Rewrite the Matlab code below correctly to generate dtection subset for $<=16$

clear

clc

format shorte

M$=16\%$Modulation Order or Number of Symbols

MM$=$M$^2$

m$=$log$2($M$)\%$Number of Bits per Symbol

nn$=4*$m; $\%$Number of Bits or Symbols

QAM$\_16=$qammod$([0$:M$-1],$M$)\%$QAM$16$ Modulation or QAM$16$ Signal Set

Epsilon$=($sum$($abs$($QAM$\_16).^2))/$length$($QAM$\_16)\%$Average Sum of Energy or Energy per Symbol

Nt$=2$

Nr$=4$

SNR$\_$db$=[5$:$3$:$23]\%[0$:$2$:$20]\%$SNR in dB

SNR$\_$dec$=(10.^($SNR$\_$db$./10))/$Nt $\%$SNR in Decimal or Linear SNR

Sigma$=$sqrt$($Epsilon$./$SNR$\_$dec$)$;

Num$\_$Err$=1\mathrm{.}0*[60050040030020010050]$;

Teta$=(1+$sqrt$(5))/2$;

Teta$\_=1-$Teta;

Alpha$=1+(1$j$*$Teta$\_)$;

Alpha$\_=1+(1$j$*(1-$Teta$\_))$;

Gamma$=1$j;

map$\_2=[00$; $01$;$10$;$11]$;

t$=0$;

for k$\_1=1$:$4$

for k$\_2=1$:$4$

t$=$t$+1$;

map$\_4($t$,$:$)=[$map$\_2($k$\_1,$:$)$ map$\_2($k$\_2,$:$)]$;

end

end

tt$=0$;

for ii$=1$:M

for jj$=1$:M

tt$=$tt$+1$;

x$11=(1/$sqrt$(5))*$Alpha$*($QAM$\_16($ii$)+$QAM$\_16($jj$)*$Teta$)$; $\%$x$11$

x$22=(1/$sqrt$(5))*$Alpha$\_*($QAM$\_16($ii$)+$QAM$\_16($jj$)*$Teta$\_)$; $\%$x$22$

x$12=(1/$sqrt$(5))*$Alpha$*($QAM$\_16($ii$)+$QAM$\_16($jj$)*$Teta$)$; $\%$x$12$

x$21=(1/$sqrt$(5))*$Alpha$\_*($QAM$\_16($ii$)+$QAM$\_16($jj$)*$Teta$\_)*$Gamma; $\%$x$21$

Golden$\_$Code$\_$Set$($tt$,$:$)=[$x$11$ x$22$ x$12$ x$21]$;

Golden$\_$Code$\_$Set$\_1($tt$)=$x$11$;

Golden$\_$Code$\_$Set$\_2($tt$)=$x$22$;

Golden$\_$Code$\_$Set$\_3($tt$)=$x$12$;

Golden$\_$Code$\_$Set$\_4($tt$)=$x$21$;

end

end

$\%$ Creating the Symbol Dection subset $($SDS$)$

$\%$ SDS $=\{($x$11\_$hat,x$22\_$hat$),|$x$11-$x$11\_$hat$|^2|$x$22-$x$22\_$hat$|^2<=$ d$,$ x$11\_$hat,x$22\_$hat E$[$Omega$\_$G$]\}$

uu$=0$;

for uu$1=1$:M

for uu$2=1$:M

uu$=$uu$+1$;

x$11=$Golden$\_$Code$\_$Set$\_1($uu$)$;

x$22=$Golden$\_$Code$\_$Set$\_2($uu$)$;

cc$=0$;

uu$\_=0$;

for uu$\_1=1$:M

for uu$\_2=1$:M

uu$\_=$uu$\_+1$;

x$11\_$hat$=$Golden$\_$Code$\_$Set$\_1($uu$\_)$;

x$22\_$hat$=$Golden$\_$Code$\_$Set$\_2($uu$\_)$;

if $(($abs$($x$11-$x$11\_$hat$).^2*$abs$($x$22-$x$22\_$hat$).^2)<=16)$

cc$=$cc$+1$;

SDS$\_$idx$\_$set$($uu$,$cc$)=$uu$\_$; $\%$ Index Set of SDS

SDS$\_$sym$\_$set$\_1($uu$,$cc$)=$Golden$\_$Code$\_$Set$\_1($uu$\_)$; $\%$ Symbols set of SDS

SDS$\_$sym$\_$set$\_2($uu$,$cc$)=$Golden$\_$Code$\_$Set$\_2($uu$\_)$;

end

end

end

Cdy$($uu$)=$cc; $\%$ Cardinality of Symbols near symbol x$\_$i$.$

L$($uu$)=$abs$($x$11-$x$11\_$hat$).^2*$abs$($x$22-$x$22\_$hat$).^2$;

end

end

sum$($Cdy$)/$length$($Cdy$)$