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 \[{{\rm{\hat X}}}\] is
\[{\rm{\hat X}} = \left\{ \begin{array}{l}
+ 1,\,\,\,{\rm{Y}} > \tau \\
- 1,\,\,\,{\rm{Y}} \le \tau
\end{array} \right.\]
To achieve a minimum probability of error \[{\rm{P}}\left\{ {{\rm{\hat X}} \ne {\rm{X}}} \right\}{\rm{,}}\] the threshold τ should be
A. strictly positive
B. zero
C. strictly negative
D. strictly positive, zero, or strictly negative depending on the nonzero value of σ2
Answer: Option C
This Question Belongs to Electronics And Communications Engineering >> Communication Systems
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