GATE EC 2012 Set 1 Q27 — Digital Communications

A BPSK scheme operating over an AWGN channel with noise power spectral density of $\frac{N_o}{2}$, uses equiprobable signals $s_1(t)=\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ and $s_2(t)=-\sqrt{\frac{2E}{T}}\sin(\omega_ct)$ over the symbol interval $(0,T)$. If the local oscillator in a coherent receiver is ahead in phase by $45^\circ$ with respect to the received signal, the probability of error in the system is