GATE Electronics and Communications (EC) 2020 Solved Papers

as ML detector is used, the decision boundary between two adjacent signal points will be their arithmetic mean. $\therefore$
for ${\mathit{s}}_1=-3$, the probability of error $\left({\mathit{p}}_1\right):$${\mathit{P}}_1=1$ - (shaded area) for ${\mathit{S}}_2$ :
The probability of error $\left({\mathit{P}}_2\right)$${\mathit{P}}_2=1-($ shaded area $)$
for ${\mathit{S}}_3:$ the probability of error ${\mathit{P}}_3$.${\mathit{P}}_3=1-($ shaded area $)$ for ${\mathit{S}}_4:$
The probability of error $\left({\mathit{P}}_4\right)$${\mathit{P}}_4=1$ - (shaded area) By concluding above graph
${\mathit{P}}_3$ i.e. probability of error when $\mathit{s}3$ is transmitted is larger among the four.
$\therefore \mathit{I}=3$