Question

$\text{A BPSK signal with equiprobable bits is transmitted through an AWGN channel and received by a correlator receiver. If there is a phase mismatch of}{90}^{\circ }\text{between the carriers used in the transmitter and receiver, then the probability of error will be}$

• A. 0.50
• B. $\text{Depends on the value of}{E}_b$
• C. 1
• D. 0

Answer 1

The correct option is A 0.50

$P_c=Q\left[\sqrt{\frac{2E_b}{N_0}}\cos {\varphi }_c\right];{\varphi }_c={90}^{\circ }$

$=Q\left[\sqrt{\frac{2E_b}{N_0}}\cos \right({90}^{\circ }\left)\right]=Q\left(0\right)=0.50$