GATE EC 2021 Set 1 — Question 63
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Communications → Digital Modulation & Detection → Line Coding
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Question
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 V. 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.
Correct answer
0.03 to 0.05
Solution
Given:
Signal for '1': V
Signal for '0': V
Noise variance V
A priori probability of '1':
A priori probability of '0': For a Maximum A Posteriori (MAP) receiver in the presence of additive white Gaussian noise (AWGN), the optimum threshold voltage is given by the formula:
Substitute the given values into the formula:
VRounded off to two decimal places, the optimum threshold voltage is V.The final answer is
Signal for '1': V
Signal for '0': V
Noise variance V
A priori probability of '1':
A priori probability of '0': For a Maximum A Posteriori (MAP) receiver in the presence of additive white Gaussian noise (AWGN), the optimum threshold voltage is given by the formula:
Substitute the given values into the formula:
VRounded off to two decimal places, the optimum threshold voltage is V.The final answer is
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