Question

A BPSK signal with equiprobable bits is transmitted through an AWGN channel and received by a correlator receiver. If there is a phase mismatch of 30° between the carrier used in transmitter and receiver, then the probability of error will be

Answer 1

Probability of error in BPSK system with a phase mismatch of ${\varphi }_{0}is,$

$P_0=Q\left[\sqrt{\frac{2E_b{\cos }^2{\varphi }_0}{N_0}}\right]=Q\left[\sqrt{\frac{2E_b{\cos }^{2}30}{N_0}}\right]$

$P_0=Q\left[\sqrt{\frac{3E_b}{2N_0}}\right]=Q\left[\sqrt{\frac{\left(1.5\right)E_b}{N_0}}\right]$