Problem $1$

Consider an $8$ element $1$D line array composed of omnidirectional sensors$.$ In this problem we consider two equal power sources impinging at $\backslash (\backslash$theta$\_\{1\}\backslash )$ and $\backslash (\backslash$theta$\_\{2\}\backslash ).$ The measurements are contaminated by white noise with $\backslash (\backslash$sigma$\_\{$v$\}^\{2\}\backslash )$ equal to one$-$tenth of the signal power. Make all assumptions and simplifications necessary, but account for these.

$1.$ How close can the two noise sources be$,$ while they can still be resolved as two independent sources, if we use the MVDR algorithm?

Assume that after determination of the optimum tap$-$weight vector for MVDR$,$ the electronics fail and the $\backslash ($ i $\backslash )$ th gain coefficient, $\backslash ($ w$\_\{$i$\}\backslash )$ is set to zero.