Distributed digital subarray analysis

clc; clear all; close all;

f = 3e8;
Nx = 10; % number of antennas in subarray 
Ns1 = 5;% number of sub array   
h = 8; % number of virtual array between subarray
c = 3e8;
lambda = c / f;
dx = 0.42*lambda;
beta = 2 * pi / lambda;
theta = [20]; 
K = length(theta);
L = round(Nx / 3); 
Ri = ones(1,K);
A = 1000;
SNR1 =20;
%% sub array
for Ns = 1 : Ns1
for SNR = 1: SNR1
for l = 1 :A
for m = 1: Ns
    for p = 1 :  Nx
        pos = (m-1)*Nx+p;
        P_mp(pos) = (p-(Ns*Nx+(Ns-1)*h+1)/2+(m-1)*(Nx+h));
        P_mp1(m,p) = (p-(Ns*Nx+(Ns-1)*h+1)/2+(m-1)*(Nx+h));
    end
end 

% P_mp1 = P_mp1 + 2*(0.5-rand(Ns,Nx))*pos_var_amp;
A_mp = [];
A_mp_a = [];
E_mp_a = [];
for i = 1:Ns
    E_mp(:,:,i) = exp(-1j*beta*P_mp1(i,:)'*dx*sind(theta)); % pole 값
    A_mp(:,:,i) = Ri.*E_mp(:,:,i); % 측정 값 
    A_mp = awgn(A_mp, SNR, 'measured'); % noise 추가
    A_mp1 = sum(A_mp,2);
    
    A_mc(:,:,i) = A_mp1(1:Nx - L + 1,:,i);
    A_mr(:,:,i) = A_mp1(Nx - L + 1:Nx,:,i);
    A_mk(:,:,i) = hankel(A_mc(:,:,i), A_mr(:,:,i)); % Create Hankel matrix with A_c as the first column and A_r as the last row

    E_mp_a = [E_mp_a; E_mp(:,:,i)];
    A_mp_a = [A_mp_a ;A_mp1(:,:,i)];  
  
end

%% Hankel stack
Y_ss = A_mk(:,:,1);

if Ns> 1
    for z = 2:Ns
        Y_ss = [Y_ss ; A_mk(:,:,z)];
    end
else
    Y_ss = A_mk(:,:,1);
end

[U, S, V] = svd(Y_ss);
V0 = V(:, 1:K);
V1 = V0(1:end-1, :);
V2 = V0(2:end, :);

z_k = eig(pinv(V1) * V2);
find_theta_realarray_MPM(l,:)= asind((imag(log(z_k))*lambda)/(2*pi*dx))';

rmse_real_mpm(l,:) = sort(theta) - sort(find_theta_realarray_MPM(l,:));
end

rmse_real_MPM_sum = sum(sum(abs(rmse_real_mpm).^2,1),2);
rmse_real_MPM_sum = sqrt(rmse_real_MPM_sum/(A*K));
rmse_real_MPM_sum1(SNR,Ns)= rmse_real_MPM_sum(rmse_real_MPM_sum ~= 0);
end
end

plot(1:SNR1 , rmse_real_MPM_sum1,'-d','LineWidth',1.4)
legend('1-subarray','2-subarray','3-subarray','4-subarray','5-subarray')

I think the RMSE should be lower as the subarray increases, but why is the RMSE reversed when the SNR is low?

plz help me.....

Answer 1

[Balavignesh]

Hi 종영,

As per my understanding, you are calculating the Root Mean Square Error (RMSE) between the estimated and true angles and analyzing how the RMSE changes with the number of subarrays and SNR values. I also find this behavior strange. Here are some potential issues that might be the reason:

• At low SNR, the noise level is high relative to the signal. This can significantly affect the accuracy of your signal processing steps. Ensure that 'awgn' is correctly implemented and consider using a noise reduction or filtering technique before processing.
• High variance in low SNR conditions can lead to inconsistent RMSE values. Increase the number of trials ('A') to get a more accurate average RMSE.
• Increase the range of SNR values to see if the trend holds for even lower SNR values, and apply regularization techniques in the SVD step to mitigate the impact of noise.

Kindly have a look at the following documentation links to have more information on:

• Regularization: https://www.mathworks.com/discovery/regularization.html
• Singular Value Decomposition: https://www.mathworks.com/help/matlab/ref/double.svd.html

Hope that helps!

Balavignesh