基于MATLAB的阵列信号处理中的延迟相加、Capon、MUSIC、Root-MUSIC、ESPRIT算法的性能比较分析.rar

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% %% %% ****************************************************** %% %% * Smart Antennas for Wireless Applications w/ Matlab * %% %% ****************************************************** %% %% %% %% Chapter 7: Ex 7.15 %% %% %% %% Author: Frank Gross %% %% McGraw-Hill, 2005 %% %% Date: 1/26/2004 %% %% %% %% This code produces the results of Ex. 7.15 & determines %% %% the angles of arrival estimated using the ESPIRIT AOA %% %% estimation technique. %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%------------------- 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 % % A - Steering vector matrix % % Rss - Source 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 % % ES - Signal subspace matrix % % E1, E2 - Subarray signal spaces formed from ES % % C - Matrix of subarray signal spaces, E1 & E2 % % EC - matrix eigendecomposed components of C % % E11, E12 - quadrant components of EC % % PSI - rotation operator % % Vp, Ep - eigenvectors and values of rotation operator % % angs - angles associated with roots of Min-Norm Polynomial % %%----------------------------------------------------------%% %%----- Given Values -----% M = 4; sig2 = .1; D = 2; th1 = -5*pi/180; th2 = 10*pi/180; %%----- 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 -----%% K=300; % K = length of time samples 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 noise correlation matrix -----%% n =sqrt(sig2)*randn(M,K); % calculate the K time samples of the noise for the M array % elements Rnn =(n*n')/K; %%----- Calculate remaining correlation matrices -----%% 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; % combine all to get the array correlation matrix %%----- Determine eigen subspaced for Rxx -----%% [V,Dia] = eig(Rxx); [Y,Index] = sort(diag(Dia)); % Sorts the eigenvalues from least to greatest %%----- Determine Signal Subspace -----%% ES = V(:,Index(M-D+1:M)); % Calculate the signal subspace matrix of eigenvectors % using the sorting done in the previous line %%----- Construct subarray signal spaces, E1 & E2 from signal subpspace -----%% E1 = ES(1:M/2+1,:); % Construct form the first K rows of ES (K = M/2+1) E2 = ES(M/2:M,:); % Construct from the last K rows of ES %%----- Determine Matrix of subarray subspaces, C -----%% C = [E1';E2']*[E1 E2]; %%---- Perform eigendecomposition of C to create matrix EC -----%% [EC,tmp] = eig(C); % Perform the eigendecomposition on the matrix C E12 = EC(1:2,3:4); % Construct the E12 submatrix E22 = EC(3:4,3:4); % Construct the E22 submatrix %%----- Determine Rotation Operator -----%% PSI = -E12*inv(E22); % Estimate PSI, the rotation operator [Vp,Ep] = eig(PSI); % Find the eigenvalues and eigenvectors of rotation operator PSI e = diag(Ep); %%----- Solve for Arrival Angles -----%% angs = asin(angle(e)/pi)*180/pi % Find the angles associated with the roots