function?res?=?SBI（paras）

%?res?=?SBI（paras）
%?
%?SBI（paras）?performs?DOA?estimation?using?Sparse?Bayesian?Inference
%?
%?Input:
%?paras.Y:?M?*?T?matrix?sensor?measurements?at?all?snapshots
%?paras.A:?M?*?N?matrix?columns?are?the?steering?vectors?for?different?directions
%?paras.B:?M?*?N?matrix?columns?are?derivatives?of?the?steering?vectors?wrt.?different?directions
%?paras.sigma2:?initialization?of?noise?variance
%?paras.alpha:?initialization?of?alpha
%?paras.beta:?initialization?of?beta
%?paras.rho:?rho
%?paras.resolution:?grid?resolution?for?the?directions
%?paras.maxiter:?maximum?iteration
%?paras.tol:?stopping?criterion
%?paras.isKnownNoiseVar:?true?if?known?variance?false?if?unknown
%?paras.K:?number?of?sources
%?Output:
%?res.mu:?mean?estimation
%?res.Sigma:?variance?estimation
%?res.sigma2:?estimated?noise?variance
%?res.sigma2seq:?estimated?noise?variance?at?all?iterations
%?res.alpha:?reconstructed?alpha
%?res.beta:?reconstructed?beta
%?res.iter:?iteration?used?in?the?algorithm
%?res.ML:?maximum?likelihood?function?value?at?all?iterations
%?
%?Written?by?Zai?Yang?19?Jul?2011
%?reference:?Zai?Yang?Lihua?Xie?and?Cishen?Zhang?
%????“Off-grid?direction?of?arrival?estimation?using?sparse?Bayesian?inference“

eps?=?1e-16;

Y?=?paras.Y;
A?=?paras.A;
B?=?paras.B;
[M?T]?=?size（Y）;
N?=?size（A?2）;

alpha0?=?1?/?paras.sigma2;
rho?=?paras.rho?/?T;
beta?=?paras.beta;
alpha?=?paras.alpha;
r?=?paras.resolution;

maxiter?=?paras.maxiter;
tol?=?paras.tolerance;
if?isfield（paras?‘isKnownNoiseVar‘）?&&?~isempty（paras.isKnownNoiseVar）
????isKnownNoiseVar?=?paras.isKnownNoiseVar;
else
????isKnownNoiseVar?=?false;
end

if?isKnownNoiseVar
???a?=?1;
???b?=?T?*?M?*?paras.knownsigma2;
else
????a?=?1e-4;
????b?=?1e-4;
end

??if?isfield（paras?‘K‘）?&&?~isempty（paras.K）
???????K?=?paras.K;
??else
??????K?=?min（T?M-1）;
????end
???
idx?=?[];
BHB?=?B‘?*?B;
converged?=?false;
iter_beta?=?1;
iter?=?0;
ML?=?zeros（maxiter1）;
alpha0seq?=?zeros（maxiter1）;

while?~converged
????iter?=?iter?+?1;
???
????Phi?=?A;
????Phi（:idx）?=?A（:idx）?+?B（:idx）?*?diag（beta（idx））;
????
????alpha_last?=?alpha;
????
????C?=?1?/?alpha0?*?eye（M）?+?Phi?*?diag（alpha）?*?Phi‘;
%?????Sigma?=?diag（alpha）?-?diag（alpha）?*?Phi‘?/?C?*?Phi?*?di