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Visible light communications is a technology with enormous potential for a wide range of applications within next generation transmission and broadcasting technologies. VLC offers simultaneous illumination and data communications by intensity modulating the optical power emitted by LEDs operating in the visible range of the electromagnetic spectrum (~370-780 nm). The major challenge in VLC systems to date has been in improving transmission speeds, considering the low bandwidths available with commercial LED devices. Thus, to improve the spectral usage, the research community has increasingly turned to advanced modulation formats such as orthogonal frequency-division multiplexing. In this article we introduce a new modulation scheme into the VLC domain; multiband carrier-less amplitude and phase modulation (m-CAP) and describe in detail its performance within the context of bandlimited systems.