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
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?