Equalizer design from training message. We consider an electronic communication system, with message to be sent given by an N$-$vector s$,$ whose entries are $1$ or $1,$ and received signal y$,$ where y $=$ c s$,$ where c is an n$-$vector, the channel impulse response. The receiver applies equalization to the received signal, which means that it computes y $=$ hy $=$ h c s$,$ where h is an n$-$vector, the equalizer impulse response. The receiver then estimates the original message using s $=$ sign$($y$1$:N$).$ This works well if h c e$1.($See exercise $7\mathrm{.}15.)$ If the channel impulse response c is known or can be measured, we can design or choose h using least squares, as in exercise $12\mathrm{.}6.$ In this exercise we explore a method for choosing h directly, without estimating or mea suring c$.$ The sender rst sends a message that is known to the receiver, called the training message, strain. $($From the point of view of communications, this is wasted transmission, and is called overhead.$)$ The receiver receives the signal ytrain $=$ c strain from the train ing message, and then chooses h to minimize $($h ytrain$)1$:N strain $2.($In practice, this equalizer is used until the bit error rate increases, which means the channel has changed, at which point another training message is sent.$)$ Explain how this method is the same as least squares classi cation. What are the training data x$($i$)$ and y$($i$)?$ What is the least squares problem that must be solved to determine the equalizer impulse response h$?$