In a binary modulation system without inter symbol interference, the waveform space has dimension…

In a binary modulation system without inter symbol interference, the waveform space has dimension I = 1 and waveforms are represented by the constellation pointss0 = 0 e s1 = 1. Assume that the noise component at the decision point has exponential PDF

and the input message,  is composed of statistically independent symbols with

a) Find the error probability of the system with the threshold v = ln 2.

b) Find the threshold vopt that minimizes the error probability.

c) Find the mutual information between ak and ˆak with threshold v.

d) Find the capacity (in bit/symbol) of the binary channel with threshold v.