(Solved): Consider a signal constellation of a digital communication system as shown in figure (1), the o ...

Consider a signal constellation of a digital communication system as shown in figure (1), the orthonormal pulses shown in figure (2) are used in this system. a) If the receiver $$\mathrm{r}=\{0.5,0.75\}$$, which signal do you expect was transmitted and why? b) If the receiver uses optimum maximum likelihood detector and the transmitted signals have equal probability, find the probability of error in $$\mathrm{AWGN}$$ channel with $${\mathrm{N}}_0=10^{?3}$$. c) If the signal shown in figure (3) is also used in this system as another transmitter signal; redraw the correcponding signal space diagram. Figure (3)