engineering recuitment GATE ECE 2023-24 Test Series Communication Systems Baseband Transmission Threshold Detection with Gaussian Noise
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 β = 0, the BER was found to be Q(a) = 1 × 10-8
\((Q\left( v \right) = \frac{1}{{\sqrt {2\pi } }}\mathop \smallint \limits_v^\infty {e^{ - {u^2}/2}}du\), and for v > 1, use \(Q\left( v \right) \approx {e^{ - {v^2}/2}})\)
When β = -0.3, the BER is closest to1
10-7
2
10-6
3
10-4
4
10-2