$9\mathrm{.}6-13$ A five$-$signal configuration in a two$-$dimensional space is shown in Fig. P$9\mathrm{.}6-13.$

$($a$)$ In the signal space, sketch the optimum decision regions, assuming an AWGN channel.

$($b$)$ Determine the error probability $\backslash ($ P$\_\{$e M$\}\backslash )$ as a function of $\backslash (\backslash$bar$\{$E$\}/\backslash$mathcal$\{$N$\}\backslash )$ of the optimum receiver.