Topic: Baseband and bandpass modulation / de-
modulation
Exercise 1 (15 points)
In an additive white Gaussian noise channel with noise power spectral density
of $N_0/2$, bits are transmitted by
$$S_1(t) = \begin{cases} \frac{A}{\sqrt{T}}, & 0 \le t < T/2\\ -\frac{A}{\sqrt{T}}, & T/2 \le t < T \end{cases}$$
and
$s_2(t) = -s_1(t)$.
The prior probability of the bits are 1/3 and 2/3.
A: Determine the output of the matched filter. Determine its value at the
sampling time.
B: Determine the structure of the optimum detector and calculate the probabil-
ity of error for $E_b/N_0$ of 5 dB when the optimum detector is used ($E_s/N_0$
is the average bit energy to one-sided noise spectral density ratio).
C: Repeat part (B) when a the maximum likelihood detector is used.
D: Compare the results from parts (B) and (C) and comment on your obser-
vation.