Could you help to fix that error of MATLAB code for b c d question:

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

Error in Untitled$11>$music$\_$spectrum $($line $61)$

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

Error in Untitled$11($line $44)$

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

$+$MATLAB code:

$\%$ Define initial parameters

M $=8$; $\%$ Number of sensors

d $=0\mathrm{.}5$; $\%$ Normalized inter$-$element spacing

N $=100$; $\%$ Number of snapshots

lambda $=1$; $\%$ Wavelength $($assuming unity for simplicity$)$

sigma$\_$n$2=0\mathrm{.}1*(1+5)$; $\%$ Noise variance

$\%$ Given k values and DOAs

k$0=0$; k$1=2$; k$2=5$;

thetas $=[-5*(1+$k$0),5*(1+$k$1),5*(2+$k$1)]$; $\%$ DOAs

P $=[2,2,1]$; $\%$ Signal powers

$\%$ Generate signal matrix S

S $=$ sqrt$($P$).\text{'}.*$ exp$(1$j $*2*$ pi $*$ rand$(3,$ N$))$; $\%$ Signals

$\%$ Function to generate steering vector matrix

steering$\_$vectorr $=$ @$($M$,$ d$,$ thetas$)$ exp$(-1$j $*2*$ pi $*$ d $*(0$:M$-1)\text{'}*$ cosd$($thetas$))$;

$\%$ Function to compute MSE

compute$\_$msee $=$ @$($true$\_$doa, estimated$\_$doa$)$ mean$(($true$\_$doa $-$ estimated$\_$doa$).^2)$;

$\%$ Function to compute MUSIC spectrum

music$\_$spectrumm $=$ @$($theta$\_$scan, A$,$ noise$\_$eigvecs$)...$

$1./$ arrayfun$($@$($theta$)$ abs$($A$($:$,$ theta$)\text{'}*$ noise$\_$eigvecs $*$ noise$\_$eigvecs' $*$ A$($:$,$ theta$))^-1,1$:length$($theta$\_$scan$))$;

$\%$ Define theta$\_$scan range for MUSIC spectrum

theta$\_$scan $=-90$:$0\mathrm{.}1$:$90$; $\%$ Adjust the range and resolution as needed

$\%$ 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$))$;

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

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$,1)+1$: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

$\%$ 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

$\%$ Function to generate the steering vector

function A $=$ steering$\_$vector$($M$,$ d$,$ thetas$)$

$\%$ M: Number of sensors

$\%$ d: Distance between sensors

$\%$ thetas: Angles of arrival $($in degrees$)$

k $=2*$ pi $/1$; $\%$ Wavenumber $($assuming lambda$=1)$

A $=$ zeros$($M$,$ length$($thetas$))$; $\%$ Initialize A with proper dimensions

for i $=1$:length$($thetas$)$

A$($:$,$ i$)=$ exp$(-1$j $*$ k $*$ d $*(0$:M$-1)\text{'}*$ cosd$($thetas$($i$)))$; $\%$ Calculate each column of A

end

end