High RF fields can easily cause interference that cause various issues with electronics in cars. The best way to prevent it is to have the radio professionally installed by a good radio shop. They will make sure that things are installed correctly and isolated to the greatest extent possible to prevent these kinds of issues.
If a professional install isn't possible (it does cost more than a do-it-yourself job), make sure to check these things are done right and remain properly connected and tight:
* Radio power is isolated from the vehicle's electronics (both power and ground wires). Since you indicate that the radio is wired directly to the battery, this is probably done, but make sure it's tight. Also if your ground is hard-wired to the battery, make sure it also has a fuse with the same rating as the power wire.
* Make sure that the antenna connection is firmly connected and there isn't kinked or holes in the insulation.
* Make sure that the antenna is mounted as far away from the vehicle's electronics as practical.
* Make sure that the antenna mount is firmly mounted and has an excellent ground connection.
* Make sure that the radio is grounded per the manufacturer's instructions. Most of the times there isn't a separate ground required, and this is handled by properly mounting the radio on the correct bracket. Some radios may require special grounding procedures depending on the design of the vehicle's electrical design which is why you must follow the manufacturer's instructions.