Direction of arrival estimation of multiple signals using Capon (MVDR) beamformer

Hello everyone. I am trying to write a script for comparing two beamforming methods of estimating direction-of-arrval: conventional (Bartlett) beamformer and MVDR (Capon) beamformer. Everything works fine when there is only one signal arriving to the antenna array. But, when I add another signal from different direction, Capon BF returns incorrect spatial power spectrum. Two peaks in this spectrum are always about 2.5 dB above the floor level (regardless of signal to noise ratio). When I change SNR, whole spectrum is shifted up or down but peak-to-floor ratio remains the same. On the other hand, conventional beamformer works fine both for one and two arriving signals. I was struggling with the code but without effect. Do you know how to obtain proper spatial power spectrum for Capon BF in case of two or more signals received? Best regards. Here is my script:

clear all; close all;

fs = 10e6; %sampling frequency
ts = 1/fs; 

T = 0.0001; %signal duration
t = 0:ts:T-ts;
Ns = length(t); %number of samples

fc = 1e6; %carrier freqiency
lambda = 3*10^8/fc; %wavelength

M = 10;%number of antenna elements in Unliform Linear Array
d = 0.5*lambda;%distance between neigbouring antennas

%------------------------------------------------------------------
s1 = exp(1i*2*pi*fc*t); %signal arriving to the array phase center (first antenna)

%SINGLE ARRIVING SIGNAL - WORKS FINE BOTH FOR CONVENTIONAL AND CAPON
%BEAMFORMERS
%teta = [40]/180*pi; %direction of arrival in degrees 

%TWO ARRIVING SIGNALS - CONVENTIONAL BF - OK, CAPON BF - INVALID SPECTRUM!!!
teta = [0, 40]/180*pi; %directions of arrivals in degrees 

amp = [1 1];% amplitudes of signals
delta_fi = -2*pi*d/lambda*sin(teta); %relative phase delay between signals received through neogbouring elements
for m=1:M;
    aU(:,m) = exp(1i*((m-1)*delta_fi)); %steering vector
end

x = zeros(M,Ns);

for k=1:length(teta);
    x = x + amp(k)*aU(k,:).'*s1*exp(1i*randn()); %data at the outputs of antenna elements
end
SNR = 10; %signal-to-noise ratio in decibels
sz = (2^(-0.5))*sqrt(10^(-SNR/10))*(randn(M,Ns)+1i*randn(M,Ns)); %complex Gaussian noise
Px = var(aU(k,1).'*s1*exp(1i*randn())); %power of signal
x = x + sz; %adding noise
Psz = var(sz(1,:)); %noise variance
Rxx = x*x'/Ns; %data covariance matrix

SNR_true = 10*log10(Px/Psz) %true SNR in dB

iRxx = inv(Rxx); %inverse of covariance matrix

teta_v = -pi/2:pi/180:pi/2; %range of scanned directions in radians
teta_v_deg = teta_v/pi*180; %same as above but in degrees
Nteta = length(teta_v); %number of scanned directions
for k=1:Nteta; %scanning loop
    %k
    teta = teta_v(k); %current scannig direction
    delta_fi = -2*pi*d/lambda*sin(teta); %relateive phase delay 
    for m=1:M;
        aT(m) = exp(1i*((m-1)*delta_fi)); %steering vector
    end

      a=aT.'; %transpose of steering vector

      wbf = a; %weight vector for conventional beamforming
      Pbf(k) = wbf'*Rxx*wbf; %spatial power spectrum of conventional beamformer 
      wMVDR = (iRxx*a)/(a'*iRxx*a); %weight vector for Caponbeamforming
      PMVDR(k) = wMVDR'*Rxx*wMVDR/1; %spatial power spectrum of Capon beamformer
  end

Pbf_dB = 10*log10(Pbf); %spectrum in log scale
PMVDR_dB = 10*log10(PMVDR);

figure
plot(teta_v_deg, Pbf_dB,'k','LineWidth',2);
axis([-90 90 0 20*log10(M)+5])
xlabel('\theta [\circ]');
ylabel('P(\theta)','rotation',0);

figure
plot(teta_v_deg, PMVDR_dB,'k','LineWidth',2);
xlabel('\theta [\circ]');
ylabel('P(\theta)','rotation',0);

Answer 1

[Honglei Chen]

I would replace your signal definition with the following

   x = x + amp(k)*aU(k,:).'*exp(1i*randn(size(t)));

HTH

[Lachlan Davies]

This enhancement gives a similar result unfortunately

Answer 2

[Shirleyuue Jiang]

I will replace your signal definition with the following

x = x + amp(k)*aU(k,:).'*s1;

Answer 3

[Reeha Syed]

I have observed the MUSIC algorithm for 1d and 2d DOA estimations and now want to know the their beamforming patterns for which do I have to write a seperate code for that?

[Sadiq Akbar]

Dear Reeha Syed, I was searching MUSIC algorithm for 1d and 2d DOA estimations and came to this page. Can you share the code of MUSIC algorithm for 1d and 2d DOA here. Regards

[Stefan Zete]

Can someone help me with an implementation of AoA algoritm for a project, please?

Answer 4

[Tony Azar]

Please see example "Conventional and Adaptive Beamformers" at:

https://www.mathworks.com/help/phased/ug/conventional-and-adaptive-beamformers.html

This example compares Conventional to Adaptive (MVDR & LCMV) Beamformers.