s3(t), and s4(1), respectively, where s1 (1) = 20/2 sin 2t s2(t) = 0 1 TM = Тм 20 s3 (1) = 10/2 cos , s4(1) = – 10/2 cos Тм Each of these signal durations is 0

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10.8-2 Asourceemits four equiprobable messages m1, m2, m3, and m4, encoded by signals s1 (t), s2(1),
s3(t), and s4(t), respectively, where
s1 (t) = 20/2 sin
TM
s2(t) = 0
s3 (1) = 10/2 cos
$4(1) = – 10/2 cos
TM =
20
-t
Each of these signal durations is 0 <t < TM and is zero outside this interval. The signals are
transmitted over AWGN channels.
(a) Represent these signals in a signal space.
(b) Determine the decision regions.
(c) Obtain an equivalent minimum energy signal set.
(d) Determine the optimum receiver.
-18
Transcribed Image Text:10.8-2 Asourceemits four equiprobable messages m1, m2, m3, and m4, encoded by signals s1 (t), s2(1), s3(t), and s4(t), respectively, where s1 (t) = 20/2 sin TM s2(t) = 0 s3 (1) = 10/2 cos $4(1) = – 10/2 cos TM = 20 -t Each of these signal durations is 0 <t < TM and is zero outside this interval. The signals are transmitted over AWGN channels. (a) Represent these signals in a signal space. (b) Determine the decision regions. (c) Obtain an equivalent minimum energy signal set. (d) Determine the optimum receiver. -18
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