In a simple binary communication system, during every T seconds, one of two possible signals s0(t) and s1(t) is transmitted. Our two hypotheses are
H0: s0(t) was transmitted.
H1 : s1(t) was transmitted.
We assume that
|
s0(t) = 0 |
and |
s1(t)= 1 |
0 < t < T |
The communication channel adds noise n(t), which is a zero mean normal random process with variance 1. Let x(t) represent the received signal :
We observe the received signal x(t) at some instant during each signaling interval. Suppose that we received an observation x = 0.6.
(a) Using the maximum likelihood test, determine which signal is transmitted.
(b) Find P1 and Pn .