Now consider a SSB$-$SC system. Let the SSB$-$SC modulated signal be

$x_c(t)=\frac{1}{2}[m(t)cos(2f_{c}t+)+(hat(m))(t)sin(2f_{c}t+)]$

Let $W$ be the bandwidth of $m(t).$ The input signal power $\frac{?}{\text{b}\text{a}\text{r}}(m^2(t))=20$ Watts. Suppose the white noise superimposed on the SSB$-$SC signal has a two$-$sided power spectral density of $\frac{N_0}{2}.$

$($a$)(1$ pts$)$ What is the output signal power of the receiver?

$($b$)(4$ pts$)$ Sketch the power density of Predection noise and the postdection noise.

$($c$)(8$ pts$)$ What are the input SNR $($Predetection SNR$)SN{R}_i,$ output SNR $($Postdetection $SNR$ and channel $SN{R}^{-}SN{R}_c?$ What are the Detection gain and Figure of Merit?