$(100$ points$)$ We want to send $4-$PAM data symbols with rate $R$ over the wireline

channel described in Problem $1.$ Suppose the transmission symbols $s[n]$ consists of

$13$ training sequence and followed by $6420$ data symbols. Let $t[n]$ be a training

sequence and $s[n]=t[n]$ for nin$\{0,1,$dots,$12\}$ is the known training data at the

receiver. The training sequence is assumed to use Baker's sequence:

$+1,+1,+1,+1,+1,-1,-1,+1,+1,-1,+1,-1,+1.$

We also let $d[n]$ be a $4-$PAM data symbol sent by a transmitter, i$.$e$.,s[n]in{C}_{4-\text{P}\text{A}\text{M}}=$

$\frac{1}{\sqrt[\phantom{2}]{5}}\{-3,-1,1,3\}$ and $E[|s[n]{|}^2]=1$ and $s[n]=d[n]$ for

$1.$

Then, the received signal boils down to

$y[n]={\displaystyle \underset{l=0}{\overset{2}{}}}h[l]s[n-l]+v[n],$

where $v[n]$ is noise and its distribution is Gaussian, i$.$e$.,v[n]N(0,{}^2).$ The initial

conditions are zero, e$.$g$.s[-1]=s[-2]=0.$

$($a$)(30$ points, Channel estimation$)$: Write the least$-$squares problem for the chan$-$

nel estimation in a matrix form and implement using MATLAB.