Assignment:
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
Pw(b) = {2e-2b, b ≥ 0 {0, b < 0
and the input message, {ak}, ak ε {0,1}, is composed of statistically independent symbols with Pa(0)= 1/4.
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.