GATE Electronics and Communications (EC) 2014 Shift 2 Solved Paper

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms 𝑠₁(𝑡) = 𝛼 cos 2𝜋𝑓₁𝑡 and 𝑠₂(𝑡) = 𝛼 cos 2𝜋𝑓₂𝑡, where 𝛼 = 4 mV. Assume an AWGN channel with two-sided noise power spectral density $\frac{{\mathit{N}}_0}{2}=0.5\times {10}^{-12}\mathit{W}∕\mathit{H}\mathit{z}$. Using an optimal receiver and the relation $\mathit{Q}\left(\mathit{v}\right)=\frac{1}{\sqrt{2\mathit{\pi }}}\underset{\mathit{v}}{\overset{\mathit{\infty }}{\int }}{\mathit{e}}^{-{\mathit{u}}^2∕2}\mathit{d}\mathit{u}$, the bit error probability for a data rate of 500 kbps is