function [ echo_rd_mtx, stat_RD, sigma_n_o ] = doppler_process_MF(echo_r_mtx, sigma_n, gamma)
% Doppler processing for echo data using matching filter
%
% Usage: 
% [echo_rd_mtx, stat_RD, sigma_n_o] = doppler_process_MF(echo_r_mtx, sigma_n, gamma)
%
% Inputs:
%   echo_r_mtx:     Range processing echo data
%   sigma_n:        Input noise standard deviation
%   gamma:          Compressed ratio(0.5)
%
% Outputs:
%   echo_rd_mtx:    Range-doppler processing echo data
%   stat_RD:        Range-doppler statistics
%   sigma_n_o:      Output noise standard deviation


    % 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