Solution:

$$ y_0(t)=\int_{-\infty}^{\infty} y_{\text {in }}(\lambda) s\left(t_1-t+\lambda\right) d \lambda=R\left(t-t_1\right) $$

Equation above describes the output of the matched filter as the cross correlation between the input signal and a delayed replica of the transmitted signal.

This implies that the matched-filter the receiver can be replaced by a cross-correlation receiver that …