For the ternary ASK system of Problem 8.3.1, what is P[DE], the probability that the receiver decodes the wrong symbol?
Problem 8.3.1
In a ternary amplitude shift keying (ASK) communications system, there are three equally likely transmitted signals {s0,s1,s2}. These signals are distinguished by their amplitudes such that if signal si is transmitted, then the receiver output will be
![](https://test.transtutors.com/qimg/7c87e6b9-2bb8-41b0-8eab-15a9250c7d33.png)
Where a is a positive constant and N is a Gaussian (0, σN ) random variable. Based on the output X, the receiver must decode which symbol si was transmitted. What are the acceptance sets Ai for the hypotheses Hi that si was transmitted?