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 ${30}^o$ between the carrier used in transmitted and receiver, then the probability of error will be

• A. $Q\left[\sqrt{\frac{\left(1.5\right)E_b}{N_o}}\right]$
• B. $Q\left[\sqrt{\frac{2E_b}{N_o}}\right]$
• C. $Q\left[\sqrt{\frac{E_b}{2N_o}}\right]$
• D. $Q\left[\sqrt{\frac{3E_b}{N_o}}\right]$

Answer 1

The correct option is A $Q\left[\sqrt{\frac{\left(1.5\right)E_b}{N_o}}\right]$

Probability of error in BPSK system with a phse mismatch of ${\Phi }_o$ is,
$P_e=Q\left[\frac{\sqrt{2E_{b}co{s}^2{\Phi }_0}}{N_o}\right]=Q\left[\frac{\sqrt{2E_b(cos{30}^o{)}^2}}{N_o}\right]$
$P_e=Q\left[\sqrt{\frac{3E_b}{2N_o}}\right]=Q\left[\sqrt{\frac{\left(1.5E_b\right)}{N_o}}\right]$