Radio Communications is a big subject.

You can't just get a Radio Module and squirt Async Data into the IN pin of a Transmitter and expect it to fall out of the OUT pin on the Receiver. If you are doing that, then you're already on the losing team.

AM is worse for Data than FM (just figure the way the Modulation works to discover why it is more susceptible to noise). If you're simply keying the carrier (CW) then again you're on the losing team for Data transmission.

Our ancestors discovered this and invented FSK, AFSK, PCM etc etc along with all kinds of packet protocols to ensure long-range Data integrity. So what are you using? Open up an RS232 Wireless Data Modem and you will find it stuffed full of filters and additional Modulation Hardware. I would lay money on the fact you've got a PIC, a Transmitter Module (and the opposite at the Receive end) and very little else in your design.