% echo_r_mtx: range processing echo data
% sigma_n: input noise standard deviation
% gamma: compressed ratio

% echo_rd_mtx: range-doppler processing echo data
% stat_RD: range-doppler statistics


function [ echo_rd_mtx, stat_RD ] = doppler_process_MF(echo_r_mtx, sigma_n, gamma)

    % parameters
    if nargin < 3
        gamma = 0.5;
    end
    [lenA, lenR, M] = size(echo_r_mtx);
    N = round(M / gamma);
    
    % generate mtx
    F_ori = dftmtx(N);
    F = F_ori(1:M,:);
    multiple_d = F(:,1)' * F(:,1);
    
    % doppler matched filtering
    echo_rd_mtx = zeros(lenA, lenR, N);
    for numA = 1: lenA
        for numR = 1: lenR
            sample = squeeze(echo_r_mtx(numA, numR, :));
            dpl_temp = transpose(F) * sample;
            dpl_norm = fftshift(dpl_temp ./ multiple_d);
            echo_rd_mtx(numA, numR, :) = dpl_norm;
        end
    end
    
    % calculate output noise
    sigma_n_o = sqrt(sigma_n^2 / multiple_d);
    stat_RD = abs(echo_rd_mtx ./ sigma_n_o).^2;
    
end