For the ternary ask system of problem 831 what is pde the

Question

For the ternary ASK system of Problem 8.3.1, what is P[D_E], 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 s_i is transmitted, then the receiver output will be

Where a is a positive constant and N is a Gaussian (0, σ_N ) random variable. Based on the output X, the receiver must decode which symbol s_i was transmitted. What are the acceptance sets A_i for the hypotheses H_i that s_i was transmitted?