ots ▁are ▁taken ▁at ▁time ▁inst ants ▁t 1 , ▁t 2 ▁... ▁t M , ▁the ▁data ▁can ▁be ▁expressed ▁as : ▁ ▁Where ▁X ▁and ▁N ▁are ▁the ▁r ▁× ▁M ▁matrices ▁and ▁S ▁is ▁q ▁× ▁M : ▁ ▁Problem ▁definition ▁“ The ▁target ▁is ▁to ▁estimate ▁the ▁DO A ’ s ▁ θ 1 , ▁ θ 2 , ▁ θ 3 , ▁ θ 4 ▁… θ q ▁of ▁the ▁sources ▁from ▁the ▁M ▁snapshot ▁of ▁the ▁array ▁x ( t 1 ) … ▁x ( t M ). ▁In ▁other ▁words ▁what ▁we ▁are ▁interested ▁in ▁is ▁estim ating ▁the ▁DO A ’ s ▁of ▁em itter ▁signals ▁imp ing ing ▁on ▁receiving ▁array , ▁ ▁when ▁given ▁a ▁finite ▁data ▁set ▁{ x ( t )} ▁observed ▁over ▁t = 1 , ▁ 2 ▁… ▁M . ▁This ▁will ▁be ▁done ▁basically ▁by ▁using ▁the ▁second - order ▁statistics ▁of ▁data ” ▁ ▁In ▁order ▁to ▁solve ▁this ▁problem ▁( to ▁guarantee ▁that ▁there ▁is ▁a ▁valid ▁solution ) ▁do ▁we ▁have ▁to ▁add ▁conditions ▁or ▁assumptions ▁on ▁the ▁oper ational ▁environment ▁and \ or ▁the ▁used ▁model ? ▁Since ▁there ▁are ▁many ▁parameters ▁used ▁to ▁specify ▁the ▁system ▁like ▁the ▁number ▁of ▁sources , ▁the ▁number ▁of ▁array ▁elements ▁... etc . ▁are ▁there ▁conditions ▁that ▁should ▁be ▁met ▁first ? ▁Tow ard ▁this ▁goal ▁we ▁want ▁to ▁make ▁the ▁following ▁assumptions : ▁ ▁The ▁number ▁of ▁signals ▁is ▁known ▁and ▁is ▁smaller ▁than ▁the