GATE EC 2014 Set 4 Q52 — Probability and Statistics

Consider a discrete-time channel $Y=X +Z$, where the additive noise $Z$ is signal-dependent. In particular, given the transmitted symbol $X \in \{-a , +a\}$ at any instant, the noise sample $Z$ is chosen independently from a Gaussian distribution with mean $\beta X$ and unit variance. Assume a threshold detector with zero threshold at the receiver.

When $\beta=0$, the BER was found to be $Q(a) = 1 \times 10^{-8}. (Q(v) = \frac{1}{\sqrt{2 \pi}} \int_v^{\infty}e^{-u^2/2} du$, and for $v>1$, use $Q(v) \approx e^{-v^2/2})$

When $\beta = -0.3$, the BER is closest to