角度和时延联合估计（JADE）算法MATLAB程序_jade_时延估计_

function [theta,tau] = jade(H,g,r,P,m1,m2); [M,PL] = size(H); if length(g) < PL, g = [g zeros(1,PL-length(g))]; end % zero pad if length(g) > PL, H = [H zeros(M,length(g)-PL)]; % zero pad [M,PL] = size(H); end % zero pad if nargin < 4, P=1; end if nargin < 5, m1=1; end if nargin < 6, m2=1; end L = PL/P; % impulse response length measured in ``symbol periods'' if m1*M <= r, error('m1 is not large enough to separate all sources'); end % STEP 1: FFT OF ROWS OF G TO GET VANDERMONDE STRUCTURE ON THE ROWS G = fft(g); H1 = fft(H.').'; % assume bandlimited signals: truncate out-of-band part % because G is very small there if ( floor(L/2)*2 == L ), % L even G = G([PL-L/2+1:PL 1:L/2]); H1 = H1(:,[PL-L/2+1:PL 1:L/2]); else % L odd L2 = floor(L/2); G = G([PL-L2+1:PL 1:L2+1]); H1 = H1(:,[PL-L2+1:PL 1:L2+1]); end % divide out the known signal waveform % (assume it is nonsing! else work on intervals) for i = 1:M, rat(i,:) = H1(i,:) ./ G; end % STEP 2: FORM HANKEL MATRIX OF DATA, WITH m1 FREQ SHIFTS AND m2 SPATIAL SHIFTS [m_rat,n_rat] = size(rat); % sanity checks if m1 >= n_rat, n_rat, error('m1 too large to form so many shifts'); end if m2 >= m_rat, m_rat, error('m2 too large to form so many shifts'); end if ((r > (m1-1)*(M-m2+1)) | (r > m1*(M-m2)) | (r > 2*m2*(n_rat-m1+1))), error('m1 too large to form so many shifts and still detect r paths'); end % spatial shifts X0 = []; for i=1:m2; X0 = [X0 rat(i:M-m2+i,:)]; end M = M-m2+1; % number of antennas is reduced by the shifting process % freq shifts X = []; Xt = []; for i=1:m1; Xshift = []; for j=1:m2; Xshift = [Xshift X0(:,(j-1)*n_rat+i:j*n_rat-m1+i)]; end Xt = [Xt; Xshift]; end % size Xt: m1(M-m2+1) * (m2-1)(n_rat-m1+1) Rat = Xt; % STEP 3: TRANSFORM TO REAL; DOUBLE NUMBER OF OBSERVATIONS % same tricks as in `unitary esprit' Q2m = qtrans(m1); Im = eye(m1,m1); Jm = Im(m1:-1:1,:); Q2M = qtrans(M); IM = eye(M,M); JM = IM(M:-1:1,:); Q2M = qtrans(M); Q2 = kron(Q2m,Q2M); J = kron(Jm,JM); [mR,NR] = size(Rat); Ratreal = []; for i=1:NR, z1 = Rat(:,i); % kron(a1,a2) z2 = J*conj(z1); % kron(J a1,J a2) Z = real(Q2' * [z1 z2] * [1 sqrt(-1); 1 -sqrt(-1)] ); Ratreal = [Ratreal Z]; end Rat = Ratreal; [mR,NR] = size(Rat); % STEP 4: SELECT (should be ESTIMATE?) NUMBER OF MULTIPATHS FROM Rat [u,s,v] = svd(Rat); % only need u: use subspace tracking... u = u(:,1:r); v = v(:,1:r); % r should be set at a gap in the singular values % STEP 5: FORM SHIFTS OF THE DATA MATRICES % AND REDUCE RANKS OF DATA MATRICES [mM,PL1] = size(Rat); % selection and transform matrices: Jxm = [eye(m1-1,m1-1) zeros(m1-1,1)]; Jym = [zeros(m1-1,1) eye(m1-1,m1-1) ]; JxM = [eye(M-1,M-1) zeros(M-1,1)]; JyM = [zeros(M-1,1) eye(M-1,M-1) ]; Q1m = qtrans(m1-1); Q1M = qtrans(M-1); Kxm = real( kron(Q1m',IM) * kron(Jxm+Jym,IM) * kron(Q2m,IM) ); Kym = real( kron(Q1m',IM) * sqrt(-1)*kron(Jxm-Jym,IM) * kron(Q2m,IM) ); KxM = real( kron(Im,Q1M') * kron(Im,JxM+JyM) * kron(Im,Q2M) ); KyM = real( kron(Im,Q1M') * sqrt(-1)*kron(Im,JxM-JyM) * kron(Im,Q2M) ); % For estimating DOA: Ex1 = KxM*u; Ey1 = KyM*u; % size: m(M-1) by r % For estimating tau: % select first/last m1-1 blocks (each of M rows) Ex2 = Kxm*u; Ey2 = Kym*u; % size: (M-1)m1 by r % sanity checks: % X1, X2, Y1, Y2 should be taller and wider than r if size(Ex1,1) < r, error('Ex1 not tall enough'); end if size(Ex2,1) < r, error('Ex2 not tall enough'); end % reduce to r columns [Q,R] = qr([Ex1,Ey1]); Ex1 = R(1:r,1:r); Ey1 = R(1:r,r+1:2*r); [Q,R] = qr([Ex2,Ey2]); Ex2 = R(1:r,1:r); Ey2 = R(1:r,r+1:2*r); % STEP 6: DO JOINT DIAGONALIZATION on Ex2\Ey2 and Ex1\Ey1 % 2-D Mathews-Zoltowski-Haardt method. There are at least 4 other methods, but % the differences are usually small. This one is easiest with standard matlab A = Ex2\Ey2 + sqrt(-1)*Ex1\Ey1; [V,Lambda] = eig(A); Phi = real( Lambda ); Theta = -imag( Lambda ); % STEP 7: COMPUTE THE DELAYS AND ANGLES Phi = diag(Phi); Theta = diag(Theta); tau = -2*atan(real(Phi))/(2*pi)*L; sintheta = 2*atan(real(Theta)); theta = asin(sintheta/pi); theta = theta*180/pi; % DOA in degrees