Question

An ON-OFF binary system uses the pulse waveforms

$s_i\left(t\right)=\{\begin{array}{cc}{s}_1\left(t\right)=Asin\frac{\pi t}{T};& 0\le t\le T\\ s_0\left(t\right)=0& 0\le t\le T\end{array}$

A = 0.1 mV and T =1 $\mu s$. The signal is transmitted through an AWGN channel with two sided noise PSD ${10}^{15}W/Hz$ and received with a correlator receiver with optimum threshold detection. If the probability of error is $Q\left(\sqrt{x}\right)$, then the value of x will be ________.
(Assume $P\left(s_1\right)=P\left(s_0\right)=1/2)$

• A. 1.25
• B. 1.15
• C. 1.05
• D. 0.25

Answer 1

The correct option is A 1.25

$P_e=Q\left(\sqrt{\frac{E_d}{2\eta }}\right)$

$E_d=A^2\frac{T}{2}$

$\frac{E_d}{2\eta }=\frac{A^{2}T}{4\eta }=\frac{(1\times {10}^{-4})(1\times {10}^{-6})}{4(2\times {10}^{-15})}=1.25$

$P_e=Q\left(\sqrt{1.25}\right)$