sa_ex7_10.m

智能天线Matlab版源代码

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%% ******************************************************  %%
%% * Smart Antennas for Wireless Applications w/ Matlab *  %%
%% ******************************************************  %%
%%                                                         %%
%% Chapter 7: Ex 7.10                                      %%
%%                                                         %%
%% Author: Frank Gross                                     %%
%% McGraw-Hill, 2005                                       %%
%% Date:  1/26/2004                                        %%
%%                                                         %%
%% This code creates Figure 7.7, plot of a Min - Norm      %%
%%     Pseudospectrum for theta1= -5 & theta2 = 5          %% 
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%%------------------- Define Variables:--------------------%%
% M - # of elements in array                                %
% sig2 - noise variance                                     %
% D - number of signals                                     %
% th1, th2 - angles of arrival                              %
% a1, a2, a - array steering vectors                        %
% u1 - Cartesian basis vector                               %
% A - Steering vector matrix                                %
% Rss - Source correlation matrix                           %
% Rxx - Array correlation matrix                            %
% V,Dia - eigen vectors, V and eigen values, D of Rxx       %
% EN - Noise subspace matrix                                %
% P - Min - Norm Psuedospectra                              % 
%%---------------------------------------------------------%%

%%----- Given Values -----%%

M = 6;  sig2 = .1;  D = 2;

th1 = -5*pi/180;  th2 = 5*pi/180;

temp = eye(M);  u1 = temp(:,1);

%%----- Create array steering vectors, a1 & a2 -----%%

a1 = [];  a2 = [];
i = 1:M;
a1 = exp(1j*(i-1)*pi*sin(th1));
a2 = exp(1j*(i-1)*pi*sin(th2));

%%----- Create A, Rss, Rxx -----%%

A=[a1.' a2.']; Rss = [1 0;0 1];  Rxx = A*Rss*A' + sig2*eye(M);

%%----- Calculate the noise subspace matrix of eigen vectors, EN -----%%

[V,Dia] = eig(Rxx); [Y,Index] = sort(diag(Dia));  % sort eigenvalues from least to greatest

EN = V(:,Index(1:M-D));    % calculate the noise subspace matrix of eigenvectors
                           % using the sorting done in the previous line
ES = V(:,Index(M-1:M));

%%----- Create Nin-Norm Psuedospectrum -----%%

for k=1:180;
    th(k) = -pi/6 + pi*k/(3*180);
    clear a
    a = [];
    for jj = 1:M
       a = [a exp(1j*(jj-1)*pi*sin(th(k)))];
    end
    P(k) = 1./abs(conj(a)*EN*EN'*u1).^2; 
end

%%----- Plot Results -----%%

plot(th*180/pi,10*log10(P/max(P)),'k')
grid on
title(['\bfFigure 7.7 - Min - Norm Psuedospectra for \theta = +/- 5^o'])
xlabel('Angle')
ylabel('|P(\theta)|')
axis([-30 30 -30 10])