【求助】Rayleigh Channel Fading Simulator

[y2000j]

我根據以下式子,用matlab來模擬Rayleigh 通道



此方程式出自於
http://ethesys.yuntech.edu.tw/ETD-db...105-112814.pdf
這篇paper的第50頁

問題1
如何用matlab,畫出envelope的PDF,如下


問題2
輸出的自相關函數如何畫?

我用了
auto1 = xcorr2(xc);
figure;
plot(auto1);
但輸出不合理論,理論圖在paper的45頁



我寫的Code如下:


%假設v=110km/h fc=900MHZ ,max Doppler freq=91.6HZ
clear all
fmax=91.6;
M=8;
N=4*M+2;
%c_i :同相增益 c_q:垂直相增益 fdoppler frequency
% 實現equation(103),(104)
for n=1:N-1
c_i(n)=2*sin(n.*pi./(N-1))./sqrt(N-0.5);
c_q(n)=2*cos(n.*pi./(N-1))./sqrt(N-0.5);
fd(n)=fmax*cos(n*pi./(2*N-1));
end
c_i(N)=1/sqrt(N-0.5);
c_q(N)=1/sqrt(N-0.5);
fd(N)=fmax;
%產生相對應之Doppler freq. cosine wave
%Equation: Ci*cos(2*pi*fd*t)
count=0;
for t=0:2*pi./200:2*pi
count=count+1;
for k=1:N
u1(count,k)=cos(2*pi*fd(k)*t)*c_i(k);
u2(count,k)=cos(2*pi*fd(k)*t)*c_q(k);
end
end
%xc: 同相波 xq:垂直波
for time=1:count
xc(time)=sum(u1(time,1:N)); %對應於eq(101)之u1(t)
xq(time)=sum(u2(time,1:N)); %對應於eq(101)之u2(t)
end
%模擬接收到的envelope
for time=1:count
envelope(time)=sqrt(xc(time).^2+xq(time).^2);
end
figure;
histfit(envelope); %envelope統計圖

%同相波的autocorrelation

auto1 = xcorr2(xc);
figure;
plot(auto1);