Could you help to fix error of this MATLAB code.

$+$Error:Index in position $2$ exceeds array bounds $($must not exceed $3).$

Error in Assignment$\_2>$music$\_$spectrum $($line $96)$

a$\_$theta $=$ A$($:$,$ i$)$;

Error in Assignment$\_2($line $14)$

P$\_$music $=$ music$\_$spectrum$($theta$\_$scan, A$,$ noise$\_$eigvecs$)$;

$+$ MATLAB code:

$\%$ Part $($b$)$: Accuracy for Different Noise Variances

noise$\_$variances $=$ linspace$(0\mathrm{.}1*$ sigma$\_$n$2,10*$ sigma$\_$n$2,10)$;

mse$\_$noise $=$ zeros$($size$($noise$\_$variances$))$;

for var$\_$idx $=1$:length$($noise$\_$variances$)$

var $=$ noise$\_$variances$($var$\_$idx$)$;

mse$\_$values $=$ zeros$(1,100)$; $\%$ Preallocate for Monte Carlo simulations

for sim $=1$:$100$

noise $=$ sqrt$($var$/2)*($randn$($M$,$ N$)+1$j $*$ randn$($M$,$ N$))$;

X $=$ A $*$ S $+$ noise;

R $=($X $*$ X$\text{'})/$ N;

$[$eigvecs$,$ eigvals$]=$ eig$($R$)$;

$[$~$,$ ind$]=$ sort$($diag$($eigvals$),$ 'descend'$)$;

noise$\_$eigvecs $=$ eigvecs$($:$,$ ind$($size$($S$,2)+1$:end$))$;

P$\_$music $=$ music$\_$spectrum$($theta$\_$scan, A$,$ noise$\_$eigvecs$)$;

$[$~$,$ max$\_$idx$]=$ max$($P$\_$music$)$;

estimated$\_$doa $=$ theta$\_$scan$($max$\_$idx$)$;

mse$\_$values$($sim$)=$ compute$\_$mse$($thetas$,$ estimated$\_$doa$)$;

end

mse$\_$noise$($var$\_$idx$)=$ mean$($mse$\_$values$)$;

end

$\%$ Part $($c$)$: Accuracy for Different Number of Sensors

sensor$\_$counts $=$ M:$10*$M;

mse$\_$sensors $=$ zeros$($size$($sensor$\_$counts$))$;

for m$\_$idx $=1$:length$($sensor$\_$counts$)$

m $=$ sensor$\_$counts$($m$\_$idx$)$;

A $=$ steering$\_$vector$($m$,$ d$,$ thetas$)$;

mse$\_$values $=$ zeros$(1,100)$; $\%$ Preallocate for Monte Carlo simulations

for sim $=1$:$100$

noise $=$ sqrt$($sigma$\_$n$2/2)*($randn$($m$,$ N$)+1$j $*$ randn$($m$,$ N$))$;

X $=$ A $*$ S$(1$:m$,$ :) $+$ noise;

R $=($X $*$ X$\text{'})/$ N;

$[$eigvecs$,$ eigvals$]=$ eig$($R$)$;

$[$~$,$ ind$]=$ sort$($diag$($eigvals$),$ 'descend'$)$;

noise$\_$eigvecs $=$ eigvecs$($:$,$ ind$($size$($S$,2)+1$:end$))$;

P$\_$music $=$ music$\_$spectrum$($theta$\_$scan, A$,$ noise$\_$eigvecs$)$;

$[$~$,$ max$\_$idx$]=$ max$($P$\_$music$)$;

estimated$\_$doa $=$ theta$\_$scan$($max$\_$idx$)$;

mse$\_$values$($sim$)=$ compute$\_$mse$($thetas$,$ estimated$\_$doa$)$;

end

mse$\_$sensors$($m$\_$idx$)=$ mean$($mse$\_$values$)$;

end

$\%$ Part $($d$)$: Accuracy for Different Number of Snapshots

snapshot$\_$counts $=$ round$($linspace$(0\mathrm{.}1*$ N$,10*$ N$,10))$;

mse$\_$snapshots $=$ zeros$($size$($snapshot$\_$counts$))$;

for n$\_$idx $=1$:length$($snapshot$\_$counts$)$

n $=$ snapshot$\_$counts$($n$\_$idx$)$;

mse$\_$values $=$ zeros$(1,100)$; $\%$ Preallocate for Monte Carlo simulations

for sim $=1$:$100$

noise $=$ sqrt$($sigma$\_$n$2/2)*($randn$($M$,$ n$)+1$j $*$ randn$($M$,$ n$))$;

X $=$ A $*$ S$($:$,1$:n$)+$ noise;

R $=($X $*$ X$\text{'})/$ n;

$[$eigvecs$,$ eigvals$]=$ eig$($R$)$;

$[$~$,$ ind$]=$ sort$($diag$($eigvals$),$ 'descend'$)$;

noise$\_$eigvecs $=$ eigvecs$($:$,$ ind$($size$($S$,2)+1$:end$))$;

P$\_$music $=$ music$\_$spectrum$($theta$\_$scan, A$,$ noise$\_$eigvecs$)$;

$[$~$,$ max$\_$idx$]=$ max$($P$\_$music$)$;

estimated$\_$doa $=$ theta$\_$scan$($max$\_$idx$)$;

mse$\_$values$($sim$)=$ compute$\_$mse$($thetas$,$ estimated$\_$doa$)$;

end

mse$\_$snapshots$($n$\_$idx$)=$ mean$($mse$\_$values$)$;

end

$\%$ Plotting MSE results

figure$(\text{'}$Position$\text{'},[100,100,1000,800])$;

$\%$ Noise Variance

subplot$(3,1,1)$;

plot$($noise$\_$variances, mse$\_$noise, $\text{'}$o$-\text{'})$;

title$(\text{'}$MSE vs$.$ Noise Variance'$)$;

xlabel$(\text{'}$Noise Variance'$)$;

ylabel$(\text{'}$MSE$\text{'})$;

$\%$ Number of Sensors

subplot$(3,1,2)$;

plot$($sensor$\_$counts, mse$\_$sensors$,\text{'}$o$-\text{'})$;

title$(\text{'}$MSE vs$.$ Number of Sensors'$)$;

xlabel$(\text{'}$Number of Sensors'$)$;

ylabel$(\text{'}$MSE$\text{'})$;

$\%$ Number of Snapshots

subplot$(3,1,3)$;

plot$($snapshot$\_$counts, mse$\_$snapshots, $\text{'}$o$-\text{'})$;

title$(\text{'}$MSE vs$.$ Number of Snapshots'$)$;

xlabel$(\text{'}$Number of Snapshots'$)$;

ylabel$(\text{'}$MSE$\text{'})$;

sgtitle$(\text{'}$MSE Analysis'$)$;

$\%$ Function to compute MSE of DOA estimates

function mse $=$ compute$\_$mse$($true$\_$doa, estimated$\_$doa$)$

mse $=$ mean$(($true$\_$doa $-$ estimated$\_$doa$).^2)$;

end

$\%$ Function to compute MUSIC spectrum

function P$\_$music $=$ music$\_$spectrum$($theta$\_$scan, A$,$ noise$\_$eigvecs$)$

P$\_$music $=$ zeros$($size$($theta$\_$scan$))$;

for i $=1$:length$($theta$\_$scan$)$

a$\_$theta $=$ A$($:$,$ i$)$;

P$\_$music$($i$)=1/($a$\_$theta' $*($noise$\_$eigvecs $*$ noise$\_$eigvecs'$)*$ a$\_$theta$)$;

end

end