Beam width of linear array using MVDR beamformer I did delay and sum beamforming technique and MVDR beamforming technique in MATLAB in time domain, but I could not make a comparison between the beam patterns as both showed same beam width. But when I did it in frequency domain, I could differentiate both the techniques as MVDR beamformer showed better resolution( low beam width) compared to delay and sum bemaformer.
I used 10 array elements, with input signal sine added with noise and the steering angle is 20 degrees. Is there something wrong with my MVDR code? Please help.

    %%
clc;
clear all;
close all;

%% Time specifications:
   Fs = 25e4;                   % samples per second
   dt = 1/Fs;                   % seconds per sample
   StopTime = 1e-3;  %0.952e-3;           % seconds
   t = (0:dt:StopTime-dt)';     % seconds

   %% Sine wave:
   Fc = 8e3;                     % hertz
   signal = sin(2*pi*Fc*t);
   x=signal+randn(size(t));
%%
N = 10;
d = 0.5;
plotangl = -90:90;
tm = plotangl * pi/180;
elementPos = (0:N-1)*d;
thetasteer=20;
c=1150;
k=exp(-1j*2*pi*elementPos'*sin(thetasteer*pi/180)/c);
x1=k*x';%10x250
Sn=(x1*x1');
a=0.01.*eye(10);
Sn1=Sn+a;

%%

as=exp(-1j*2*pi*elementPos*sin(thetasteer*pi/180));%1x10
w1=(inv(Sn1)*as');
w2=(conj(as)*inv(Sn1));
w3=w2*as';
w=w1/w3;%10x1
%w=ones(10,1);%10x1
W=w*as;%10x10
%%
vv = exp (1j *2*pi*d* (0: N-1)'* (sin (tm)));%10x181 
B1=W*vv;
B2=B1'*x1;
B3=abs(B2/max(B2))';%normalize
figure(2);subplot(2,1,1);polar (plotangl*pi/180, B3);title('polar plot of mvdr ');

B = 10*log10(B3);
figure(2);
subplot(2,1,2);
plot(plotangl,B);
grid on
xlabel(' Angle (degrees)');
ylabel('Normalized Beam Power[dB]');
legend('20 deg');
title('mvdr Array Pattern, 10 array elements');
I think you're mixing time domain and frequency domain, your signal $x$ is in time and you're multiplying it by a complex exponential, generating a complex signal that is not the Fourier transform of $x$, if you want to delay $x$ in order to simulate the angle of arrival of the signal you have to do $x_{m}(n)=x(n-\tau_{m})$ (in the time domain) or $X_{m}(\omega)=e^{-j \tau_{m}}X(\omega) $ being "m" the microphone number. 

Also you have to include the wave number in the steering vector $k=\dfrac{2\pi}{\lambda}$.