Can a GSM base station, a handheld radio or Wi-Fi disturb the remote control?
It can. A strong transmitter very close by can saturate the receiver front end and desensitise it even if it is not in your band; this effect is called blocking or desensitization. Devices operating in the same band also interfere directly: at sub-GHz, garage remotes, car keys and telemetry; at 2.4 GHz, Wi-Fi, Bluetooth and microwave ovens.
Two different mechanisms have to be separated. The first is in-band interference: another device uses the same frequency as you, the channel fills up, packets collide. The second is out-of-band blocking: a strong transmitter such as a handheld radio a few metres away saturates the receiver input stage. Even if the filter suppresses out-of-band content, the weak wanted signal cannot be decoded because the input stage is already saturated.
Practical symptoms and solutions:
- Dropouts at a particular spot while a particular person is talking on a radio: out-of-band blocking. Move the antenna away from that source.
- Erratic performance at 2.4 GHz in a busy office or warehouse: channel occupancy. Frequency hopping systems behave better in this scenario.
- Generally low range in an installation very close to a base station: try changing the antenna position and height, and choose the best spot by measurement.
Choosing the location is the cheapest and most effective engineering solution for most of these problems. Temporarily mounting the antenna at a few different points and running a range test before commissioning gains you more than all the improvements made afterwards.
Full topic: Wireless remote control installation: pairing, relay, safety