rxy_laplacian.m

mimo系统中相关多波束仿真方法

function result = Rxy_laplacian(d_norm,phi_0_deg,sigma_deg,delta_phi_deg)
% result = Rxy_laplacian(d_norm,phi_0_deg,sigma_deg,delta_phi_deg)
%
% Computes the correlation of the real and the imaginary part of
% the signals in the case of a laplacian Power Azimuth Spectrum
% (PAS) at spacings given by d_norm. The PAS is characterised by
% the Angle Of Arrival (AOA) phi_0_deg and by its standard
% deviation sigma_deg.
%
%
% STANDARD DISCLAIMER
%
% CSys is furnishing this item "as is". CSys does not provide any
% warranty of the item whatsoever, whether express, implied, or
% statutory, including, but not limited to, any warranty of
% merchantability or fitness for a particular purpose or any
% warranty that the contents of the item will be error-free.
%
% In no respect shall CSys incur any liability for any damages,
% including, but limited to, direct, indirect, special, or
% consequential damages arising out of, resulting from, or any way
% connected to the use of the item, whether or not based upon
% warranty, contract, tort, or otherwise; whether or not injury was
% sustained by persons or property or otherwise; and whether or not
% loss was sustained from, or arose out of, the results of, the
% item, or any services that may be provided by CSys.
%
% (c) Laurent Schumacher, AAU-TKN/IES/KOM/CPK/CSys - July 2001

D             = 2*pi*d_norm;
% Conversion degree -> rad
phi_0_rad     = phi_0_deg*(pi/180);
sigma_rad     = sigma_deg*(pi/180);
delta_phi_rad = delta_phi_deg*(pi/180);

m      = 0;
result = (4.*besselj(1,D).*sin(phi_0_rad) ...
	  .*((sqrt(2)./sigma_rad)+(exp((-1)*sqrt(2)*delta_phi_rad/sigma_rad) ...
	        *(sin(delta_phi_rad)-sqrt(2)*cos(delta_phi_rad)/ ...
		  sigma_rad)))) ...
	 ./(sqrt(2)*sigma_rad*((sqrt(2)/sigma_rad)^2+1));
tmp_xy_laplacian = ones(size(result));
while (m < 100)
    m                = m +1;
    tmp_xy_laplacian =  (4.*besselj(2*m+1,D).*sin((2*m+1)*phi_0_rad) ...
			 .*((sqrt(2)./sigma_rad)+(exp((-1)*sqrt(2)* ...
						     delta_phi_rad/ ...
						     sigma_rad) ...
                               *((2*m+1)*sin((2*m+1)*delta_phi_rad)-sqrt(2)*cos((2*m+1)*delta_phi_rad)/sigma_rad)))) ...
			./(sqrt(2)*sigma_rad*((sqrt(2)/sigma_rad)^2+(2*m+1)^2));
    result = result + tmp_xy_laplacian;
end;