% echo_mtx: echo data
% A: chirp matrix
% sigma_n: input noise standard deviation

% echo_r_mtx: range processing echo data
% signal_n_o: output noise standard deviation


function [ echo_r_mtx, sigma_n_o ] = range_process_MF(echo_mtx, A, sigma_n)

    % parameters
    multiple_r = A(:, 1)' * A(:, 1);
    [M, N] = size(A);
    [lenA, M, lenP] = size(echo_mtx);
    
    % matched filtering
    echo_r_mtx = zeros(lenA, N, lenP);
    for numA = 1: lenA
        for numP = 1: lenP
            sr = echo_mtx(numA, :, numP);
            mf_res = A' * transpose(sr);
            mf_norm = mf_res ./ multiple_r;
            echo_r_mtx(numA, :, numP) = mf_norm;
        end
    end
    
    % calculate output noise
    sigma_n_o = sqrt(sigma_n^2 / multiple_r);
    
end