Consider antipodal signaling with amplitude imbalance That is, a logic 1 is transmitted as a rectangular pulse of amplitude A 1 and duration T, and a logic 0 is transmitted as a rectangular pulse of amplitude A 2 where A 1 yen A 2 0 The receiver theshold is still set at 0 Define the ratio p A 2 A 1...

a Since the amplitudes A 1 and A 2 each occur 12 the time ...

Consider antipodal signaling with amplitude imbalance. That is, a logic 1 is transmitted as a rectangular pulse

Question:

Consider antipodal signaling with amplitude imbalance. That is, a logic 1 is transmitted as a rectangular pulse of amplitude A₁and duration T, and a logic 0 is transmitted as a rectangular pulse of amplitude -A₂where A₁‰¥ A₂> 0. The receiver theshold is still set at 0.

Define the ratio p = A₂ / A₁and note that the average signal energy, for equally likely 1s and 0s, is A + A? AT T = (1 + p²) 2

(a) Show that the error probability with amplitude imbalance can be written as Pr (error |A, sent) + PE Pr (error |A, sent) 2 2

(b) Plot P_E versus z in dB for p² = 1, 0.8, 0.6, 0.4, respectively. Estimate the degradation in dB at P_E = 10^-6 due to amplitude imbalance for these values of p².