As 5G devices and networks continue to roll out, new broadcasting services and capabilities have been introduced to the entire ecosystem, opening up additional new applications and granular business opportunities, where indoor joint communication and sensing are critical. Under this trend, in this paper, we propose a new system using multi-band carrierless amplitude and phase (m-CAP) modulation associated with received signal strength (RSS)-based trilateration to achieve visible light sensing and communication from the same signal. The architecture of this system is first detailed, with an emphasis on how the light source limitations in terms of dynamic range and modulation bandwidth may be taken into account. The proposed setup is then shown through simulations to provide an illuminance between 300 and 500 lux over the whole room, positioning with an error lower than 7.17 cm in 90% of the cases, and a continuous data connectivity at 32 Mbps. The influence of several parameters, including that of the main m-CAP settings, on this performance is studied in order to define some general rules for the design of such a system.