Solve the following problem:
Two equiprobable messages are transmitted via an additive white Gaussian noise channel with noise power spectral density of N0/2 = 1. The messages are transmitted by the following two signals
s1(t) = {1 0≤t≤T
{0 otherwise
and s2(t) = s1(t - 1). It is intended to implement the receiver by using a correlation-type structure, but due to imperfections in the design of the correlators, the structure shown in Figure has been implemented. The imperfection appears in the integrator in the upper branch where instead of ∫10 we have ∫1.5 0
The decision device, therefore, observes r1 and r2 and based on this observation has to decide which message was transmitted. What decision rule should be adopted by the decision device for an optimal decision?
