ECE 154B
Homework #7
Due March 14, 2007
1.
Consider the transmission of two FSK sinusoidal signals whose frequencies are chosen
such that the signals are orthogonal.
Let the amplitude of each signal be A, the duration of
each signal be T, and the energy of each signal be E = A
2
T/2.
Make the usual assumptions
(AWGN, equal a priori probabilities, etc).
If the phases of the two sinusoids are unknown
at the receiver, we know to use a noncoherent receiver.
As was shown in class, the
probability of binary error for this receiver is:
P[binary error] =
½ exp[A
2
T/4N
0
] = ½ exp[E/2N
0
].
(a)
Assume that A is a fixed constant.
Give an expression for the probability of error
in a byte consisting of 8 binary digits.
(b)
Assume that A takes on the value A
1
and A
2
with probabilities p and 1p
respectively.
Calculate the average probability of error per binary digit.
(c)
Again assume that A takes on the value A
1
and A
2
with probabilities p and 1p
respectively.
For the two cases described below, calculate the average probability
of error per byte.
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 Winter '07
 WOlf
 Probability theory, Rayleigh, average probability, binary digit

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