Question

A BPSK signal, with equiprobable bits, is transmitted through an AWGN channel and received by a correlator receiver. The two-sided power spectral density of the channel noise is 1 nW/Hz and the average bit energy transmitted is $10\mu J.$ If there is no phase mismatch between the carrier signals used in transmitter and receiver, then the probability of error of the system will be.

• A. $Q\left(10\sqrt{2}\right)$
• B. $Q\left(100\sqrt{2}\right)$
• C. $Q\left(100\right)$
• D. $Q\left(10\right)$

Answer 1

The correct option is C $Q\left(100\right)$

For coherent BPSK,
$P_c=Q\left(\sqrt{\frac{2E_b}{N_0}}\right)=Q\left(\sqrt{\frac{E_b}{N_0/2}}\right)$
$=Q\left(\sqrt{\frac{10\times {10}^{-6}}{1\times {10}^{-9}}}\right)=Q\left(\sqrt{{10}^4}\right)=Q\left(100\right)$