A brief overview of this (very complex) type of system...
The remote key/fob, unlike traditional remotes, is actually a transceiver.
The vehicle is equipped with a number of interior and exterior antennae:
Interior - areas including the dash, centre console and load compartment just behind the rear seats.
Exterior - areas including both front door and the boot (trunk) handles.
The door handles and boot (trunk) handle also have capacitive sensors to detect the presence of a hand.
A traditional transponder chip and reader coil are still used, along with a mechanical key blade & lock, in case of a flat battery (vehicle or transceiver).
The system works on a challenge/response basis, using different frequencies, something like this:
The driver approaches the vehicle and touches a door/boot handle. The PKE control unit picks up the 'Open' request from the capacitive sensor and sends out a challenge, via the appropriate antenna, to the transceiver. IIRC, this is performed at 125kHz, but other manufacturers may use a different frequency. The transceiver responds with it's unique serial code, which is picked up by the appropriate antenna and compared in the PKE control unit. Provided the code matches with that which is stored in the PKE control unit, the vehicle is unlocked.
Once unlocked and the driver has entered the vehicle, the interior antennae are used for the ignition on/start process. This is usually performed at 315 or 433mHz, depending upon global locality, IIRC. Again, the transceiver is challenged and expected to respond. Should the transceiver be found to be out of range of the interior antennae, the on/start process is usually blocked and a warning light may be illuminated. If the transceiver battery is low or flat, the vehicle will likely require unlocking mechanically and the transceiver be placed either in a specific location (such as when a model range is only available with PKE) or somewhere around the steering column/dash (such as when a model range is available with traditional open/start, or PKE as an option) in order for the reader coil to activate, challenge, then pick up the response from the transponder chip.
HTH.