Battery powered radios that periodically wake up to listen

In the context of battery powered radios people usually think of things like remote sensors that spend most of their time sleeping and only need to be woken up when data needs to be transmitted. This scheme can allow for weeks or months of battery life.

I'm thinking of a similar thing, except that it is a battery powered radio that briefly wakes up to listen for a transmission from a base station. Are some radios more power friendly at doing the sleep-listen-sleep cycle than others? Or to put it another way, which radios have the smallest power penalty for simply energizing their receive circuitry for a few milliseconds?

Can you provide more information on the project ?

No point in people suggesting radios that are not on the right frequency, dont provide the distance needed or dont have the data rate needed etc.

2.4GHz or 433MHz. In my region z-wave is assigned 919.8 MHz to 921.4 MHz.
Pretty much everything else is licensed spectrum. 433MHz isn't an official ISM band, but low powered radios are allowed.
Distance 50 meters, data rate 1200 bits per second (or perhaps faster if it reduces power consumption).
Think of a home with a number of radios scattered around used to control battery operated lights that spend 99% of their time switched off.