1. A transmission system employs three waveforms with probabilities The signal space has dimension…

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).