ARRAY_GEOMETRY = '2D_RANDOM';
HAS_NULLS = 0;
lambda = 1;
theta_tar = 60;
half_beamwidth = 10;
if HAS_NULLS
theta_nulls = [95 110 120 140 225];
end
if strcmp( ARRAY_GEOMETRY, '2D_RANDOM' )
rand('state',0);
n = 40;
L = 5;
loc = L*rand(n,2);
angleRange = 360;
elseif strcmp( ARRAY_GEOMETRY, '1D_UNIFORM_LINE' )
n = 30;
d = 0.45*lambda;
loc = [d*[0:n-1]' zeros(n,1)];
angleRange = 180;
elseif strcmp( ARRAY_GEOMETRY, '2D_UNIFORM_LATTICE' )
m = 6; n = m^2;
d = 0.45*lambda;
loc = zeros(n,2);
for x = 0:m-1
for y = 0:m-1
loc(m*y+x+1,:) = [x y];
end
end
loc = loc*d;
angleRange = 360;
else
error('Undefined array geometry')
end
theta = [1:angleRange]';
A = kron(cos(pi*theta/180), loc(:,1)') + kron(sin(pi*theta/180), loc(:,2)');
A = exp(2*pi*i/lambda*A);
[diff_closest, ind_closest] = min( abs(theta - theta_tar) );
Atar = A(ind_closest,:);
if HAS_NULLS
Anull = []; ind_nulls = [];
for k = 1:length(theta_nulls)
[diff_closest, ind_closest] = min( abs(theta - theta_nulls(k)) );
Anull = [Anull; A(ind_closest,:)];
ind_nulls = [ind_nulls ind_closest];
end
end
ind = find(theta <= (theta_tar-half_beamwidth) | ...
theta >= (theta_tar+half_beamwidth) );
if HAS_NULLS, ind = setdiff(ind,ind_nulls); end;
As = A(ind,:);
cvx_begin
variable w(n) complex
minimize( max( abs(As*w) ) )
subject to
Atar*w == 1;
if HAS_NULLS
Anull*w == 0;
end
cvx_end
disp(['Problem is ' cvx_status])
if ~strfind(cvx_status,'Solved')
return
end
min_sidelobe_level = 20*log10( max(abs(As*w)) );
fprintf(1,'The minimum sidelobe level is %3.2f dB.\n\n',...
min_sidelobe_level );
figure(1), clf
plot(loc(:,1),loc(:,2),'o')
title('Antenna locations')
if angleRange == 180,
theta = [1:360]';
A = [ A; -A ];
end
y = A*w;
figure(2), clf
ymin = floor(0.1*min_sidelobe_level)*10-10; ymax = 0;
plot([1:360], 20*log10(abs(y)), ...
[theta_tar theta_tar],[ymin ymax],'r--',...
[theta_tar+half_beamwidth theta_tar+half_beamwidth],[ymin ymax],'g--',...
[theta_tar-half_beamwidth theta_tar-half_beamwidth],[ymin ymax],'g--');
if HAS_NULLS
hold on;
for k = 1:length(theta_nulls)
plot([theta_nulls(k) theta_nulls(k)],[ymin ymax],'m--');
end
hold off;
end
xlabel('look angle'), ylabel('mag y(theta) in dB');
axis([0 360 ymin ymax]);
figure(3), clf
zerodB = -ymin;
dBY = 20*log10(abs(y)) + zerodB;
ind = find( dBY <= 0 ); dBY(ind) = 0;
plot(dBY.*cos(pi*theta/180), dBY.*sin(pi*theta/180), '-');
axis([-zerodB zerodB -zerodB zerodB]), axis('off'), axis('square')
hold on
plot(zerodB*cos(pi*theta/180),zerodB*sin(pi*theta/180),'k:')
plot( (min_sidelobe_level + zerodB)*cos(pi*theta/180), ...
(min_sidelobe_level + zerodB)*sin(pi*theta/180),'k:')
text(-zerodB,0,'0 dB')
tt = text(-(min_sidelobe_level + zerodB),0,sprintf('%0.1f dB',min_sidelobe_level));
set(tt,'HorizontalAlignment','right');
theta_1 = theta_tar+half_beamwidth;
theta_2 = theta_tar-half_beamwidth;
plot([0 55*cos(theta_tar*pi/180)], [0 55*sin(theta_tar*pi/180)], 'k:')
plot([0 55*cos(theta_1*pi/180)], [0 55*sin(theta_1*pi/180)], 'k:')
plot([0 55*cos(theta_2*pi/180)], [0 55*sin(theta_2*pi/180)], 'k:')
if HAS_NULLS
for k = 1:length(theta_nulls)
plot([0 55*cos(theta_nulls(k)*pi/180)], ...
[0 55*sin(theta_nulls(k)*pi/180)], 'k:')
end
end
hold off
Calling sedumi: 1366 variables, 422 equality constraints
For improved efficiency, sedumi is solving the dual problem.
------------------------------------------------------------
SeDuMi 1.21 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
Put 2 free variables in a quadratic cone
eqs m = 422, order n = 1026, dim = 1368, blocks = 343
nnz(A) = 55743 + 0, nnz(ADA) = 62144, nnz(L) = 31283
it : b*y gap delta rate t/tP* t/tD* feas cg cg prec
0 : 2.29E+02 0.000
1 : -8.28E-01 1.31E+02 0.000 0.5712 0.9000 0.9000 3.26 1 1 2.2E+02
2 : -1.53E-01 1.00E+02 0.000 0.7640 0.9000 0.9000 15.87 1 1 2.5E+01
3 : -9.46E-02 7.23E+01 0.000 0.7217 0.9000 0.9000 5.45 1 1 9.7E+00
4 : -8.27E-02 4.22E+01 0.000 0.5836 0.9000 0.9000 2.24 1 1 4.3E+00
5 : -8.03E-02 2.20E+01 0.000 0.5222 0.9000 0.9000 1.56 1 1 2.0E+00
6 : -7.57E-02 8.92E+00 0.000 0.4053 0.9000 0.9000 1.33 1 1 7.2E-01
7 : -7.40E-02 4.95E+00 0.000 0.5545 0.9000 0.9000 1.13 1 1 3.9E-01
8 : -7.26E-02 2.75E+00 0.000 0.5567 0.9000 0.9000 1.08 1 1 2.1E-01
9 : -7.14E-02 1.21E+00 0.000 0.4401 0.9000 0.9000 1.04 1 1 9.3E-02
10 : -7.06E-02 2.35E-01 0.000 0.1942 0.9224 0.9000 1.01 1 1 2.1E-02
11 : -7.04E-02 7.36E-02 0.000 0.3127 0.9046 0.9000 1.00 1 1 6.9E-03
12 : -7.03E-02 2.76E-02 0.000 0.3747 0.9015 0.9000 1.00 1 1 2.6E-03
13 : -7.03E-02 5.69E-03 0.000 0.2063 0.9000 0.0000 1.00 1 1 7.6E-04
14 : -7.03E-02 6.05E-04 0.000 0.1063 0.9123 0.9000 1.00 2 2 1.1E-04
15 : -7.03E-02 8.09E-05 0.000 0.1337 0.9132 0.9000 1.00 2 2 1.8E-05
16 : -7.03E-02 1.82E-05 0.000 0.2256 0.9196 0.9000 1.00 5 5 5.1E-06
17 : -7.03E-02 5.29E-06 0.000 0.2900 0.9155 0.9000 1.00 4 7 1.7E-06
18 : -7.03E-02 1.22E-06 0.000 0.2303 0.9086 0.9000 1.00 15 15 4.5E-07
19 : -7.03E-02 1.78E-07 0.000 0.1460 0.9062 0.9000 1.00 22 50 7.6E-08
20 : -7.03E-02 3.25E-08 0.000 0.1824 0.9010 0.9000 1.00 69 99 1.4E-08
iter seconds digits c*x b*y
20 0.7 8.7 -7.0302086004e-02 -7.0302086150e-02
|Ax-b| = 1.1e-08, [Ay-c]_+ = 2.7E-09, |x|= 5.7e-01, |y|= 1.1e+02
Detailed timing (sec)
Pre IPM Post
8.000E-02 6.800E-01 1.000E-02
Max-norms: ||b||=1, ||c|| = 1,
Cholesky |add|=38, |skip| = 2, ||L.L|| = 3566.47.
------------------------------------------------------------
Status: Solved
Optimal value (cvx_optval): +0.0703021
Problem is Solved
The minimum sidelobe level is -23.06 dB.