parameter_gauss.m

高斯白噪声信道的仿真

%--------------------------------------------------------------------
% parameter_Gauss.m -------------------------------------------------
%% Program for the computation of the discrete Doppler frequencies,
% Doppler coefficients, and Doppler phases by using the Gaussian
% power spectral density.
%
% Used m-files: LPNM_opt_Gauss.m, fun_Gauss.m,
% grad_Gauss.m, acf_mue.m
%--------------------------------------------------------------------
% [f_i_n,c_i_n,theta_i_n]=parameter_Gauss(METHOD,N_i,sigma_0_2,...
% f_max,f_c,PHASE,PLOT)
%--------------------------------------------------------------------
% Explanation of the input parameters:
%
% METHOD:
% |----------------------------------------------|------------------|
% | Methods for the computation of the discrete | Input |
% | Doppler frequencies and Doppler coefficients | |
% |----------------------------------------------|------------------|
% |----------------------------------------------|------------------|
% | Method of equal distances (MED) | 'ed_g' |
% |----------------------------------------------|------------------|
% | Mean square error method (MSEM) | 'ms_g' |
% |----------------------------------------------|------------------|
% | Method of equal areas (MEA) | 'ea_g' |
% |----------------------------------------------|------------------|
% | Monte Carlo method (MCM) | 'mc_g' |
% |----------------------------------------------|------------------|
% | Lp-norm method (LPNM) | 'lp_g' |
% |----------------------------------------------|------------------|
% | Method of exact Doppler spread (MEDS) | 'es_g' |
% |----------------------------------------------|------------------|
%
% N_i: number of harmonic functions
% sigma_0_2: average power of the real deterministic Gaussian
% process mu_i(t)
% f_max: maximum Doppler frequency
% f_c: 3-dB-cutoff frequency
%
% PHASE:
% |----------------------------------------------|------------------|
% | Methods for the computation of the Doppler | Input |
% | phases | |
% |----------------------------------------------|------------------|
% |----------------------------------------------|------------------|
% | Random Doppler phases | 'rand' |
% |----------------------------------------------|------------------|
% | Permuted Doppler phases | 'perm' |
% |----------------------------------------------|------------------|
%
% PLOT: plot of the ACF and the PSD of mu_i(t), if PLOT==1

function [f_i_n,c_i_n,theta_i_n]=parameter_Gauss(METHOD,N_i,...
sigma_0_2,f_max,f_c,PHASE,PLOT)

if nargin<7,
error('Not enough input parameters')
end
sigma_0=sqrt(sigma_0_2);
% The frequency range of Gaussian power spectral density must be limited
% the relevant range.
kappa_c=f_max/f_c;

%-------------------- Method of equal distances(MED)-----------------------
if METHOD=='ed_g',
    n=(1:N_i)';

    f_i_n=kappa_c*f_c/(2*N_i)*(2*n-1);  % Formula (5.12) on page 87
    c_i_n=sigma_0*sqrt(2)*sqrt(erf(n*kappa_c*...
    sqrt(log(2))/N_i)-erf((n-1)*kappa_c*...
    sqrt(log(2))/N_i) );               % Formula (5.13) on page 87
    K=1;

%-------------------- Mean square error method (MSEM)--------------------
elseif METHOD=='ms_g',
    n=(1:N_i)';
    f_i_n=kappa_c*f_c/(2*N_i)*(2*n-1);  % Formula (5.12) on page 87
    tau_max=N_i/(2*kappa_c*f_c);       
    N=1E3;
    tau=linspace(0,tau_max,N);
    f1=exp(-(pi*f_c*tau).^2/log(2));
    c_i_n=zeros(size(f_i_n));
    for k=1:length(c_i_n),
        c_i_n(k)=2*sigma_0*sqrt(trapz(tau,f1.*...
        cos(2*pi*f_i_n(k)*tau))/tau_max); % Formula (5.24) on page 93
    end
    K=1;
   
%------------------------Method of equal areas(MEA)--------------------
elseif METHOD=='ea_g'
    n=(1:N_i)';
    c_i_n=sigma_0*sqrt(2/N_i)*ones(size(n)); % Formula (5.31) on page 96
    
    f_i_n=f_c/sqrt(log(2))*erfinv(n/N_i);
    f_i_n(N_i)=f_c/sqrt(log(2))*erfinv(0.9999999);% Formula (5.42) on page 101
    K=1;
%------------------------ Monte Carlo method (MCM)------------------------ 
elseif METHOD=='mc_g'
    n=rand(N_i,1);
    f_i_n=f_c/sqrt(log(2))*erfinv(n);     % Formula (5.49) on page 112
    c_i_n=sigma_0*sqrt(2/N_i)*ones(size(n)); % Formula (5.47) on page 105
    K=1;
    
% ------------------------Lp-norm method (LPNM)------------------------
elseif METHOD=='lp_g',
    if exist('fminu')~=2
        disp([' =====> This method requires ',...
        'the Optimization Toolbox !!'])
        return
    else
        N=1e3;
        p=2;
        [f_i_n,c_i_n]=LPNM_opt_Gauss(N,f_max,f_c,...
        sigma_0_2,p,N_i,PLOT);
        K=2;
    end

%--------------- Method of exact Doppler spread(MEDS)------------
elseif METHOD=='es_g',
    n=(1:N_i)';
    c_i_n=sigma_0*sqrt(2/N_i)*ones(size(n));         % Formula (5.73) on page 129
    f_i_n=f_c/sqrt(log(2))*erfinv((2*n-1)/(2*N_i)); % Formula (5.76a) on page 131
    K=1;
    else
    error([setstr(10),'Method is unknown'])
end

    % Computation of the Doppler phases:
   if PHASE=='rand',
       theta_i_n=rand(N_i,1)*2*pi;
    elseif PHASE=='perm',
        n=(1:N_i)';
        Z=rand(size(n));
        [dummy,I]=sort(Z);
        theta_i_n=2*pi*n(I)/(N_i+1);
   end
    
   if PLOT==1,
        subplot(1,2,1)
        stem([-f_i_n(N_i:-1:1);f_i_n],...
        1/4*[c_i_n(N_i:-1:1);c_i_n].^2)
        xlabel('f (Hz)')
        ylabel('Power Spectral Density')
        tau_max=N_i/(K*kappa_c*f_c);
        tau=linspace(0,tau_max,500);
        r_mm=sigma_0_2*exp(-(pi*f_c/sqrt(log(2))*tau).^2);
        r_mm_tilde=acf_mue(f_i_n,c_i_n,tau);
        subplot(1,2,2)
        plot(tau,r_mm,'r-',tau,r_mm_tilde,'g--')
        xlabel('tau(s)')
        ylabel('Autocorrelation Function')
  end