在Matlab中用mvnrn生成2个高斯相关矩阵
这是我在这里问的第一个问题，请耐心听我说。我对Matlab并不陌生，但以前从未使用过MVNRND函数，而且我的统计知识也不强。我尝试做的工作总结如下：我尝试创建一个函数，生成2个相关相位屏（NxN矩阵），用于电磁高斯-谢尔模型波束传播模拟。对于X和Y偏振状态，光束需要单独的随机相位屏。到目前为止，我的代码如下在Matlab中用mvnrn生成2个高斯相关矩阵,matlab,matrix,correlation,gaussian,cross-correlation,Matlab,Matrix,Correlation,Gaussian,Cross Correlation,这是我在这里问的第一个问题，请耐心听我说。我对Matlab并不陌生，但以前从未使用过MVNRND函数，而且我的统计知识也不强。我尝试做的工作总结如下：我尝试创建一个函数，生成2个相关相位屏（NxN矩阵），用于电磁高斯-谢尔模型波束传播模拟。对于X和Y偏振状态，光束需要单独的随机相位屏。到目前为止，我的代码如下 function [phz_x,phz_y]=GSM_phase_screen_2(l_phi_x,l_phi_y,sigma_phi_x, ... sigma_phi_y,gamma,N
function [phz_x,phz_y]=GSM_phase_screen_2(l_phi_x,l_phi_y,sigma_phi_x, ...
sigma_phi_y,gamma,N,delta)
%GSM_PHASE_SCREEN_2
% This code generates two correlated 2-D NxN Gaussian Schell-Model (GSM)
% phase screens (matrices) of unit variance circular complex Gaussian
% random numbers for the X and Y polarization states provided l_phi_x,
% l_phi_y, sigma_phi_x, sigma_phi_y, and gamma. It utilizes the MVNRND
% Matlab function.
%
% l_phi_x: [m] correlation length in X phase screen
% l_phi_y: [m] correlation length in Y phase screen
% sigma_phi_x: phase variance in X phase screen
% sigma_phi_y: phase variance in Y phase screen
% gamma: correlation coefficient
% N: number of samples per side of grid
% delta: [m] sample grid spacing
%
% phz_x: [rad] 2-D phase screen for X polarization state
% phz_y: [rad] 2-D phase screen for Y polarization state
% ORIGINAL AUTHOR: Santasri Basu
% MODIFIED BY: Matthew Gridley
% Added input arguments needed to generate 2 correlated phase
% screens, updated PSD equations, and replaced RANDN with MVNRND
%
% Setup the Power Spectral Density (PSD)
del_f = 1 / (N*delta); % frequency grid spacing [1/m]
fx = (-N/2 : N/2-1) * del_f;
% Frequency grid
[fx,fy] = meshgrid(fx);
% GSM phase PSD
PSD_phi_x = (sigma_phi_x^2) * pi * (l_phi_x^2) * gamma * ...
exp(-((pi * l_phi_x)^2) * (fx.^2 + fy.^2));
PSD_phi_y = (sigma_phi_y^2) * pi * (l_phi_y^2) * gamma * ...
exp(-((pi * l_phi_y)^2) * (fx.^2 + fy.^2));
% Random draws of Fourier series coefficients
% (zero mean Gaussian random numbers)
%
% the 2 lines of code below need changed to generate the correlated random
% draws using MVNRND and GAMMA
cn_x = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_x) * del_f;
cn_y = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_y) * del_f;
% Synthesize the phase screens
phz_x = real(ift2(cn_x,1));
phz_y = real(ift2(cn_y,1));
end
function [g, x] = ift2(G, df)
% [g, x] = ift2(G, df)
% 2-D inverse Fourier transform that keeps the origin at the center of
% the grid.
%
% G: Complex field in frequency space
% df: Spacing in frequency space [m^-1]
% g: Complex field in coordinate space
% Core function written by Jason Schmidt
% Modified: 17 Apr 2010
% By: Daniel J. Wheeler
%
% x output added functionality by Michael Steinbock 6/8/2014
%
g = ifftshift(ifft2(ifftshift(G))) * (length(G) * df)^2;
%% Calc x:
if nargout == 2
N = size(G, 1);
x = (0 : N-1) / (N*delta_f);
end
在上面的代码中，注释下面以“%Random Drawing of Fourier级数系数”开头的两行代码是我需要帮助的地方。我之前用你们看到的代码做了两个矩阵，但意识到它们不是高斯相关的。根据我的学术顾问的建议，我应该使用MVNRND生成这些阶段屏幕。在查看了MVNRND的帮助文件后，我不知道如何使用它。我在这里搜索，试图找到类似的问题和答案，但运气不好，我也搜索了谷歌。任何人都可以帮助更改这两行代码以利用MVNRND。谢谢大家! 输入代码经过大量研究，我找到了如何使用MVNRND来满足我的目的。我的意图是创建4个随机NxN矩阵，以替换下面代码段中randn（N）的4个用法。我需要用MVNRND生成的随机矩阵替换这些矩阵的原因是为了使它们相互关联。在MVNRND中，必须提供协方差矩阵。这就是困扰我的问题
cn_x = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_x) * del_f;
cn_y = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_y) * del_f;
% Multivariate normal parameters
mu = zeros([1,4]); % Zero mean Gaussian
% Covariance matrix for 4 circular complex Gaussian random numbers:
% rx_real, rx_imag, ry_real, ry_imag
%
% [<rx_real rx_real> <rx_real rx_imag> <rx_real ry_real> <rx_real ry_imag>;
% <rx_imag rx_real> <rx_imag rx_imag> <rx_imag ry_real> <rx_imag ry_imag>;
% <ry_real rx_real> <ry_real rx_imag> <ry_real ry_real> <ry_real ry_imag>;
% <ry_imag rx_real> <ry_imag rx_imag> <ry_imag ry_real> <ry_imag ry_imag>]
sigma = [1 0 gamma 0;
0 1 0 gamma;
gamma 0 1 0;
0 gamma 0 1];
cases = N^2; % matrix of random vectors
r = mvnrnd(mu, sigma, cases); % gives a 512^2x4 double matrix
rx_real = reshape(r(:,1),[N N]);
rx_imag = reshape(r(:,2),[N N]);
ry_real = reshape(r(:,3),[N N]);
ry_imag = reshape(r(:,4),[N N]);
% Correlated random draws of Fourier series coefficients
cn_x = (rx_real + 1i*rx_imag) .* sqrt(PSD_phi_x) * del_f;
cn_y = (ry_real + 1i*ry_imag) .* sqrt(PSD_phi_y) * del_f;
%多元正态参数
μ=零（[1,4]）；%零均值高斯分布
%4个循环复高斯随机数的协方差矩阵：
%rx_real，rx_imag，ry_real，ry_imag
%
% [ ;
% ;
% ;
% ]
西格玛=[1 0伽马0；
1010伽马；
伽马0 1 0；
0伽马0 1]；
案例=N^2；%随机向量矩阵
r=mvnrnd（μ，σ，事例）；%给出一个512^2x4的双矩阵
rx_real=重塑（r（：，1），[N]）；
rx_imag=重塑（r（：，2），[N]）；
r_real=重塑（r（：，3），[N]）；
r_imag=重塑（r（：，4），[N]）；
%傅里叶级数系数的相关随机抽取
cn_x=（rx_real+1i*rx_imag）。*sqrt（PSD_phi_x）*del_f；
cn_y=（y_real+1i*y_imag）。*sqrt（PSD_phi_y）*del_f；
cn_x = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_x) * del_f;
cn_y = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_y) * del_f;
% Multivariate normal parameters
mu = zeros([1,4]); % Zero mean Gaussian
% Covariance matrix for 4 circular complex Gaussian random numbers:
% rx_real, rx_imag, ry_real, ry_imag
%
% [<rx_real rx_real> <rx_real rx_imag> <rx_real ry_real> <rx_real ry_imag>;
% <rx_imag rx_real> <rx_imag rx_imag> <rx_imag ry_real> <rx_imag ry_imag>;
% <ry_real rx_real> <ry_real rx_imag> <ry_real ry_real> <ry_real ry_imag>;
% <ry_imag rx_real> <ry_imag rx_imag> <ry_imag ry_real> <ry_imag ry_imag>]
sigma = [1 0 gamma 0;
0 1 0 gamma;
gamma 0 1 0;
0 gamma 0 1];
cases = N^2; % matrix of random vectors
r = mvnrnd(mu, sigma, cases); % gives a 512^2x4 double matrix
rx_real = reshape(r(:,1),[N N]);
rx_imag = reshape(r(:,2),[N N]);
ry_real = reshape(r(:,3),[N N]);
ry_imag = reshape(r(:,4),[N N]);
% Correlated random draws of Fourier series coefficients
cn_x = (rx_real + 1i*rx_imag) .* sqrt(PSD_phi_x) * del_f;
cn_y = (ry_real + 1i*ry_imag) .* sqrt(PSD_phi_y) * del_f;
%多元正态参数
μ=零（[1,4]）；%零均值高斯分布
%4个循环复高斯随机数的协方差矩阵：
%rx_real，rx_imag，ry_real，ry_imag
%
% [ ;
% ;
% ;
% ]
西格玛=[1 0伽马0；
1010伽马；
伽马0 1 0；
0伽马0 1]；
案例=N^2；%随机向量矩阵
r=mvnrnd（μ，σ，事例）；%给出一个512^2x4的双矩阵
rx_real=重塑（r（：，1），[N]）；
rx_imag=重塑（r（：，2），[N]）；
r_real=重塑（r（：，3），[N]）；
r_imag=重塑（r（：，4），[N]）；
%傅里叶级数系数的相关随机抽取
cn_x=（rx_real+1i*rx_imag）。*sqrt（PSD_phi_x）*del_f；
cn_y=（y_real+1i*y_imag）。*sqrt（PSD_phi_y）*del_f；
cn_x = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_x) * del_f;
cn_y = (randn(N) + 1i*randn(N)) .* sqrt(PSD_phi_y) * del_f;
% Multivariate normal parameters
mu = zeros([1,4]); % Zero mean Gaussian
% Covariance matrix for 4 circular complex Gaussian random numbers:
% rx_real, rx_imag, ry_real, ry_imag
%
% [<rx_real rx_real> <rx_real rx_imag> <rx_real ry_real> <rx_real ry_imag>;
% <rx_imag rx_real> <rx_imag rx_imag> <rx_imag ry_real> <rx_imag ry_imag>;
% <ry_real rx_real> <ry_real rx_imag> <ry_real ry_real> <ry_real ry_imag>;
% <ry_imag rx_real> <ry_imag rx_imag> <ry_imag ry_real> <ry_imag ry_imag>]
sigma = [1 0 gamma 0;
0 1 0 gamma;
gamma 0 1 0;
0 gamma 0 1];
cases = N^2; % matrix of random vectors
r = mvnrnd(mu, sigma, cases); % gives a 512^2x4 double matrix
rx_real = reshape(r(:,1),[N N]);
rx_imag = reshape(r(:,2),[N N]);
ry_real = reshape(r(:,3),[N N]);
ry_imag = reshape(r(:,4),[N N]);
% Correlated random draws of Fourier series coefficients
cn_x = (rx_real + 1i*rx_imag) .* sqrt(PSD_phi_x) * del_f;
cn_y = (ry_real + 1i*ry_imag) .* sqrt(PSD_phi_y) * del_f;
%多元正态参数
μ=零（[1,4]）；%零均值高斯分布
%4个循环复高斯随机数的协方差矩阵：
%rx_real，rx_imag，ry_real，ry_imag
%
% [ ;
% ;
% ;
% ]
西格玛=[1 0伽马0；
1010伽马；
伽马0 1 0；
0伽马0 1]；
案例=N^2；%ran矩阵