Electronics and Communication Engineering - Exam Questions Papers - Discussion

Consider a baseband binary PAM receiver shown below. The additive channel noise n(t) is whit with power spectral density S_N(f) = N₀/2 = 10^-20 W/Hz. The low-pass filter is ideal with unity gain and cutoff frequency 1 MHz. Let Y_k represent the random variable y(t_k).
Y_k = nN_k if transmitted bit b_k = 0
Y_k = a + N_k if transmitted bit b_k = 1
Where N_k represents the noise sample value. The noise sample has a probability density function, P_Nk(n) = 0.5ae^-a|n| (This has mean zero and variance 2/a²). Assume transmitted bits to be equiprobable and threshold z is set to a/2 = 10^-6 V.

The probability of bit error is