# 52. Consider a discrete-time channel Y =- X + ...

52. Consider a discrete-time channel Y =- X + Z, where the additive noise z is signal-dependent. In particular, given the transmitted symbol X ∈ {-a,+a} . at any instant, the noise sample Z is  chosen independently from a Gaussian distribution with mean βX and unit variance. Assume a threshold detector with zero threshold at the receiver.
When 0, β= the BER was found to be Q(a) = 1 × 10-8

$(Q(v)=1\sqrt{2\pi}\int^\infty_v e^{-v^2/2})$

When β= −0.3, the BER is closest to

(A) 10-7

(B) 10-6

(C) 10-4

(D) 10-2

Hint: