Digital receivers for the reception of non pulse shaped signals
Since you are talking about digital communication you are going to have a symbols.
When u send a symbol $s(t)$ you are going to send it with a symbol time $T_{sym}$
so we can say that any symbol that is sent equals to $s(t)\Pi(\dfrac{t}{2T_{sym}})$ where $\Pi$ is the rectangular function.
So basically any discrete time signal has a rectangular shaping pulse.

E.g.

In BPSK you will be sending one of the following symbols:
$$
    S_1(t)=1
$$
$$
    S_0(t)=-1
$$
Since I am sending the symbols for a known time $T$

I am practically multiplying them with a rectangular window with the length of $T$

so for the data series $a$ the signal $S(t)$ will be :
$$
   S(t) =  \sum_{k=0}^\infty S_{a_k}(t)\Pi(\dfrac{t-kT_{sym}}{ 2T_{sym} })
$$

And the matched filter in the receiver will be the average over $T_{sym}$ (or integration over $T_{sym}$) which is otherwise known as a rect.

Which is the same way you would do with other shaping pulses