How to optimize the antenna weight of a two-dimensional array to generate null in a specific direction

I have read the” Array Pattern Synthesis Part II: Optimization“，the optimization example is for one-dimensional array（ULA）, and there are problems in my process of weight optimization for two-dimensional array（URA），Please give me some guidance，thanks！

N = 8;

M=8;

URA1 = phased.URA('Size',[N,M],'ArrayNormal','z');

pos = getElementPosition(URA1);

% position of elements

ang_i = [-70 -40 -20;0 0 0]; % interference angles

ang_d = [0;0]; % desired angle

Rn = sensorcov(pos,ang_i,db2pow(-40)); % Noise covariance matrix

sv_c = steervec(pos,[ang_d ang_i]); % Linear constraints

r_c = [1 zeros(size(ang_i))]'; % Desired response

w_lcmv = lcmvweights(sv_c,r_c,Rn); % LCMV weights

ang_plot = -90:0.1:90;

sv_plot = steervec(pos,ang_plot);

plcmv = plot(ang_plot,mag2db(abs(w_lcmv'*sv_plot)));

xline(ang_i,"--")

ylim([-100 0])

grid on

legend(plcmv,"LCMV - Analytic")

xlabel("Azimuth Angle (deg)")

ylabel("Beam Pattern (dB)")

Answer 1

[Honglei Chen]

Your script is pretty close, you just need to set up the desired response properly. However, you could take advantage of the pattern plot to plot the pattern for a planar array.

Hope this helps,

N = 8;

M = 8;

URA1 = phased.URA('Size',[N,M],'ArrayNormal','z');

pos = getElementPosition(URA1);

% position of elements

ang_i = [-40 -20 10;10 20 -10]; % interference angles

ang_d = [0;0]; % desired angle

Rn = sensorcov(pos,ang_i,db2pow(-40)); % Noise covariance matrix

sv_c = steervec(pos,[ang_d ang_i]); % Linear constraints

r_c = [1 zeros(1,size(ang_i,2))]'; % Desired response

w_lcmv = lcmvweights(sv_c,r_c,Rn); % LCMV weights

pattern(URA1,3e8,-90:90,-90:90,'CoordinateSyste','Rectangular',...

'Type','powerdb','Weights',w_lcmv);

view(0,90);