A discrete memory-less source generates either 0 or 1 at a rate of 160 kbps; 0 is generated three times more frequently than 1. A coherent binary PSK modulator is employed to transmit these bits over a noisy channel. The received bits are detected in a correlator fed with the basis function of unit energy (for this binary PSK scheme) as the reference signal. The receiver makes a decision in favour of 1 if the correlator output is positive, else decides in favour of 0. If 0 and 1 are represented as  and  respectively, then        

(a) Determine the transmitted signal energy per bit.

(b) Determine the basis function of unit energy for this binary PSK scheme.

(c) Determine the probability that the receiver makes a decision in favour of 1 when the channel noise is characterized as zero-mean AWGN with power spectral density