Three equally probable messages are to be transmitted over an. LAWGN channel with noise power spectral density No/2. The messages are: s,(t) = -s,(t) = 2 E cos(w, t), 0stsT T 2 E sin(w, t), 0stST S3(t) =

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Digital Communication
Three equally probable messages are to be transmitted over an
AWGN channel with noise power spectral density No/2. The messages are:
2 E
cos(w, t), 0stsT
s,(t) = -s,(t) =
T
2 E
S3(t) =
sin(@, t), 0stsT
a) Find an appropriate orthonormal basis functions for the signal space (Hint: without
using the Gram-Schmidt procedure).
b) Derive and sketch the optimal decision regions R1, R2and R3.
c) Derive the symbol error rate of the system without evaluating the resulting integrals.
Transcribed Image Text:Three equally probable messages are to be transmitted over an AWGN channel with noise power spectral density No/2. The messages are: 2 E cos(w, t), 0stsT s,(t) = -s,(t) = T 2 E S3(t) = sin(@, t), 0stsT a) Find an appropriate orthonormal basis functions for the signal space (Hint: without using the Gram-Schmidt procedure). b) Derive and sketch the optimal decision regions R1, R2and R3. c) Derive the symbol error rate of the system without evaluating the resulting integrals.
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