先說結論：
method 1是 Emil Björnson 回覆的可信度最高。 method 2/3 少了 Emil 說的 LOS path random phase，而 method 2/3 不同處是 NLOS path的 \(\sigma\) 以及分母的 \(2k+1\)。 method 4/5 應該是不同的 formatting 方式。 Method 1: Emil Björnson
來源
有 Emil Björnson 大神回覆可信度最高，他本人也寫了一篇文章 解釋 rician fading 很多人都做錯。跟MATLAB 和這裡 的生成方式一樣。
h LOS = e ( j 2 π N ( 1 , 1 ) ) h NLOS = C N ( 0 , σ 2 ) h = h LOS K K + 1 + h NLOS 1 K + 1
\footnotesize
\begin{align}
&h_{\text{LOS}} &&= e^{(j2\pi\mathcal{N}(1,1))} \newline
&h_{\text{NLOS}} &&= \mathcal{CN}(0, \sigma^2) \newline
&h &&= h_{\text{LOS}}\sqrt{\dfrac{K}{K + 1}} + h_{\text{NLOS}}\sqrt{\frac{1}{K + 1}}
\end{align}
h LOS h NLOS h = e ( j 2 π N ( 1 , 1 )) = C N ( 0 , σ 2 ) = h LOS K + 1 K + h NLOS K + 1 1 Method 2
來源
h rayleigh = σ 2 2 ∗ ( N ( 1 , 1 ) + j N ( 1 , 1 ) ) h rician = k k + 1 + h rayleigh 1 k + 1
\footnotesize
\begin{align}
&h_\text{rayleigh} &&= \sqrt{\frac{\sigma^2}{2}} *(\mathcal{N}(1,1) + j\mathcal{N}(1,1)) \newline
&h_\text{rician} &&= \sqrt{\frac{k}{k+1}} + h_\text{rayleigh}\sqrt{\frac{1}{k+1}}
\end{align}
h rayleigh h rician = 2 σ 2 ∗ ( N ( 1 , 1 ) + j N ( 1 , 1 )) = k + 1 k + h rayleigh k + 1 1 Method 3
來源
h NLOS = ( N ( 1 , N ) + j N ( 1 , N ) ) h = ∣ K K + 1 + h NLOS 1 2 ( K + 1 ) ∣
\footnotesize
\begin{align}
&h_{\text{NLOS}} &&= (\mathcal{N}(1,N)+j\mathcal{N}(1,N)) \newline
&h &&= \left|\sqrt{\dfrac{K}{K+1}}+h_{\text{NLOS}}\sqrt{\dfrac{1}{2(K+1)}}\right|
\end{align}
h NLOS h = ( N ( 1 , N ) + j N ( 1 , N )) = K + 1 K + h NLOS 2 ( K + 1 ) 1 Method 4
來源
s = 1 2 ( K + 1 ) , μ = K 2 ( K + 1 ) h = ( s N ( 1 , 1 ) + μ ) + j ( s N ( 1 , 1 ) + μ )
\footnotesize
\begin{align}
&s &&= \sqrt{\dfrac{1}{2(K+1)}}, \mu = \sqrt{\dfrac{K}{2(K+1)}} \newline
&h &&= ( s\mathcal{N}(1,1) + \mu ) + j( s\mathcal{N}(1,1) + \mu )
\end{align}
s h = 2 ( K + 1 ) 1 , μ = 2 ( K + 1 ) K = ( s N ( 1 , 1 ) + μ ) + j ( s N ( 1 , 1 ) + μ ) Method 5
來源
% LOS components
a = sqrt ( K / 2 ); b = a ;
% in-phase component
i = a + randn ([ 1 size ]);
% quadtature component
q = b + randn ([ 1 size ]);
% build fading component
s = ( i + 1 j * q );
Method 6
來源
mu = sqrt ( k1 / ( k1 + 1 )); % mean
sigma = sqrt ( 1 / ( 2 * ( k1 + 1 ))); %variance
Nr2 = randn ( N , 1 ) * sigma + mu ;
Ni2 = randn ( N , 1 ) * sigma ;
% To generate the Rician Random Variable
h_rac = sqrt ( Nr2 .^ 2 + Ni2 .^ 2 ); %Rician fading coefficient
TODO:
對method 2/3: 查原文書確認些分母是 \(k+1\) 或 \(2k+1\) 對method 2/3: 查原文書對Rayleigh fading 母數 \(\sigma\) 的解釋 確認 method 4 中對 Nakagami fading 的模擬是否正確 確認 method 5 錯在哪裡