1. A transmission system employs three waveforms with probabilities The signal space has dimension I = 1 and constellation
In the presence of AWGN with PSD evaluate:
a) The error probability with decision region thresholds at ±V0/3.
b) The error probability with optimum decision regions.
2. A binary transmission system with dimension I = 1 has constellation s1 = −A and s2 = +A. Let the receiver employ two decision regions with threshold v = A/5.
a) Evaluate the probability of error when p1 = p2 and the additive Gaussian noise has standard deviation σI = A/5.
b) Evaluate the probabilities p1 and p2 which guarantee that the chosen regions are optimum (consider again σI = A/5).