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In this paper, we experimentally demonstrate a multiband carrierless amplitude and phase modulation format for the first time in VLC. We split a conventional carrierless amplitude and phase modulated signal into m subcarriers in order to protect from the attenuation experienced at high frequencies in low-pass VLC systems. We investigate the relationship between throughput/spectral efficiency and m, where m = {10, 8, 6, 4, 2, 1} subcarriers over a fixed total signal bandwidth of 6.5 MHz. We show that transmission speeds (spectral efficiencies) of 31.53 (4.85), 30.88 (4.75), 25.40 (3.90), 23.65 (3.60), 15.78 (2.40), and 9.04 (1.40) Mb/s (b/s/Hz) can be achieved for the listed values of m, respectively.