smartantenna.zip_mixture52k_principalezi_天线阵列_智能天线_阵列天线

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% %% ****************************************************** %% %% * Smart Antennas for Wireless Applications w/ Matlab * %% %% ****************************************************** %% %% %% %% Chapter 7: Ex 7.14 %% %% %% %% Author: Frank Gross %% %% McGraw-Hill, 2005 %% %% Date: 1/26/2004 %% %% %% %% This code creates Figures 7.12 & 7.13, a plot of the %% %% roots determined by the Min-Norm AOA estimate in %% %% cartesian coordinates and a plot of a Min-Norm %% %% Pseudospectrum for theta1= -2 & theta2 = 4. Use %% %% time averages instead of expected values by assuming %% %% ergodicity of the mean and ergodicity of the %% %% correlation. %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%------------------- Define Variables:---------------------%% % M - # of elements in array % % sig2 - noise variance % % D - number of signals % % th1, th2 - angles of arrival % % K - Length of time samples % % u1 - cartesian basis vector % % a1, a2, a - array steering vectors % % A - Steering vector matrix % % Rss - Source correlation matrix % % Rnn - noise correlation matrix % % Rns - noise/signal correlation matrix % % Rsn - signal/noise 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 % % C - hermetian matrix composed of noise subspace EN % % c1 - first column vector of matrix C % % cc - coefficients of Min-Norm polynomial % % rts - roots of Min-Norm polynomial % % angs - angles associated with roots of Min-Norm Polynomial % %%----------------------------------------------------------%% %%----- Given Values -----%% M = 4; sig2 = .3; D = 2; th1 = -2*pi/180; th2 = 4*pi/180; K = 300; temp = eye(M); u1 = temp(:,1); %%----- Create array steering vectors, a1 & a2, steering matrix -----%% a1 = []; a2 = []; i = 1:M; a1 = exp(1j*(i-1)*pi*sin(th1)); a2 = exp(1j*(i-1)*pi*sin(th2)); A = [a1.' a2.']; %%----- Calculate signal correlation matrix -----%% s = sign(randn(D,K)); % Calculate the K time samples of the signals for the % two arriving directions Rss = s*s'/K; % source correlation matrix with uncorrelated signals %%----- Calculate Correlation Matrices -----%% n = sqrt(sig2)*randn(M,K); % Calculate the K time samples of the noise for the 6 array % elements Rnn = (n*n')/K; % Calculate the noise correlation matrix (which is no longer diagonal) Rns = (n*s')/K; % Calculate the noise/signal correlation matrix Rsn = (s*n')/K; % Calculate the signal/noise correlation matrix Rxx = A*Rss*A' + A*Rsn + Rns*A' + Rnn; %%----- Determine Noise Subspace Matrix -----%% [V,Dia] = eig(Rxx); [Y,Index] = sort(diag(Dia)); % sorts 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 %%----- Determine Min-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(a'*EN*EN'*u1)^2; end %%----- Part A: Find the matrix C -----%% C = EN*EN'; %%----- Part B: Find the first column vector of the matrix C -----%% c1 = (EN*EN')*u1; CC = c1*c1'; %%----- Part C: Find the coefficients for the Root Min-Norm polynomial -----%% for kk = -M+1:M-1 cc(kk+M) = sum(diag(CC,kk)); end %%----- Part D: Display the roots of the Root Min-Norm Polynomial -----%% rts = roots(cc); %%----- Part E: Display the angles of the Root Min-Norm Polynomial -----%% angs = -asin(angle(rts)/pi)*180/pi; %%----- Plot Results -----%% figure(1), zplane(rts) title('\bfFigure 7.12 - 6 Roots in Cartersian Coordinates for Min-Norm AOA Estimate') figure(2), plot(th*180/pi,P/max(P),'k',angs,abs(rts),'kX','markersize',10) xlabel('Angle'), ylabel('|P(\theta)|') title('\bfFigure 7.13 - Min-Norm Psuedospectrum and Roots Found Using Root Min-Norm') axis([-15 15 0 1.6]), grid on