Question

In a BPSK system, equiprobable bits are transmitted through an AWGN channel at a rate of 1 Mbps. The two-sided power spectral density of the channel noise is 16$\mu$W/Hz At the output of the channel, the signal is received by a correlator receiver with exact carrier synchronization and optimum threshold detection. If the probability of error achieved by this system is Q(5), the average bit energy transmitted is________$\mu J$
$\left[\text{Assume that, Q(x)=}\frac{1}{\sqrt{2\pi }}{\int }_x^{\infty }{e}^{-u^2/2}du\right]$

• A. 400

Answer 1

The correct option is A 400
$\text{For a BPSK system with correlator receiver,}\text{probability of error,}{P}_c=Q\left[\sqrt{\frac{2E_b}{N_0}}\right]=Q\left(5\right)\text{So,}\sqrt{\frac{2E_b}{N_0}}=5E_b=25\times \frac{N_0}{2}\text{Given that,}\frac{N_0}{2}=16\mu W/Hz.\text{So}{E}_b=25\times 16\mu J=400\mu J$