esprit算法MATLAB代码

### Esprit Algorithm Implementation in MATLAB

The Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is a popular method used for estimating the direction-of-arrival (DOA) or frequency of signals. Below demonstrates an implementation approach using MATLAB, focusing on DOA estimation.

function [angles] = esprit_algorithm(Rxx, d, M, N)
% Rxx: Covariance matrix of received signal
% d : Element spacing between array elements
% M : Number of sensors in ULA
% N : Total number of snapshots

lambda = eig(Rxx); % Compute eigenvalues
[V,D] = eig(Rxx);

% Sort eigenvalues from largest to smallest and sort corresponding eigenvectors accordingly.
[~, idx] = sort(diag(D), 'descend');
V = V(:,idx);

% Separate noise subspace and signal subspace based on predefined criteria such as thresholding technique[^1].
Vs = V(:, 1:M);
Vn = V(:, M+1:end);

% Construct matrices A1 and A2 which are subarrays' steering vectors
for m = 1:M
    A1(m,:) = exp(-j*2*pi*(m-1)*d*[0:N-1]/(M*d));
    A2(m,:) = exp(-j*2*pi*m*d*[0:N-1]/(M*d));
end

% Formulate rotational invariance relationship Phi=inv(A1'*Vn)*(A2'*Vn).
Phi = inv((conj(transpose(A1))*Vn))*(conj(transpose(A2))*Vn);

% Estimate angles through arctan function considering phase information contained within Phi's diagonal entries.
omega_hat = angle(diag(Phi));

angles = omega_hat * 180 / pi; % Convert radians into degrees
end

This code snippet provides a basic framework for implementing ESPRIT in MATLAB. Note that practical applications may require additional preprocessing steps like covariance matrix estimation and more sophisticated methods for separating signal and noise subspaces.