基于matlab的相干信号的doa 估计,基于空间平滑MUSIC算法的相干信号DOA估计(1)

基于空间平滑MUSIC算法的相干信号DOA估计(1)

基于空间平滑MUSIC算法的相干信号DOA估计(1)

空间平滑MUSIC算法(1)

在上一篇博客中有提到，当多个入射信号相干时，传统MUSIC算法的效果就会不理想。具体原因是多个入射信号相干时，有部分能量就会散发到噪声子空间，使得MUSIC算法不能对其进行有效估计。

针对这种情况，解相干方法被提出。本文主要讲解通过降维处理解相干，之所以叫降维处理是因为这种方法将原阵列拆分成很多个子阵列，通过子阵列的协方差矩阵重构接收数据协方差矩阵，阵列的自由度DOF会随之降低，即可分辨的相干信号数降低。

先看看传统MUSIC算法对相干信号进行DOA估计的效果。

MATLAB代码

% Code For Music Algorithm

% The Signals Are All Coherent

% Author:痒羊羊

% Date：2020/10/29

clc; clear all; close all;

%% -------------------------initialization-------------------------

f = 500; % frequency

c = 1500; % speed sound

lambda = c/f; % wavelength

d = lambda/2; % array element spacing

M = 20; % number of array elements

N = 100; % number of snapshot

K = 6; % number of sources

coef = [1; exp(1i*pi/6);...

exp(1i*pi/3); exp(1i*pi/2);...

exp(2i*pi/3); exp(1i*2*pi)]; % coherence coefficient, K*1

doa_phi = [-30, 0, 20, 40, 60, 75]; % direction of arrivals

%% generate signal

dd = (0:M-1)'*d; % distance between array elements and reference element

A = exp(-1i*2*pi*dd*sind(doa_phi)/lambda); % manifold array, M*K

S = sqrt(2)\(randn(1,N)+1i*randn(1,N)); % vector of random signal, 1*N

X = A*(coef*S); % received data without noise, M*N

X = awgn(X,10,'measured'); % received data with SNR 10dB

%% calculate the covariance matrix of received data and do eigenvalue decomposition

Rxx = X*X'/N; % covariance matrix

[U,V] = eig(Rxx); % eigenvalue decomposition

V = diag(V); % vectorize eigenvalue matrix

[V,idx] = sort(V,'descend'); % sort the eigenvalues in descending order

U = U(:,idx); % reset the eigenvector

P = sum(V); % power of received data

P_cum = cumsum(V); % cumsum of V

%% define the noise space

J = find(P_cum/P>=0.95); % or the coefficient is 0.9

J = J(1); % number of principal component