engineering recuitment GATE ECE 2023-24 Test Series Communication Systems Baseband Transmission Threshold Detection with Gaussian Noise
In a binary communication system the input to the detector is Y = X + N1 + N2, where X is the desired signal which takes either +1 or -1 with equal probability, N1 is a zero mean gaussian random variable with a variance of 1 and N2 represents the ISI due to channel distortion. The ISI term is a random variable which takes the values \(\left\{-\frac{1}{2},\frac{1}{2}\right\}\)with probabilities \(\left\{\frac{3}{4},\frac{1}{4}\right\}\) respectively. If the threshold detector value used in detector is zero, then the average probability of error will be ______. Assume that \(Q(\nu)=\frac{1}{\sqrt{2\pi}}\displaystyle\int^\infty_ve^{\frac{-y^2}{2}}dy\)
1
0.25 Q(0.5) + 0.75 Q(0.75)
2
0.5 Q (0.5) + 0.5 Q (0.25)
3
0.5 Q(0.5) + 0.5 Q(1.5)
4
0.25 Q (1.5) + 0.5 Q (0.5)