A trap can be that the receiver always receives data (noise) even if the transmitter is not transmitting at the moment. This means if we use a baudrate of 9600 than the 4 checksum bytes are received 300 times per second. With 32 Bits checksum the possibility is 1/4.294.967.296 that the checksum is coincidentally correct. This means further this happens once every 165 days. Maybe you should better use even more checksum bytes…
It's not as bad as that, because you would only be testing checksums at that rate if you were receiving nothing but checksums (checksums of what?)
You should always have a Start-of-message sequence, especially on a radio link. A single byte isn't great when there's idle noise, 4 bytes isn't bad (and easy to test with a 32 bit shift register). Then you would have a length (unless fixed length messages), and at least one data byte (unless you make zero-length messages mean something). This means:
165 days to see a false SOM
and a length that just happens to lead to a CRC which is exactly right.
So counting a data byte (6 bytes min), the maximum effective sample rate is 200times/sec
5 bytes have to match up, which leads to 63629 days, times the original 165 day trigger
or approximately 29k years. 1/2 of that for a mean time.
Dependency of above on length==1 makes the math a bit loosey-goosey, but all other variations are lower effective sample rate so longer time.
This is also assuming your idle noise is pure unbiased random noise. If you know the characteristics of the receiver you can choose you encoding, SOM sequence and CRC algorithm/encoding to lower the probability of false hits.
And there's always chance (albeit very low) that the false transmission hit could occur in the first 5 mins. Robust comms protocols are fairly easy... 100% bulletproof ones not so much.
Dave