EC > GATE 2014 SET-4 > Detection Theory
Consider a communication scheme where the binary valued signal X satisfies P{X = +1} = 0.75 and P{X = −1} = 0.25. The received signal Y = X + Z, where Z is a Gaussian random variable with zero mean and variance σ2. The received signal Y is fed to the threshold detector. The output of the threshold detector X̂ is:
X̂ = +1 if Y > τ, −1 if Y ≤ τ.
To achieve a minimum probability of error P(X̂ ≠ X), the threshold τ should be
X̂ = +1 if Y > τ, −1 if Y ≤ τ.
To achieve a minimum probability of error P(X̂ ≠ X), the threshold τ should be
Correct : c
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