GATE 2021 EC – Question 63
Consider a polar non-return to zero (NRZ) waveform, using $+2$ V and $-2$ V for representing binary '1' and '0', respectively, is transmitted in the presence of additive zero-mean white Gaussian noise with variance $0.4\ \text{V}^2$. If the a priori probability of transmission of a binary '1' is 0.4, the optimum threshold voltage for a maximum a posteriori (MAP) receiver (rounded off to two decimal places) is ________ V.
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Correct answer: 0.03 to 0.05
Explanation
The MAP rule decides '1' when $P(1)f(r|1)>P(0)f(r|0)$. With Gaussian densities centred at $\pm A$ ($A=2$ V) and variance $\sigma^2=0.4$, the threshold is $V_{th}=\frac{\sigma^2}{2A}\ln\frac{P(0)}{P(1)}=\frac{0.4}{4}\ln\frac{0.6}{0.4}=0.1\times0.4055\approx0.04$ V.