Consider the following communication system. Define the half-sine pulse ps(t) by #). sin P;(t) = 0 y or < y AWGN Determine the energy of the half-sine pulse.

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Consider the following communication system. Define the half-sine pulse p,(t) by
sin
0 <t<T,
P;(t) =
else.
We assume that the channel is an AWGN channel with power spectral density No/2.
rTo+T
dt
To
>y or < y
AWGN
a. Determine the energy of the half-sine pulse.
b. Suppose that we send Ap,(t) if the bit to send is "s", and -Ap,(t) if the bit to
send is "0", where A > 0 is the amplitude of the transmitted pulse. The threshold
y is zero. Determine the average probability of error, in terms of E»/No, if
i. the starting time of the integrator T, = 0,
ii. the starting time of the integrator T, = T /2.
Transcribed Image Text:Consider the following communication system. Define the half-sine pulse p,(t) by sin 0 <t<T, P;(t) = else. We assume that the channel is an AWGN channel with power spectral density No/2. rTo+T dt To >y or < y AWGN a. Determine the energy of the half-sine pulse. b. Suppose that we send Ap,(t) if the bit to send is "s", and -Ap,(t) if the bit to send is "0", where A > 0 is the amplitude of the transmitted pulse. The threshold y is zero. Determine the average probability of error, in terms of E»/No, if i. the starting time of the integrator T, = 0, ii. the starting time of the integrator T, = T /2.
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