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Unformatted text preview: 1/26 EEL 5544 Lectures 11 EXAMPLES USING CONDITIONAL DENSITIES ﬂ Ex Binary Communication System 1 A binary signal (0 or 1) is sent through a channel
with additive white Gaussian noise. 2/26 EEL 5544 Lectures 11 EXAMPLES USING CONDITIONAL DENSITIES xi? Ex Binary Communication System 1 A binary signal (0 or 1) is sent through a channel
with additive white Gaussian noise. The received
signal is processed to form a decision statistic X,
which can be used to estimate the transmitted signal. EEL 5544 Lectures 11 EXAMPLES USING CONDITIONAL DENSITIES xi? Ex Binary Communication System 1 A binary signal (0 or 1) is sent through a channel
with additive white Gaussian noise. The received
signal is processed to form a decision statistic X,
which can be used to estimate the transmitted signal.
X is a random variable, which can be specified as
follows: EEL 5544 L111 3/26 4/26 {X N Gaussian(+1,02), 0 transmitted 5
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d 6/26 X N Gaussian(+1,02), 0 transmitted
X N Gaussian(—1,02), 1 transmitted The demodulation system generates decisions
according to the following figure: generate decide 1 erasure decide () ‘l—l—l—l—l— l 0.25 0 0.25 H Thus, the demodulator provides one of three
decisions at its output: {erasure, 0, 1}. 7/26 X m Gaussian(+1,02), 0 transmitted
X N Gaussian(—1,02), 1 transmitted The demodulation system generates decisions
according to the following figure: generate decide 1 erasure decide () ‘i—l—l—l—l— l 0.25 0 0.25 H Thus, the demodulator provides one of three
decisions at its output: {erasure, 0, 1}. Note that in
what follows, an erasure is not an error. EEL 5544 L112 8/26 a) Determine the probability that a symbol is erased if EEL 5544 L113 9/26 L114 COVSQL
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kaleQ) 1 Q0 €\ #Q (2 5—) EEL5544 L115 11/26 EEL 5544 L11—6 12/26 b) Determine the probability that a symbol is in error if
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probability of error of 10—”. Me? @032 i =* i6"
kzs— :_ @400“ch EEL 5544 L118 14/26 «‘9 Ex Binary Communication System 2 Consider the following ogtimal detection problem: 15/26 Hie? Ex Binary Communication System 2 Consider the following optimal detection problem: A binary signal (0 or 1) is sent through a channel
with additive white Gaussian noise. 16/26 Hie? Ex Binary Communication System 2 Consider the following optimal detection problem: A binary signal (0 or 1) is sent through a channel
with additive white Gaussian noise. The received
signal is processed to form a decision statistic X,
which can be used to estimate the transmitted signal. Hie? Ex Binary Communication System 2 Consider the following optimal detection problem: A binary signal (0 or 1) is sent through a channel
with additive white Gaussian noise. The received
signal is processed to form a decision statistic X,
which can be used to estimate the transmitted signal.
X is a random variable, which can be specified as
follows: EEL 5544 L119 17/26 18/26 {X m GaUSSian(p0,02), 0 transmitted 19/26 X N GaussiaanpQ), 0 transmitted
X m Gaussian(p,1,02), 1transmitted 20/26 .w X m Gaussianmomg), 0 transmitted
'WBJ . 9 .
\‘ I X N Gaussuan(p,1,a~), 1transmltted QM / '7 Find the MAP and ML decision 4' . _ : ‘34 Q (’3, Tx 1%) EEL 5544 L1110 21/26 2:1?5' O
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