+N_theta = 512;
+theta_min = 12/180*pi; theta_max = 90/180*pi;
+theta_vals = linspace(theta_min, theta_max, N_theta);
+theta_vals = [-fliplr(theta_vals),theta_vals];
+N_theta = length(theta_vals);
+V = zeros(M,N_theta);
+for m=1:M
+ V(m,:) = exp(-1i*pi*sin(theta_vals)*m);
+end
+
+epsilon = SLL;
+as = ones(M,1);
+
+b = [-1;zeros(M+1,1)];
+A1 = [0,0;1,0;zeros(M,1),conj(as)];
+c1 = [sqrt(epsilon);1];
+
+A2 = [-1,zeros(1,M);0,zeros(1,M);zeros(M,1),-L.'];
+c2 = zeros(M+1,1);
+
+
+A = [A1,A2];
+c = [c1;c2];
+
+for n_theta=1:N_theta
+ Aj = [0,0;-1,0;zeros(M,1),-conj(V(:,n_theta))];
+ cj = zeros(2,1);
+
+
+ A = [A, Aj];
+ c = [c;cj];
+
+end
+
+K.f = 2;
+K.q = [M+1,2*ones(1,N_theta)];
+K.ycomplex=3:size(A,1);
+K.xcomplex=1:size(A,2);
+
+[x,y,info]=sedumi(A,b,c,K);
+
+
+N_theta2=1024;
+theta_min = -90/180*pi; theta_max = 90/180*pi;
+theta_vals = linspace(theta_min, theta_max, N_theta2);
+
+BP = zeros(1, N_theta2);
+BP_das = zeros(1, N_theta2);
+
+for m=1:M
+ BP = BP + conj(y(2+m))*exp(-1i*pi*sin(theta_vals)*m);
+ BP_das = BP_das + (1/M)*exp(-1i*pi*sin(theta_vals)*m);
+end
+
+figure;
+plot(theta_vals/pi*180, 20*log10(abs(BP)),'r');
+hold on;
+plot(theta_vals/pi*180, 20*log10(abs(BP_das)));
+ylim([-50,10]);
+ax=axis;
+line(ax(1:2),10*log10(SLL)*ones(1,2));
--- /dev/null
+clear all;
+close all;
+
+M = 16;
+R = eye(M);
+N_time=1;
+vi = exp(1i*pi*sind(50)*[1:M]');
+%vi = 10^(45/20)*repmat(vi, 1, N_time);
+%noise=randn(M,N_time);
+%sigplusnoise = vi + noise;
+%R = sigplusnoise*sigplusnoise'/N_time;
+R = 10^(45/10)*(vi*vi') + 10^(-45/10)*eye(M);
+
+%N_intangle = 512;
+%intangle_min = -90/180*pi; intangle_max = 90/180*pi;
+%intangle_vals = linspace(intangle_min, intangle_max, N_intangle);
+%Vint = zeros(M,N_intangle);
+%for m=1:M
+% Vint(m,:) = exp(-1i*pi*sin(intangle_vals)*m);
+%end
+
+%R = Vint*Vint' + 10^(-45/10)*eye(M);
+
+L = chol(R);
+SLLdB = -30;
+SLL = 10^(SLLdB/10);
+%SLL = 1E-3;
+
+N_theta = 512;
+theta_min = 12/180*pi; theta_max = 90/180*pi;
+theta_vals = linspace(theta_min, theta_max, N_theta);
+theta_vals = [-fliplr(theta_vals),theta_vals];
+N_theta = length(theta_vals);
+V = zeros(M,N_theta);
+for m=1:M
+ V(m,:) = exp(-1i*pi*sin(theta_vals)*m);
+end
+
+epsilon = SLL;
+as = ones(M,1);
+
+b = [-1;zeros(M+1,1)];
+A1 = [0,0;1,0;zeros(M,1),conj(as)];
+c1 = [sqrt(epsilon);1];
+
+A2 = [-1,zeros(1,M);0,zeros(1,M);zeros(M,1),-L.'];
+c2 = zeros(M+1,1);
+
+
+A = [A1,A2];
+c = [c1;c2];
+
+for n_theta=1:N_theta
+ Aj = [0,0;-1,0;zeros(M,1),-conj(V(:,n_theta))];
+ cj = zeros(2,1);
+
+
+ A = [A, Aj];
+ c = [c;cj];
+
+end
+
+K.f = 2;
+K.q = [M+1,2*ones(1,N_theta)];
+K.ycomplex=3:size(A,1);
+K.xcomplex=1:size(A,2);
+
+[x,y,info]=sedumi(A,b,c,K);
+
+
+N_theta2=1024;
+theta_min = -90/180*pi; theta_max = 90/180*pi;
+theta_vals = linspace(theta_min, theta_max, N_theta2);
+
+BP = zeros(1, N_theta2);
+BP_das = zeros(1, N_theta2);
+
+for m=1:M
+ BP = BP + conj(y(2+m))*exp(-1i*pi*sin(theta_vals)*m);
+ BP_das = BP_das + (1/M)*exp(-1i*pi*sin(theta_vals)*m);
+end
+
+figure;
+plot(theta_vals/pi*180, 20*log10(abs(BP)),'r');
+hold on;
+plot(theta_vals/pi*180, 20*log10(abs(BP_das)));
+ylim([-50,10]);
+ax=axis;
+line(ax(1:2),10*log10(SLL)*ones(1,2));
--- /dev/null
+c = 340;
+f = 1E3;
+lambda = c/f;
+
+M=20;
+X1 = [-(M-1)/2:(M-1)/2]'*lambda/4;
+X2 = [-(M-1)/2:(M-1)/2]'*lambda/2;
+Y = X1*0;
+
+
+BW = 0;
+N_pts = 360;
+WNG_min = 0;
+alpha = 1.0;
+
+w1 = lsweights_okt2012(X1, Y, f, BW, N_pts, WNG_min,alpha);
+w2 = lsweights_okt2012(X2, Y, f, BW, N_pts, WNG_min,alpha);
+
+figure;
+plot(db(abs(fft(w1,1024))));
+hold on;
+plot(db(abs(fft(w2,1024))), 'r');
\ No newline at end of file
+++ /dev/null
-% Generate test case (ULA, M=10). a) Signal only, b) noise only,
-% c) signal-plus-noise
-
-load xy_tass;
-
-x = x(1:16);
-y = y(1:16)*0;
-
-M = length(x);
-N = 44100;
-F = 2E3;
-Fs = 44100;
-c = 340;
-
-doa = 0.0;
-doa_steer = 53.5;
-
-data = zeros(M,N);
-
-N_fft = 64;
-h = zeros(M, N_fft);
-
-for m=1:M
- data(m,:) = cos(2*pi*F*(1/Fs*[0:N-1] + cosd(doa)*x(m)/c));
-end
-
-N_theta = 512; theta_min = -90;, theta_max = 90;
-theta_vals = theta_min:theta_max;%linspace(theta_min, theta_max, N_theta);
-N_theta = length(theta_vals);
-
-y = zeros(N_theta, N_fft);
-
-DATA = fft(data(:,1:N_fft),[],2);
-
-w = hamming(M);
-
-for n_theta=1:N_theta
- delays = round(cosd(theta_vals(n_theta))*x/c*Fs);
- %delays = delays-min(delays);
-
- for m=1:M
- h(m,:) = w(m)*exp(-1i*delays(m)*2*pi*[0:N_fft-1]/N_fft);
- end
-
- y(n_theta,:) = ifft(mean(DATA.*h,1));
-
- DATA_vec = DATA(:);
- X =
-
-end
-
-figure;
-imagesc([0:N_fft-1],theta_vals,db(abs(y/max(abs(y(:))))), [-40,0])
\ No newline at end of file
N_fft = 128*R;
h = zeros(M, N_fft);
h_das = zeros(M, N_fft);
+h_mvdr = zeros(M, N_fft);
-N_ix = 18*R;
-F = Fs/N_fft*(N_ix + 0.5);
+N_ix = 9*R;
+F = Fs/N_fft*(N_ix + 0.0);
+%F = 1.5E3;
+%N_ix = round(F/Fs*N_fft);
for m=1:M
%data(m,:) = cos(2*pi*F*(1/Fs*[0:N-1] + sind(doa)*x(m)/c));
y = zeros(N_theta, N_fft);
y_das = zeros(N_theta, N_fft);
+y_mvdr = zeros(N_theta, N_fft);
DATA = fft(data(:,1:N_fft),[],2);
delays = (sind(doa_steer)*x/c*Fs);
data = exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(theta_vals(n_theta))*repmat(x,1,N)/c));
+ %data = data + exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(0)*repmat(x,1,N)/c));
DATA = fft(data(:,1:N_fft),[],2);
%delays = delays-min(delays);
%l
%H
- R_toep_v(l+1) = sum(sum(H.*R)); %(diag(R,m-1))/M;
- %R_toep_v(l+1) = sum(diag(R,l))/M;
+ %R_toep_v(l+1) = sum(sum(H.*R)); %(diag(R,m-1))/M;
+ R_toep_v(l+1) = sum(diag(R,l))/M;
end
R_toep = toeplitz(R_toep_v);
%R_toep = eye(M);
%[n_fft, kappa, rank(R_toep)]
R_toep_ = inv(R_toep);
+ R_ = inv(R);
h(:,n_fft) = R_toep_*d/(d'*R_toep_*d);
+ h_mvdr(:,n_fft) = R_*d/(d'*R_*d);
h_das(:,n_fft) = d/M;
end
h(:,1) = ones(M,1)/M;
+ h_mvdr(:,1) = ones(M,1)/M;
h_das(:,1) = ones(M,1)/M;
+ if 0
+ y(n_theta,:) = ifft(sum(DATA.*conj(h),1));
+ y_das(n_theta,:) = ifft(sum(DATA.*conj(h_das),1));
+ else
- y(n_theta,:) = ifft(sum(DATA.*(h),1));
- y_das(n_theta,:) = ifft(sum(DATA.*(h_das),1));
-
- y(n_theta,:) = (sum(DATA.*conj(h),1));
y_das(n_theta,:) = (sum(DATA.*conj(h_das),1));
+ y_mvdr(n_theta,:) = (sum(DATA.*conj(h_mvdr),1));
+ y(n_theta,:) = sum(DATA.*conj(h),1);
+ y(n_theta,:) = min(y_das(n_theta,:),y(n_theta,:));
+ end
+ if 1
figure(f1);
%imagesc([0:N_fft-1],theta_vals,db(abs(y/max(abs(y(:))))),[-40,0])
hold off;
hold on;
%plot(db(abs(y_das(:,N_fft-N_ix+1))), 'g')
plot(db(abs(y(:,N_ix+1))), 'r')
+ plot(db(abs(y_mvdr(:,N_ix+1))), 'g')
%plot(db(abs(y(:,N_fft/2+2))), 'r')
+ else
+ subplot(1,2,1);
+ imagesc([0:N_fft-1],theta_vals,db(abs(y_das)))
+ colorbar;
+ subplot(1,2,2);
+ imagesc([0:N_fft-1],theta_vals,db(abs(y)))
+ colorbar;
+ end
drawnow;
end
%%
figure;
-imagesc([0:N_fft-1],theta_vals,db(abs(y/max(abs(y(:))))), [-40,0])
+z=y(:,10:end-10);
+imagesc([0:N_fft-1],theta_vals,db(abs(z/max(abs(z(:))))), [-40,0])
%plot(db(abs(y(:,N_fft/2+2))))
%plot(db(abs(y(:,N_ix+1))))
\ No newline at end of file
doa2 = 12.0;
delta = 1E-2;
-sigma_n = 1E-2;
+sigma_n = 7E-2;
N_avg = 1;
noise = sigma_n*(randn(M,N_avg) + 1i*randn(M,N_avg));
data = exp(1i*2*pi/lambda*sind(doa)*x') + exp(1i*2*pi/lambda*sind(doa2)*x');% + noise;
--- /dev/null
+% Generate test case (ULA, M=10). a) Signal only, b) noise only,
+% c) signal-plus-noise
+
+load xy_tass;
+
+x = x(1:16);
+y = y(1:16)*0;
+
+M = length(x);
+N = 44100;
+L = 8;
+K=M-L+1;
+
+R = 1;
+
+Fs = 44100*R;
+c = 340;
+
+doa = 10.0;
+doa_steer = 0;
+
+data = zeros(M,N);
+
+N_fft = 128*R;
+h = zeros(M, N_fft);
+h_das = zeros(M, N_fft);
+h_mvdr = zeros(M, N_fft);
+
+N_ix = 9*R;
+F = Fs/N_fft*(N_ix + 0.0);
+%F = 1.5E3;
+%N_ix = round(F/Fs*N_fft);
+
+for m=1:M
+ %data(m,:) = cos(2*pi*F*(1/Fs*[0:N-1] + sind(doa)*x(m)/c));
+ %data(m,:) = exp(1i*2*pi*F*(1/Fs*[0:N-1] + sind(doa)*x(m)/c));
+ %data(m,:) = exp(1i*2*pi*F*(1/Fs*[0:N-1] + round(Fs*sind(doa)*x(m)/c)/Fs));
+ %data(m,:) = exp(1i*2*pi*F*round([0:N-1] + Fs*sind(doa)*x(m)/c)/Fs);
+end
+
+N_theta = 256; theta_min = -10; theta_max = 10;
+theta_vals = linspace(theta_min, theta_max, N_theta);
+theta_vals = sort([theta_vals,-5.7,5.5]);
+N_theta = length(theta_vals);
+
+y = zeros(N_theta, N_fft);
+y_das = zeros(N_theta, N_fft);
+y_mvdr = zeros(N_theta, N_fft);
+y_mvdrss = zeros(N_theta, N_fft);
+
+DATA = fft(data(:,1:N_fft),[],2);
+
+%z = exp(-1i*round(cosd(doa)*x/c*Fs)*2*pi*(25-1)/N_fft);
+
+delta_x = x(2) - x(1);
+[n_ix, m_ix] = meshgrid(1:M,1:M);
+%l = m_ix - n_ix;
+
+f1=figure;
+for n_theta=1:N_theta
+ n_theta/N_theta
+
+ delays = (sind(theta_vals(n_theta))*x/c*Fs);
+
+ %data = exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(theta_vals(n_theta))*repmat(x,1,N)/c));
+ data = exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(5.7)*repmat(x,1,N)/c));
+ data = data + exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(-5.5)*repmat(x,1,N)/c));
+ DATA = fft(data(:,1:N_fft),[],2);
+
+ %delays = delays-min(delays);
+ %D = exp(-1i*delays*2*pi*[0:N_fft-1]/N_fft);
+ for n_fft = 2:N_fft
+ d = exp(-1i*delays*2*pi*(n_fft-1)/N_fft);
+ R = DATA(:,n_fft)*DATA(:,n_fft)';
+
+ Rss = zeros(L);
+ for k=1:K
+ Rss = Rss + DATA(k:k+L-1,n_fft)*DATA(k:k+L-1,n_fft)';
+ end
+
+ %R = ones(size(R));
+
+ F_fft = (n_fft-1)/N_fft*Fs;
+
+ if (n_fft-1) > N_fft/2
+ F_fft = (N_fft - n_fft + 1)/N_fft*Fs;
+ d = exp(-1i*delays*2*pi*(N_fft - n_fft + 1)/N_fft);
+ end
+
+ lambda_fft = c/F_fft;
+ kappa = 2*delta_x/lambda_fft;
+ k_max = pi*kappa;
+
+ %if (n_fft == N_ix + 1) %(n_fft == (N_fft-N_ix+1)) || (n_fft == N_ix + 1)
+ % [DATA(:,n_fft)/N_fft, d]
+ %end
+
+ R_toep_v = zeros(1,M);
+ H = zeros(M);
+ for l=0:M-1
+ l_mark = l + (m_ix - n_ix);
+
+ H = 1./(1i*l_mark).*(exp(1i*kappa*pi*l_mark) - exp(-1i*kappa*pi*l_mark));
+ H_ix = find(l_mark==0);
+
+ H(H_ix) = 2*pi*kappa;
+
+ %l
+ %H
+
+ R_toep_v(l+1) = sum(sum(H.*R)); %(diag(R,m-1))/M;
+ %R_toep_v(l+1) = sum(diag(R,l))/M;
+ end
+
+ R_toep = toeplitz(R_toep_v);
+ %R_toep = eye(M);
+ %[n_fft, kappa, rank(R_toep)]
+ R_toep_ = inv(R_toep);
+ R_ = inv(R);
+ Rss_ = inv(Rss);
+
+ h(:,n_fft) = R_toep_*d/(d'*R_toep_*d);
+ h_mvdr(:,n_fft) = R_*d/(d'*R_*d);
+ h_mvdrss(:,n_fft) = Rss_*d(1:L)/(d(1:L)'*Rss_*d(1:L));
+ h_das(:,n_fft) = d/M;
+ end
+ h(:,1) = ones(M,1)/M;
+ h_mvdr(:,1) = ones(M,1)/M;
+ h_mvdrss(:,1) = ones(L,1)/L;
+ h_das(:,1) = ones(M,1)/M;
+
+ if 0
+ y(n_theta,:) = ifft(sum(DATA.*conj(h),1));
+ y_das(n_theta,:) = ifft(sum(DATA.*conj(h_das),1));
+ else
+
+ y_das(n_theta,:) = (sum(DATA.*conj(h_das),1));
+ y_mvdr(n_theta,:) = (sum(DATA.*conj(h_mvdr),1));
+ y_mvdrss(n_theta,:) = (sum(DATA(1:L,:).*conj(h_mvdrss),1));
+ y(n_theta,:) = sum(DATA.*conj(h),1);
+ %y(n_theta,:) = min(y_das(n_theta,:),y(n_theta,:));
+ end
+
+ if 1
+ figure(f1);
+ %imagesc([0:N_fft-1],theta_vals,db(abs(y/max(abs(y(:))))),[-40,0])
+ hold off;
+ plot(theta_vals, db(abs(y_das(:,N_ix+1))), 'b')
+ %plot(db(abs(y_das(:,N_fft/2+2))), 'b')
+ hold on;
+ %plot(db(abs(y_das(:,N_fft-N_ix+1))), 'g')
+ plot(theta_vals, db(abs(y(:,N_ix+1))), 'r')
+ plot(theta_vals, db(abs(y_mvdr(:,N_ix+1))), 'g')
+ plot(theta_vals, db(abs(y_mvdrss(:,N_ix+1))), 'k')
+ %plot(db(abs(y(:,N_fft/2+2))), 'r')
+ else
+ subplot(1,2,1);
+ imagesc([0:N_fft-1],theta_vals,db(abs(y_das)))
+ colorbar;
+ subplot(1,2,2);
+ imagesc([0:N_fft-1],theta_vals,db(abs(y)))
+ colorbar;
+ end
+ drawnow;
+end
+%%
+figure;
+z=y(:,10:end-10);
+imagesc([0:N_fft-1],theta_vals,db(abs(z/max(abs(z(:))))), [-40,0])
+%plot(db(abs(y(:,N_fft/2+2))))
+%plot(db(abs(y(:,N_ix+1))))
\ No newline at end of file
h = zeros(M, N_fft);
h_das = zeros(M, N_fft);
-N_ix = 64*R;
-F = Fs/N_fft*(N_ix + 0.0);
+N_ix = 32*R;
+F = Fs/N_fft*(N_ix + 0.5);
for m=1:M
%data(m,:) = cos(2*pi*F*(1/Fs*[0:N-1] + sind(doa)*x(m)/c));
data = 0;
for n_fft=N_ix:N_ix
- F = Fs/N_fft*(n_fft + 0*rand_skift(n_fft));
+ F = Fs/N_fft*(n_fft + rand_skift(n_fft));
data = data + exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(theta_vals(n_theta))*repmat(x,1,N)/c));
end
--- /dev/null
+% Generate test case (ULA, M=10). a) Signal only, b) noise only,
+% c) signal-plus-noise
+
+load xy_tass;
+load testsignals;
+
+R = 1;
+data_src = resample(y, 44100*R, Fs)';
+
+x = x(1:16);
+y = y(1:16)*0;
+
+M = length(x);
+N = 44100;
+
+Fs = 44100*R;
+c = 340;
+
+doa = 10.0;
+doa_steer = 0;
+
+data = zeros(M,N);
+
+N_fft = 128*R;
+h = zeros(M, N_fft);
+h_das = zeros(M, N_fft);
+
+N_ix = 32*R;
+F = Fs/N_fft*(N_ix + 0.5);
+
+for m=1:M
+ %data(m,:) = cos(2*pi*F*(1/Fs*[0:N-1] + sind(doa)*x(m)/c));
+ %data(m,:) = exp(1i*2*pi*F*(1/Fs*[0:N-1] + sind(doa)*x(m)/c));
+ %data(m,:) = exp(1i*2*pi*F*(1/Fs*[0:N-1] + round(Fs*sind(doa)*x(m)/c)/Fs));
+ %data(m,:) = exp(1i*2*pi*F*round([0:N-1] + Fs*sind(doa)*x(m)/c)/Fs);
+end
+
+N_theta = 256; theta_min = -90; theta_max = 90;
+theta_vals = theta_min:theta_max;%linspace(theta_min, theta_max, N_theta);
+N_theta = length(theta_vals);
+
+y = zeros(N_theta, N_fft);
+y_das = zeros(N_theta, N_fft);
+
+DATA = fft(data(:,1:N_fft),[],2);
+
+%z = exp(-1i*round(cosd(doa)*x/c*Fs)*2*pi*(25-1)/N_fft);
+
+delta_x = x(2) - x(1);
+[n_ix, m_ix] = meshgrid(1:M,1:M);
+%l = m_ix - n_ix;
+
+rand_skift = rand(1, N_fft);
+delta = 1E-2;
+cond_vec = zeros(N_theta,N_fft);
+
+f1=figure;
+f2=figure;
+for n_theta=1:N_theta
+ n_theta/N_theta
+ delays = (sind(theta_vals(n_theta))*x/c*Fs);
+ delays = (sind(doa_steer)*x/c*Fs);
+
+ %for m=1:M
+ % delay(m) = round(sind(theta_vals(n_theta))*x(m)/c*Fs);
+ %end
+
+ %delay = delay - min(delay) + 1;
+ %data = repmat(data_src, M,1);
+ %for m=1:M
+
+ % data(m,1:N_fft) = data(m,delay(m):delay(m)+N_fft-1);
+ %end
+
+ data = 0;
+ for n_fft=N_ix:N_ix
+ F = Fs/N_fft*(n_fft + rand_skift(n_fft));
+ data = data + exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(theta_vals(n_theta))*repmat(x,1,N)/c));
+ end
+
+
+ %data = exp(1i*2*pi*F*(1/Fs*repmat([0:N-1],M,1) + sind(theta_vals(n_theta))*repmat(x,1,N)/c));
+ DATA = fft(data(:,1:N_fft),[],2);
+
+ %delays = delays-min(delays);
+ %D = exp(-1i*delays*2*pi*[0:N_fft-1]/N_fft);
+ for n_fft = 1:N_fft
+
+ d = exp(-1i*delays*2*pi*(n_fft-1)/N_fft);
+ R = DATA(:,n_fft)*DATA(:,n_fft)';
+
+ %R = ones(size(R));
+
+ F_fft = (n_fft-1)/N_fft*Fs;
+
+ if (n_fft-1) > N_fft/2
+ F_fft = (N_fft - n_fft + 1)/N_fft*Fs;
+ d = exp(-1i*delays*2*pi*(N_fft - n_fft + 1)/N_fft);
+ end
+
+ lambda_fft = c/F_fft;
+ kappa = 2*delta_x/lambda_fft;
+ k_max = pi*kappa;
+
+ %if (n_fft == N_ix + 1) %(n_fft == (N_fft-N_ix+1)) || (n_fft == N_ix + 1)
+ % [DATA(:,n_fft)/N_fft, d]
+ %end
+
+ R_toep_v = zeros(1,M);
+ H = zeros(M);
+ for l=0:M-1
+ l_mark = l + (m_ix - n_ix);
+
+ H = 1./(1i*l_mark).*(exp(1i*kappa*pi*l_mark) - exp(-1i*kappa*pi*l_mark));
+ H_ix = find(l_mark==0);
+
+ H(H_ix) = 2*pi*kappa;
+
+ %l
+ %H
+
+ R_toep_v(l+1) = sum(sum(H.*R)); %(diag(R,m-1))/M;
+ %R_toep_v(l+1) = sum(diag(R,l))/M;
+ end
+
+ R_toep = toeplitz(R_toep_v);
+ cond_vec(n_theta,n_fft) = cond(R_toep);
+ %if rank(R_toep)==size(R_toep,1)
+ %if rank(R_toep)==size(R_toep,1) && cond(R_toep)<1E3
+
+ %rank(R_toep)
+
+ if 1
+ R_toep_ = inv(R_toep + delta*trace(R_toep)/M*eye(M));
+
+ h(:,n_fft) = R_toep_*d/(d'*R_toep_*d);
+ else
+ h(:,n_fft) = d/M;
+ end
+ h_das(:,n_fft) = d/M;
+ end
+ %h(:,1) = ones(M,1)/M;
+ %h_das(:,1) = ones(M,1)/M;
+
+
+ %y(n_theta,:) = ifft(sum(DATA.*(h),1));
+ %y_das(n_theta,:) = ifft(sum(DATA.*(h_das),1));
+
+ y(n_theta,:) = (sum(DATA.*conj(h),1));
+ y_das(n_theta,:) = (sum(DATA.*conj(h_das),1));
+
+ das_better_ixs = find(abs(y_das(n_theta,:))<abs(y(n_theta,:)));
+ y(n_theta,das_better_ixs) = y_das(n_theta,das_better_ixs);
+
+ if 0
+ figure(f1);
+ %imagesc([0:N_fft-1],theta_vals,db(abs(y/max(abs(y(:))))),[-40,0])
+ hold off;
+ plot(db(abs(y_das(:,N_ix+1))), 'b')
+ %plot(db(abs(y_das(:,N_fft/2+2))), 'b')
+ hold on;
+ %plot(db(abs(y_das(:,N_fft-N_ix+1))), 'g')
+ plot(db(abs(y(:,N_ix+1))), 'r')
+ %plot(db(abs(y(:,N_fft/2+2))), 'r')
+ drawnow;
+ end
+
+ if 1
+ figure(f2);
+ subplot(1,2,1);
+ imagesc([0:N_fft-1],theta_vals,db(abs(y)/max(abs(y_das(:)))), [-75,0]);
+ %imagesc([0:N_fft-1],theta_vals,db(abs(y)));
+ subplot(1,2,2);
+ imagesc([0:N_fft-1],theta_vals,db(abs(y_das)/max(abs(y_das(:)))), [-75,0]);
+ %imagesc([0:N_fft-1],theta_vals,db(abs(y_das)));
+ %subplot(1,3,3);
+ %imagesc(cond_vec);
+ end
+ drawnow;
+end
+%%
+figure;
+imagesc([0:N_fft-1],theta_vals,db(abs(y/max(abs(y(:))))), [-40,0])
+%plot(db(abs(y(:,N_fft/2+2))))
+%plot(db(abs(y(:,N_ix+1))))
\ No newline at end of file
DATA = fft(data(:,1:N_fft),[],2);
-
-
%z = exp(-1i*round(cosd(doa)*x/c*Fs)*2*pi*(25-1)/N_fft);
delta_x = x(2) - x(1);
n_theta/N_theta
delays = (sind(theta_vals(n_theta))*x/c*Fs);
%delays = delays-min(delays);
-
-
+
%D = exp(-1i*delays*2*pi*[0:N_fft-1]/N_fft);
for n_fft = 2:N_fft
d = exp(-1i*delays*2*pi*(n_fft-1)/N_fft);
\relax
+\citation{nilsen:wiener}
\@writefile{toc}{\contentsline {section}{\numberline {I}Introduction}{1}}
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+\@writefile{toc}{\contentsline {section}{References}{3}}
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--- /dev/null
+\documentclass[journal,onecolumn,english,a4paper]{IEEEtran}\r
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+\newcommand{\outerp}[1]{#1 #1^{H}}\r
+\r
+\title{Review of AAA-D-13-00058: ``Design and Performance Analysis of Live Model of Bessel Beamformer for Adaptive Array System''}\r
+\r
+\begin{document}\r
+\maketitle\r
+\r
+\section{Summary}\r
+\r
+\section{Major concerns}\r
+\r
+{\bf X)} The authors should get their paper proofread by a native\r
+English speaker, if possible. In any way, the language needs\r
+improvement. I have not included specific comments on this in the review.\r
+\r
+\section{Minor concerns}\r
+\r
+{\bf X)} Is the LMS algorithm really the ``{\it most} commonly used''\r
+technique for adaptive antenna array beamforming? Do you have a\r
+reference for this? If not, the description should be changed to\r
+something like ``The LMS algorithm is a commonly used (...)''. \r
+\r
+{\bf X)} After Eq. (2), should ``Bessel vector'' be ``Bessel\r
+function''? If it truly is a vector, what kind of vector-vector\r
+product between the Bessel vector and the weight vector is implied\r
+here? Additionally, what are the elements of the Bessel vector?\r
+\r
+{\bf X)} The authors state that the initial weight value ideally has\r
+no impact on the end result. Is this true in practice? If so, does it affect\r
+other aspects than the end result? If not so, why bother using a\r
+specific non-zero value at all, why not simply set the initial weight\r
+vector to zero?\r
+\r
+\section{Conclusions}\r
+\r
+\end{document}
\ No newline at end of file
--- /dev/null
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--- /dev/null
+\documentclass[journal,onecolumn,english,a4paper]{IEEEtran}\r
+\usepackage{graphicx,varioref,mathrsfs,amssymb,amsmath}\r
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+\r
+\title{Review of MM-004756}\r
+\r
+\begin{document}\r
+\maketitle\r
+\r
+\section{Summary}\r
+The paper ``High Quality Low Bitrate Spatial Audio Coding'' is\r
+concerned with optimizing spatial encoding for audio\r
+compression. The authors point out that existing techniques for spatial audio coding do not seek\r
+to minimize the decoded audio reconstruction error, and they suggest that\r
+this should be done. \r
+\r
+The idea seems both reasonable and appealing, and the results seem\r
+convincing, but I have some concerns with repect to the\r
+presentation. The difference of the paper's contribution from similar\r
+material covered in [59] is a bit unclear.\r
+\r
+\section{List of concerns}\r
+\begin{enumerate}\r
+\item The paper has a lot of overlap with the authors' previous work\r
+ in [59], something that I personally feel should be acknowledged\r
+ already at the beginning of the paper. The difference of this paper\r
+ from [59] should be specified, as some of the extensions from\r
+ [59] are not quite clear. Specifically, Secs. III and IV are very confusing to me. I do not follow\r
+ the authors' explanation of AbS in the context of spatial encoding,\r
+ and it is especially unclear to me how the results in Sec. III\r
+ are the basis for the computations described in Sec. IV. I will try\r
+ to describe this confusion further in the following points:\r
+\item The general model described by Fig. 3 (and the accompanying\r
+ description) is confusing in that it has no definite final output\r
+ and that it is not clear what is communicated back to the ``Spatial\r
+ analysis'' block. Also, it seems like the ``Error minimisation''\r
+ block depends on the ``Spatial Parameters'', even though they are\r
+ not fed through. Do not get me wrong, I understand what the authors\r
+ are trying to express here. But it is my opinion that if you choose\r
+ a schematic diagram to convey your idea, it should be complete and\r
+ consistent.\r
+% \item It is very hard to follow the authors' derivations in\r
+% Sec. III-B. (The follwing comment is based on the assumptions that\r
+% $x_{1,2}[n]$ are real signals.) After Eq. (17) the authors state that they assume\r
+% that $\mat{e}_{1}=\mat{x}_{1}-\hat{a}\mat{\hat{y}} - \mat{\hat{r}}$\r
+% and $\vec{e}_{2}=\mat{x}_{2}-\hat{b}\mat{\hat{y}} + \mat{\hat{r}}$\r
+% are not zero vectors, but that they should both be orthogonal to all\r
+% of their respective components\r
+% (i.e. $\mat{x}_{1},\mat{\hat{y}},\mat{\hat{r}}$ for $\mat{e}_{1}$\r
+% and $\mat{x}_{2},\mat{\hat{y}},\mat{\hat{r}}$ for\r
+% $\mat{e}_{2}$). Now; if a vector can be written as a sum of vectors,\r
+% all of which it is orthogonal to, does that not mean the vector must\r
+% in deed be a zero vector? And why do the authors talk about minimum MSE and\r
+% zero MSE as one and the same?\r
+\item It seems like the conclusion after Eqs. (22) and (23) is simply\r
+ that if the downmix signal is calculated from the quantized (or\r
+ estimated) energy constants instead of the actual energy constants,\r
+ then the reconstruction is error free. However, I do not see what is\r
+ gained by the derivation in III-B; it does not seem to open for any other solutions, extensions, or\r
+ conclusions. I think that the authors need to look over their\r
+ presentation of the method and evaluate whether this is the most\r
+ effective method of getting their points across. Especially, since\r
+ this derivation is already given in [59], maybe some of the more\r
+ repetitive material coudl be removed.\r
+\item I realize that no background section is ever complete, but I\r
+ would still encourage the authors to include a section on Ambisonics\r
+ and Higher-Order Ambisonics (HOA). This is especially relevant\r
+ because spatially targeted compression techniques have been applied\r
+ here (see e.g. E. Hellerud, A. Solvang, U. P. Svensson, ``Spatial\r
+ redundancy in Higher Order Ambisonics and its use for lowdelay\r
+ lossless compression'', ICASSP 2009).\r
+\r
+\end{enumerate}\r
+\r
+\section{Conclusion}\r
+My main problem with this paper is that a lot of space is used to\r
+cover material that has been thoroughly covered by an earlier paper of\r
+the authors. The connections to the new additions to the theory are\r
+not quite clear to me, and I think the authors should perhaps make\r
+Secs. III and IV a bit more accessible.\r
+\r
+\end{document}
\ No newline at end of file
--- /dev/null
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+\r
+\title{Review of MM-004756}\r
+\r
+\begin{document}\r
+\maketitle\r
+\r
+\section{Summary}\r
+The paper ``High Quality Low Bitrate Spatial Audio Coding'' is\r
+concerned with optimizing spatial encoding for audio\r
+compression. The authors point out that existing techniques for spatial audio coding do not seek\r
+to minimize the decoded audio reconstruction error, and they suggest that\r
+this should be done. \r
+\r
+The idea seems both reasonable and appealing, and the results seem\r
+convincing, but I have some concerns with repect to the presentation.\r
+\r
+\section{Concerns}\r
+\begin{enumerate}\r
+\item The paper has a lot of overlap with the authors' previous work\r
+ in [59], something that I personally feel should be acknowledged\r
+ already at the beginning of the paper, and the difference in the\r
+ current contribution should be stated explicitly. Some of the extensions from\r
+ [59] are not quite clear. Specifically, Secs. III and IV are very confusing to me. I do not follow\r
+ the authors' explanation of AbS in the context of spatial encoding,\r
+ and it is especially unclear to me how the results in Sec. III\r
+ are the basis for the computations described in Sec. IV. I will try\r
+ to describe this confusion further in the following points:\r
+\item The general model described by Fig. 3 (and the accompanying\r
+ description) is confusing in that it has no definite final output\r
+ and that it is not clear what is communicated back to the ``Spatial\r
+ analysis'' block. Also, it seems like the ``Error minimisation''\r
+ block depends on the ``Spatial Parameters'', even though they are\r
+ not fed through. Do not get me wrong, I understand what the authors\r
+ are trying to express here. But it is my opinion that if you choose\r
+ a schematic diagram to convey your idea, it should be complete and\r
+ consistent.\r
+\item I do not understand how the optimization can be made iterative,\r
+ and why the synthesis step is even necessary to achieve the minimum\r
+ MSE indicated by (22) and (23). If the single-step solution is\r
+ simply to replace $a$ and $b$ in (8) by their approximations\r
+ $\hat{a}$ and $\hat{b}$, why is this not done directly in the\r
+ analysis step without including the\r
+ extensive AbS framework, which I cannot see is used for anything\r
+ else than the derivation of this result. I believe this would even remove\r
+ the synchronization problem described in Sec. III-C.\r
+\item Again, I do not understand why a complete search of all possible\r
+ quantizations (as described in Sec. IV) is necessary. How does this\r
+ relate to the seemingly simple solutions of (22) and (23)?\r
+\item I realize that no background section is ever complete, but I\r
+ would still encourage the authors to include a section on Ambisonics\r
+ and Higher-Order Ambisonics (HOA). This is especially relevant\r
+ because spatially targeted compression techniques have been applied\r
+ here (see e.g. E. Hellerud, A. Solvang, U. P. Svensson, ``Spatial\r
+ redundancy in Higher Order Ambisonics and its use for lowdelay\r
+ lossless compression'', ICASSP 2009).\r
+\end{enumerate}\r
+\r
+\section{Conclusion}\r
+My main problem with this paper is that a lot of space is used to\r
+cover material that has been thoroughly covered by an earlier paper of\r
+the authors. The connections to the new additions to the theory are\r
+not quite clear to me, and I think the authors should perhaps make\r
+Secs. III and IV a bit more accessible.\r
+\r
+\end{document}
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+\documentclass[journal,onecolumn,english,a4paper]{IEEEtran}\r
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+\r
+\title{Review of TUFFC-05633-2013}\r
+\r
+\begin{document}\r
+\maketitle\r
+\section{Summary}\r
+The authors suggest a combination of two MV beamforming techniques; the beamspace adaptive beamformer\r
+and the eigenspace adaptive beamformer. This combination achieves\r
+increased contrast (like the eigenspace beamformer) with reduced computational complexity (compared to\r
+MV). \r
+\r
+Establishing a high-performance, low-complexity method is both\r
+scientifiically interesting and practically desirable. Unfortunately,\r
+the paper has some unfortunate flaws because the authors have\r
+not correctly identified all the effect of their new\r
+method. My current impression is that the actual interesting aspects\r
+of the new methods are not enough to warrant publication as a full\r
+paper, but the conclusions could be rewritten as a letter or a\r
+correspondence if certain changes and better comparisons are made.\r
+\r
+\section{List of concerns}\r
+\begin{enumerate}\r
+\item The authors state that ``(...) contrast improvement has not yet\r
+ been satisfactory''. Where does this conclusion come from? Why was\r
+ resolution improvement deemed satisfactory, while contrast\r
+ improvement was not?\r
+\item If the motivation of the authors is to find a method that has\r
+ the resolution of MV and improved contrast without significantly increased\r
+ computational complexity, the interesting alternatives are found in the\r
+ world of coherence-based beamformers (where MV is combined with a\r
+ scalar, SNR-dependent coherence factor). The authors must either\r
+ state (convincingly) why these methods have not been considered, or\r
+ include them in the simulations. To leap ahead a bit, I am already\r
+ convinced that MV/CF-based methods are sufficiently related to\r
+ ``pure'' MV methods that a comparison is warranted in this context.\r
+\item In Sec. III-C, the authors claim that reducing the number of rows in $\mat{T}$\r
+ from $L$ to $P$ will reduce the complexity of the eigendecomposition\r
+ from $O(L^{3})$ to $O(P^{3})$. However, the eigen-decomposition\r
+ problem actually remains unchanged, independent of the beamspace\r
+ reduction that is applied afterwards. This is easily seen as the matrix $\mat{U}_{s}$ in (22)\r
+ is the same as that in (10), and must be acquired the same way with\r
+ an identical complexity of $O(L^{3})$. In\r
+ other words, the only complexity reduction in B-ESBMV is due to the\r
+ calculation of $\vec{w}_{B-MV}$, which has already been established\r
+ in [15]. Therefore, it is not at all surprising that B-ESBMV\r
+ executes quicker than MV. What would be surprising is if it executed\r
+ faster than B-MV. \r
+\item The MV result in Fig. 7 b) should be explained; why are the noise/interference\r
+ levels for MV (and also sometimes for ESBMV) seemingly higher than\r
+ for DAS? Is this related to image normalization?\r
+\item The authors must get their manuscript proof-read by a native\r
+ English speaker. There are quite a lot of spelling errors, clumsy sentences, and\r
+ formulations that must be corrected. There are too many obvious\r
+ examples to go into further detail (like ``passed without distortionless'' $\rightarrow$ ``passed without distortion'').\r
+\item The statement ``(...) DAS beamformer has a wide mainlobe and\r
+ high sidelobes'' is somewhat unclear. An adaptive beamformer cannot\r
+ cheat the fundamental mainlobe-width/sidelobe-level tradeoff, but\r
+ they can rather use all degrees of freedom in an optimal manner. I\r
+ obviously see that the authors are trying to express that ``DAS is limited'', but they\r
+ should find another way.\r
+\item The adaptive beamformers are perhaps ``conserving'', not\r
+ ``enhancing'' useful signals while suppressing\r
+ interference. Enhancement of useful signal content in the output is\r
+ done through interference suppression, not as a separate process.\r
+\item Is lowering the computational complexity of a method the same as making the\r
+ method easier to implement?\r
+\item ``always'' is a somewhat strong modifier in the sentence ``(...)\r
+ study of low complexity adaptive beamformer has always been an area\r
+ of great interest (...)''. I assume the authors mean after the\r
+ introduction of adaptive beamformers to ultrasound (even then, it\r
+ took a few years to catch on).\r
+\item The reason for discarding Synnevåg's low-complexity\r
+ data-dependent beamformer because it depends too much on the\r
+ predefined weights and is hard to handle in practical use is\r
+ both vague and undocumented. If the authors know of studies\r
+ that indicate these shortcomings, they should cite them. Otherwise,\r
+ they should stick to valid reasons for discrediting existing\r
+ alternative techniques, or refrain from discrediting them at all.\r
+\item While I agree with the authors that the constrasts of the ESBMV\r
+ beamformers in Fig. 6 are superior to DAS and MV, I would challenge\r
+ them with the fact that the shape of the cyst is clear and the edge\r
+ is easy to judge for all six images, including DAS and MV. Could\r
+ some more extreme scenarios be used as examples?\r
+\end{enumerate}\r
+\r
+\section{Conclusion}\r
+In my opinion, all of the above points can be corrected with the\r
+possible exception of two important points:\r
+\begin{itemize}\r
+\item The suggested method might be out-performed wrt. both contrast\r
+ and computational complexity by well-known coherence-based\r
+ methods. This should be investigated.\r
+\item The suggested method does not actually contribute any\r
+ non-trivial reduction in computational complexity than what is\r
+ already given by the beamspace dimensionality reduction of B-MV,\r
+ which has already been published and established. If so, then it is a trivial combiantion of\r
+ two existing methods, constituting a (brief) correspondence at best.\r
+\end{itemize}\r
+The authors should first of all approach these two points, and if they\r
+are successful correct the remaining points to change my mind about publication.\r
+\r
+\end{document}
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--- /dev/null
+\documentclass[journal,onecolumn,english,a4paper]{IEEEtran}\r
+\usepackage{graphicx,varioref,mathrsfs,amssymb,amsmath}\r
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+\r
+\title{Review of TUFFC-05649-2013: ``A Fast Minimum Variance\r
+ Beamforming Method Using Principal Component Analysis''}\r
+\r
+\begin{document}\r
+\maketitle\r
+\r
+\section{Summary}\r
+The authors present a PCA-based fast MV beamformer that displays\r
+performance close to the full MV beamformer with reduced computational\r
+complexity. The method is tested on simulated and experimental data.\r
+\r
+\r
+\section{Concerns}\r
+\r
+\begin{enumerate}\r
+\r
+\item $w_m[n]$ should be complex conjugated in (1).\r
+\item No motivation is given for Section II. Is this simply general\r
+ background theory, or will it be used later. This should be stated.\r
+\item Specify that (5) is the {\it spatially smoothed} covariance\r
+ matrix. Is this the covariance matrix that will be treated in your\r
+ algorithm and used in Section III-A? This should be specified. \r
+\item It is not a good explanation that MV beamformed images tend to\r
+ ``look awkward''. What are the actual errors; amplitude errors,\r
+ misplaced sources, something else? What is ``this problem''; the\r
+ authors need to be more specific.\r
+\item Are you averaging across time, or across the depth direction or\r
+ both in (10)? Is this applied throughout the paper, or are you\r
+ simply stating what is commonly done by other people. \r
+\r
+\item It is very confusing that the results of (5), (8), and (10) are\r
+ all denoted by $\mat{\tilde{R}}[n]$ when they are quite\r
+ different. It is not at all clear which one is applied in Section\r
+ III-A. Can anyone be applied, and if so what are the differences?\r
+\r
+\item Section III-A should be started with some sort of motivation. It\r
+ should also be made quite clear which results from Section II you\r
+ are using. A suggestion would be to specify what you mean by\r
+ ``standard MV'' (which covariance matrix from Section II is actually\r
+ used) and make it much more clear what you mean by ``applying\r
+ PCA''. \r
+\r
+\item ``Sample number'' after (11) should be ``number of\r
+ samples''. Actually, it should be neither, because it is not at all\r
+ clear that you are here referring to the number of calculated\r
+ weights. ``Sample'' is a very vague description.\r
+\r
+\item The authors should repeat the definitions of $L$ and $K$ in\r
+ Section III-A for clarity; you could e.g. call them ``subarray\r
+ length'' and ``temporal snapshot length''.\r
+\r
+\item Have the authors investigated the beampatterns of the\r
+ eigenvectors $\mat{v}_l$? If the resulting weight vectors can be\r
+ written as a linear combination of a small number of such\r
+ eigenvectors, it is my intuition that these eigenvectors might make\r
+ sense on their own. It would be especially interesting to compare\r
+ them to the transformation vectors in the beamspace transformation\r
+ matrix from [11], the better to understand the relationship between\r
+ beamspace and PCA.\r
+\r
+\item Theoretically, the method is interesting. However, I am not\r
+ convinced about the practical application of the method. I am\r
+ referring to the fact that you assume that the weights can be\r
+ calculated off-line for a ``similar situation''. This is both\r
+ unlikely and unrealistic, especially for adaptive beamformers such\r
+ as MV, which are very sensitive to the situation. In fact, this\r
+ large restriction of the method was not mentioned neither in the\r
+ abstract nor in the introduction, which gives an unfair impression\r
+ that the PCA method is an ``equal peer'' to alternatives such as [11] and\r
+ [15]. The authors should discuss this critical and limiting aspect\r
+ of the method to a much larger extent, thus I would also like to see more\r
+ simulations of weights calculated from different scenarios. \r
+\r
+\item [11] and [17] refer to the same document.\r
+\r
+\end{enumerate}\r
+\r
+\section{Conclusion}\r
+The derivation in Sections II and III-A should be made much more\r
+consistent. They are actually highly dependent on each other, but in\r
+this paper they seem like two separate parts. In addition, the fact\r
+that the weights must be calculated for similar situations should be\r
+discussed more and the specification of what constitutes a ``similar\r
+scenario'' should be presented. If the conclusion is that practically any scenario will do, I\r
+suspect that there exists a theoretically much simpler method (perhaps like [11] or\r
+[15]) that does the job just as well. If not, then the effect of\r
+different scenarios must be investigated much more.\r
+\r
+\end{document}
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+\relax
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+\@writefile{toc}{\contentsline {section}{\numberline {II}Major concerns}{1}}
+\@writefile{toc}{\contentsline {section}{\numberline {III}Minor concerns}{2}}
+\@writefile{toc}{\contentsline {section}{\numberline {IV}Conclusions}{2}}
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+\documentclass[journal,onecolumn,english,a4paper]{IEEEtran}\r
+\usepackage{graphicx,varioref,mathrsfs,amssymb,amsmath}\r
+\usepackage{subfigure}\r
+%\usepackage[cmex10]{amsmath}\r
+%\bibliographystyle{IEEETran}\r
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+\r
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+\newcommand{\outerp}[1]{#1 #1^{H}}\r
+\r
+\title{Review of TUFFC-05673-2013: ``Wiener Coherence Factor with\r
+ Spatial-temporal Smothing Applied to Ultrasound Imaging''}\r
+\r
+\begin{document}\r
+\maketitle\r
+\r
+\section{Summary}\r
+The authors present a new variation on the adaptive imaging technique\r
+known as the Coherence Factor (CF). This variation, called the Wiener\r
+Coherence Factor, incorporates spatial and temporal averaging for improved performance.\r
+\r
+All existing CF-type methods have stability issues to some extent, and the\r
+suggested method seems to improve on these. However, the paper suffers\r
+under the fact that the connection between the authors' motivating theoretical work and the final\r
+implementation feels somewhat contrived. It seems to me that the authors\r
+set out to do one thing, and ends up with a result that could have\r
+been motivated in a simpler manner resulting in much less confusion. I will try\r
+to motivate my opinion through the lists of concerns below.\r
+\r
+\section{Major concerns}\r
+{\bf 1)} The authors suggested method is identical to the coherence factor with\r
+spatial and temporal smoothing in both numerator and denominator. They\r
+state that the method is a result of ``Wiener theory'', hence the suggested\r
+name ``Wiener Coherence Factor''. This is a problematic statement\r
+because the introductions of both temporal and spatial averaging are\r
+alterations of the problem and solution (respectively) that are suggested by the\r
+authors which are ultimately unrelated to the ``Wiener''\r
+derivation. \r
+\r
+Temporal averaging is introduced somewhat vaguely between Eqs. (6) and\r
+(7). The only explanation I can find is that Eq. (6) should have been:\r
+\begin{equation}\r
+F_{wcf} = \arg \min_F \sum_{n=n_1}^{n_2}{\E{\left\|A[n] - F\vec{w}^{H}\vec{x}[n]\right\|^2_2}},\r
+\end{equation}\r
+or that the expectation is somewhow both spatial and temporal. However, this\r
+does not satisfy the authors' motivation given immediately before (7),\r
+which is: that $F_{wcf}$ is ``obtained through minimizing the MSE estimate of the desired signal amplitude\r
+$A(t)$''. If the motivation is to minimize the average MSE across the\r
+duration of a pulse, then this is a revision of the problem and should\r
+be clearly stated.\r
+\r
+Spatial averaging is introduced to ``decorrelate the\r
+signal and interference'' in (7), but it is not clear why this\r
+decorrelation is warranted. Eqs. (6) and (7) are not based on any\r
+assumptions of signal and noise being uncorrelated, and the authors\r
+have earlier stated the importance of using an accurate signal model.\r
+Therefore, it stands to reason that if there is actual correlation\r
+between signal and interference, then it should not be removed from\r
+the estimate. If spatial averaging is meant as a general robustness\r
+technique for estimating $\E{\vec{w}^{H}\vec{x}}$, it is not clear why\r
+the resulting reduction from $M$-element model in (6), (7), and (8) to\r
+an $L$-element model in (9) and the removal of model-accurate\r
+correlation is an acceptable price to pay for the increased robustness. The authors\r
+are quite clear on the point that model accuracy is important, which\r
+means that they should not introduce such drastic changes without proper\r
+justification.\\\r
+\\\r
+{\bf 2)} Another problem is that the authors, to arrive at their\r
+final solution, introduce $\E{\vec{w}^{H}\vec{x}[n]}$ into (7) as an\r
+``estimate'' of $A[n]$. This is an unusual substitution, and it must\r
+be adressed since it is a vital step towards the final expression. Now, it is not quite clear whether the authors\r
+consider $A[n]$ to be deterministic or a random variable. At any rate,\r
+we are left with the following options:\\\r
+{\it a)} If $A[n]$ is unknown and deterministic with $\E{\vec{w}^{H}\vec{x}[n]}=A[n]$, then the authors\r
+have intentionally made Eq. (8) more uncertain than Eq. (7). A more suitable\r
+replacement for $A[n]$ would probably be $\vec{w}^{H}\vec{x}[n]$,\r
+wchich actually is a proper estimator of $A[n]$.\\\r
+{\it b)} If $A[n]$ is a random variable that is equal to the random variable\r
+$\vec{w}^{H}\vec{x}$, then the numerator and denominator of Eq. (7)\r
+are identical and we get $F_{wcf}=1$. In this case, substituting just one occurence\r
+of $\vec{w}^{H}\vec{x}$ in the equation to avoid this trivial\r
+solution seems rather arbitrary.\\\r
+{\it c)} If $A[n]$ is a random variable (with an uncertain relationship to the random\r
+vector $\vec{x}[n]$), then the implications of the substitution are unclear.\\\r
+\\\r
+{\bf 3)} At any rate, a coherence factor that includes\r
+spatial and temporal smoothing for increased robustness can just as\r
+easily be motivated directly from (1). As I reasoned in {\bf 1)}, the\r
+decision to average across a pulse length is (probably) simply a revision of\r
+the problem, and can just as easily be introduced directly as a\r
+revision of (1). The effects of spatial smoothing can be interpreted\r
+as broadening the numerator beam and making the denominator elements\r
+directive in CF. These modifications are just as reasonably applied\r
+directly to CF as they are through the ``Wiener'' derivation. In\r
+short, the ``Wiener derivation'' is not necessary to achieve the\r
+specific equation that the authors end up with, and it does not result\r
+in any new, general solution that can be adapted by the readers. It\r
+is redundant, and should probably be removed.\\\r
+\\\r
+{\bf 4)} The authors mistakenly think that the Wiener postfilter derived\r
+in [15] is based solely on an assumption of spatially white noise, and that\r
+their derivation is the first attempt to correct this ``incomplete model''. If they\r
+inspect [15] closer, they will find that the general solution\r
+given in [15]-(19) contains no such assumptions about the spatial\r
+noise distribution. The specific solution with the white noise-assumption is only given as an example\r
+that explains the CF in the context of the much more general Wiener\r
+postfilter. In fact, the invalidity of the spatially white noise\r
+assumption is repeatedly stated in [15]. Because [15]-(19) is\r
+completely general, the method suggested by the authors in (9) could actually just as\r
+easily be derived from this expression by introducing temporal and spatial\r
+smoothing (for robustness) when estimating the expressions in both numerator and denominator. In addition, the covariance\r
+matrix estimator given by [15]-(23) that is applied throughout the\r
+paper is based on a completely general, non-white noise model and\r
+contains both spatial and temporal averaging for increased robustness. Hence\r
+the authors must revise their summary of earlier work done on Wiener\r
+postfilters and also cite [15] as an application of both spatial and\r
+temporal averaging for robustness that pre-dates their suggested method.\\\r
+\\\r
+{\bf 5)} The suggested name of ``Wiener Coherence Factor'' is poorly\r
+chosen seeing as how the final result is not a general expression with\r
+several realizations through user-defined estimators (unlike the ones\r
+given in [15]) but rather the very limited and specific variant of the coherence factor with spatial and temporal smoothing. ``Smoothed Coherence\r
+ Factor'', or something to that effect, is a much more descriptive\r
+ and correct name for the method.\r
+\r
+\r
+\section{Minor concerns}\r
+\begin{enumerate}\r
+\item ``Spatio-temporal'' is a better term than ``Spatial-temporal''\r
+ in the title.\r
+\item in my opinion there is no need to include PCF in this paper, as it is\r
+ significantly different from ordinary CF. PCF should be removed completely.\r
+\end{enumerate}\r
+\r
+\section{Conclusions}\r
+I do think that a CF with spatial and temporal\r
+averaging is a good idea, but I would like to see it presented as such and not in\r
+this ``Wiener Coherence Factor''-context. The authors confuse the\r
+readers by giving the impression that their solution and derivation\r
+are strongly linked, while the solution in reality could be derived\r
+from any number of existing solutions. There is nothing significantly new in the\r
+authors' application of Wiener theory as compared to the general\r
+derivations in [15] (from which the authors have mistakenly chosen one specific\r
+realization to represent the entire Wiener postfilter framework), and the\r
+authors should refrain from giving the impression that there is. The\r
+only novel contribution is the application of spatial and temporal\r
+smoothing, which does not follow explicitly from the derivation, and this should\r
+be stated clearly. If the authors were to change the focus of their\r
+paper and change the somewhat ad-hoc-nature of the contribution, I\r
+would be happy to re-evaluate my decision.\r
+\r
+\end{document}
\ No newline at end of file
--- /dev/null
+\relax
+\bibstyle{IEEEtran}
+\@writefile{toc}{\contentsline {section}{\numberline {I}Summary}{1}}
+\@writefile{toc}{\contentsline {section}{\numberline {II}Major concerns}{1}}
+\@writefile{toc}{\contentsline {section}{\numberline {III}Minor concerns}{2}}
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--- /dev/null
+\documentclass[journal,onecolumn,english,a4paper]{IEEEtran}\r
+\usepackage{graphicx,varioref,mathrsfs,amssymb,amsmath}\r
+\usepackage{subfigure}\r
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+\r
+\title{Review of TUFFC-05732-2013: ``Coherence-weighted synthetic focusing applied to ultrasound and photoacoustic imaging using a high- frequency annular-array transducer''}\r
+\r
+\begin{document}\r
+\maketitle\r
+\r
+\section{Summary}\r
+The authors present an adaptive synthetic focusing scheme applied to\r
+an annular array to improve focusing and enhance both spatial\r
+resolution and contrast. The effectiveness of the scheme is\r
+demonstrated using an experimental setup.\\\r
+\\\r
+While most of the results seem convincing, I have a few concenrs that\r
+mus be adressed if this paper is to be published. I have divided my\r
+concerns into two lists; one containing major concerns that I believe\r
+must lead to revision, and one concerning minor concerns that may be\r
+only my personal opinions.\r
+\r
+\section{Major concerns}\r
+{\bf 1)} I am a bit concerned about the authors' characterization of\r
+their contribution. Reading the abstract and the conclusion, they\r
+describe their contribution as the development of a ``scheme'' or a\r
+``protocol''. However, at the end of the introduction, it seems to me\r
+that they are simply applying unmodified CF weighting to improve an already\r
+tested and reported technique. Unless there is some reason that CF\r
+weighting should not work in this case, the reported improvements are\r
+as expected from what we already know about CF processing and not very\r
+surprising. In my opinion, this means that the novelty of the\r
+contribution is not large enough to warrant publication as a full\r
+paper and the authors should resubmit the revised paper as a technical\r
+correspondence. In any case, the authors should be more consistent\r
+with how they describe the nature of their contribution, especially in\r
+light of their previous publications on related matters.\\\r
+\\\r
+{\bf 2)} It is problematic to infer the resolution of the DAS+CF\r
+beamformer from its response to a single scatterer. This is because, unlike DAS, the DAS+CF beamformer is adaptive in a way that does not follow the\r
+principle of superposition. In other words; if there were another point\r
+scatterer located close to the imaged point scatterer, then the\r
+additional attenuation offered by CF would be reduced in a non-linear way. This should be\r
+investigated further, and mentioned in connection with the\r
+resolution-related results.\r
+\r
+\section{Minor concerns}\r
+\r
+{\bf 1)} I would rather see Eq. (1) and the theory behind CF explained\r
+as part of Sec. II.\\\r
+\\\r
+{\bf 2)} After Eq. (1), the authors state that the CF-weighted DAS\r
+approach significantly ``reduces incoherent noise and signals\r
+originating from off-axis positions (...)'', which could be\r
+misinterpreted as an improvement of per-pixel SNR by reducing\r
+noise/interference while keeping the signal intact. In reality,\r
+CF-weighting only suppresses parts of the image inversely proportional\r
+to their coherence. In other words, wherever noise is reduced, signals\r
+are similarly reduced. The explanation of CF weighting could be edited\r
+to include a more thorough explanation of its workings.\\\r
+\\\r
+{\bf 3)} Why was the CF map smoothed with a median filter, and what\r
+would the results be without this smoothing? Please elaborate.\\\r
+\\\r
+{\bf 4)} The change in speckle characteristics, as well as other image\r
+artifacts, are well-known in the CF literature. Existing techniques\r
+for managing this are the Generalized Coherence Factor (Li and Li,\r
+``Adaptive Imaging Using the Generalize Coherence Factor'') and Scaled\r
+Wiener Filters (Nilsen and Holm, ``Wiener Beamforming and the\r
+Coherence Factor in Ultrasound Imaging''). I was wondering whether the\r
+authors have applied any of these techniques, or if this could easily\r
+be done?\\\r
+\\\r
+{\bf 5} Reference [18] does not have anything to do with CF imaging,\r
+as it solely focuses on Minimum Variance adaptive beamforming.\r
+\r
+\section{Conclusions}\r
+The authors should address my concerns about their conclusions on the\r
+resolution improvement of DAS+CF, and they should evaluate whether\r
+their contribution is novel enough to constitute a full paper or a\r
+technical correspondence.\r
+\r
+\end{document}
\ No newline at end of file
git://git.uio.no / private-carlingn-dsb.git / commitdiff