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GATE EC 2014 Set 4 — Question 62

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MCQ+2 / -0.67HardError ProbabilityDigital Modulation & DetectionCommunications

Communications → Digital Modulation & Detection → Error Probability

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Question

Consider a discrete-time channel Y=X+ZY = X + Z, where the additive noise ZZ is signal-dependent. In particular, given the transmitted symbol X∈{−a,+a}X \in \{-a, +a\} at any instant, the noise sample ZZ is chosen independently from a Gaussian distribution with mean βX\beta X and unit variance. Assume a threshold detector with zero threshold at the receiver.
When β=0\beta = 0, the BER was found to be Q(a)=1×10−8Q(a) = 1 \times 10^{-8}.
(Q(v)=12π∫v∞e−u2/2duQ(v) = \frac{1}{\sqrt{2\pi}} \int_{v}^{\infty} e^{-u^2/2} du, and for v>1v > 1, use Q(v)≈e−v2/2Q(v) \approx e^{-v^2/2})
When β=−0.3\beta = -0.3, the BER is closest to
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