engineering recuitment GATE ECE 2023-24 Test Series Communication Systems Baseband Transmission Threshold Detection with Gaussian Noise
Consider a communication scheme where the binary-valued signal X satisfies {𝑋 = +1} = 0.75 and {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:
\(\hat X = \left\{ {\begin{array}{*{20}{c}} { + 1,\;\;\;Y > \tau }\\ { - 1,\;\;\;Y \le \tau } \end{array}} \right.\)
The achieve a minimum probability of error P{X̂ ≠ X}, the threshold τ should be1
strictly positive
2
zero
3
strictly negative
4
strictly positive, zero, or strictly negative depending on the nonzero value of 𝜎2