parameter_gauss.m

《移动衰落信道》Mobiel_Fading_Channels一书后面的相关仿真程序。

%-------------------------------------------------------------------- 
% 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); 
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); 
       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) ); 
       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); 
       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); 
       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)); 
       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); 
       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); 
       c_i_n=sigma_0*sqrt(2/N_i)*ones(size(n)); 
       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)); 
       f_i_n=f_c/sqrt(log(2))*erfinv((2*n-1)/(2*N_i)); 
       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('PSD') 
   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('ACF') 
end