rxy_gaussian.m

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function result = Rxy_gaussian(d_norm,phi_0_deg,sigma_deg,delta_phi_deg)
% result = Rxy_gaussian(d_norm,phi_0_deg,sigma_deg,delta_phi_deg)
%
% Computes the envelope correlation of the signals in the case
% of a truncated gaussian 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.
%
% This program calls a procedure named erfcomp. It computes the
% error function of a complex argument according to Abramowitz,
% "Error Functions and Fresnel Integrals", p. 299.
%
%
% 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;
B      = erfcomp((delta_phi_rad./(sigma_rad.*sqrt(2)))-(j.*.5.*sigma_rad.*sqrt(2)))...
       - erfcomp(((-1).*delta_phi_rad./(sigma_rad.*sqrt(2)))-(j.*.5.*sigma_rad.*sqrt(2)));
result = besselj(1,D).*sin(phi_0_rad).*exp((-2)*(sigma_rad^2)*.25).*real(B);

tmp_xy_gaussian = ones(size(result));
while (m < 100)
    m = m +1;
    B = erfcomp((delta_phi_rad/(sigma_rad*sqrt(2)))-(j*(m+.5)*sigma_rad*sqrt(2)))...
      - erfcomp(((-1)*delta_phi_rad/(sigma_rad*sqrt(2)))-(j*(m+.5)*sigma_rad*sqrt(2)));
    if (isnan(B))
        disp('Warning: NaN reached in Rxy_gaussian - Breaking loop');
        break;
    end;
    tmp_xy_gaussian = besselj(2*m+1,D).*sin((2*m+1)*phi_0_rad).*exp((-2)*(sigma_rad^2)*((m+.5)^2)).*real(B);
    result          = result + tmp_xy_gaussian;
end;