Problem 12

One of two equally likely messages, $m_0$ or $m_1$ is to be transmitted over an additive white Gaussian noise channel by means of the two signals

$$\begin{array}{cl} s_0(t) =& \left\{ \begin{array}{cc} \... ...} \\ 0; & \mbox{ elsewhere,} \end{array} \right. \end{array}$$

where $T=2ms$, $f_1=1MHz$, and $\Delta=250Hz$. The noise has power density spectrum $N_0/2$. Calculate the probability of error as a function of $E_s/N_0$. Repeat for $\Delta=500Hz$.