music算法误差eff_doa music

%%% 经典谱估计MUSIC算法 估计误差协方差 smile_D clc; clear all; close all; M=8; % 阵元数量 theta_steer=0*pi/180;%波束指向，精确计算波束宽度时用 WD=0.886*2/M/cos(theta_steer)*180/pi %%%近似3db波束宽度，单位度 theta0=(-90:.1:90)*pi/180; snap=10000; % 快拍数 a=[0:M-1]'; % array vector c=3e8; f=300e6; lamda=c/f; %wavelength dr=lamda/2 ; %天线间距 SNR=20; %signal to noise ratio theta=[10 20 30]*pi/180; %the parameters of source P=length(theta); %nmber of source A=exp(-j*2*pi/lamda*dr*a*sin(theta)); %导向矢量阵 s=10^(SNR/10)*exp(j*rand(P,snap)*2*pi); %signals vector noise=(randn(M,snap)+j*randn(M,snap))/sqrt(2); %% %%%估计误差的协方差 deta = 1; I_1= eye(M); I_2= eye(P); D_theta = -j*2*pi/lamda*dr*a*cos(theta).*exp(-j*2*pi/lamda*dr*a*sin(theta)); %D_theta = -j*exp(-j*2*pi/lamda*dr*a*sin(theta)); H = D_theta'*(I_1-A*inv(A'*A)*A')*D_theta; R_s=s*s'/snap; ATA = inv(R_s)+deta*inv(R_s)*inv(A'*A)*inv(R_s); % VVS = inv(H.*eye(3)); % VVS2 = real(H.*(ATA.')); C_MUSIC = deta/(2*snap)*inv(H.*I_2)*real(H.*(ATA).')*inv(H.*I_2)%%估计误差 sum_real = 0; for kk=1:snap S = diag(s(:,kk)); sum_real = sum_real+real(S'*H*S); end C_CRB = deta/2*inv(sum_real) eff = norm(C_CRB,2)/norm(C_MUSIC,2)