1. (40%) Consider the binary hypothesis detection problem: x(t)= [s(t) +n(t) So (t)+n(t) : H 0tT : Ho wheres, (t), s, (t) are known waveforms and n(t) is AWGN with PSD = N/2. (a) Derive the LRT (likelihood ratio test). (b) Find and plot the ML receiver. (Assume E = so (t)dt = s(t)dt) (c) If s(t)= Acost and so (t) = Acos wt (@, w-w >>0), what is the error probability for ML receiver? (d) If the signal (equal energy) is transmitted in a multipath fading channel, find and plot the ML receiver. That is, as(tt)+n(t) x(t)=4 1=1 aso (tt)+n(t) =1 : H 0tT : Ho and assume L, a's, t's are known. (Note: express your results in time-domain notations, x(t), so (t-t), s(t-t), ...)