Question

BPSK signal with equiprobable bits is transmitted through an AWGN channel and received by a correlator receiver. If there is a phase mismatch of ${90}^0$ between the carrier received in transmitter and receiver, then the probability of error will be

• A. 0
• B. 1
• C. Depends on the value of $E_b$
• D. $$\frac{1}{2}$$

Answer 1

The correct option is D

$$\frac{1}{2}$$

(b)
Probability of error in BPSK sytem with a phase mismatch of ${\varphi }^{}$ is,

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

For ${\varphi }_e={90}^0$

$P_e=Q\left[\sqrt{\frac{2E_b{\cos }^2\left({90}^0\right)}{N_0}}\right]=Q\left(0\right)=\frac{1}{2}$