Q96
Consider a communication scheme where the binary values signal X satisfies PX = 1 = 0.75 and PX = -1 = 0.25. The received signal Y = X + Z, where Z is 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 \[ X\] is \[ X = \ arrayl + 1,\,\,\, Y > \\ - 1,\,\,\, Y array .\] To achieve a minimum probability of error \[ P \ X X \ ,\] the threshold τ should be
Consider a communication scheme where the binary values signal X satisfies P{X = 1} = 0.75 and P{X = -1} = 0.25. The received signal Y = X + Z, where Z is 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 is
To achieve a minimum probability of error the threshold τ should be
To achieve a minimum probability of error the threshold τ should be
A.
strictly positive
B.
zero
C.
strictly negative
AnswerD.
strictly positive, zero, or strictly negative depending on the nonzero value of σ2
Answer: Option C
Solution
Answer: Option C
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