A system includes a sensor device adapted to be associated with a tyre of a vehicle, and a sensor coordinator device adapted to be installed on a body of the vehicle. The sensor coordinator device includes an antenna. The antenna includes a single-piece metallic plate shaped so as to define a first plate portion designed for the wireless reception of data from the sensor device in a first frequency band, and a second plate portion designed for the wireless transmission of data to the sensor device in a second frequency band different from the first frequency band. The antenna further includes a ground plate common to both the first and second plate portions.