Consider a quaternary (M=4) communication system that transmits every T seconds one of four equally probable signals, s1(t), -s1(t), s2(t), and -s(t) . The signals, s1(t) and s2(t) are orthogonal with equal energy. The noise is additive white Gaussian noise with power spectral density, N0 / 2 . The demodulator consists of two filters matched to s1(t) and s2(t) , and their outputs at the sampling instances are U1 and U2 . The detector bases it decision on the following rules U1>|U2| ⇒s1(t) U1 < −|U2| ⇒ −s1(t) U2> |U1|⇒s2(t) U2 < − |U1|⇒ −s2(t) Since the signa set if biorthogonal, the error probability is given by (1- Pc). a. Determine the decision region for this problem. b. Make the following change of variables, W1=U1+U2, and W2= U1- U. Determine the decision regions in the new variable space. c. Determine the probability of error. Compare this result to that expected for 4- PSK