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There is a growing interest in applying carrierless amplitude-phase (CAP) modulation in intensity modulated optical links. CAP as a multilevel modulation scheme can reach high spectral efficiency and be generated at low cost. An interesting feature of CAP is that its signal basis can be extended to three or more dimensions (D). This paper aims to complete the knowledge on 3-D CAP. Discussed are design of transceiver filters, spectral efficiency, and digital equalization in 3-D. Several problems accompanying 3-D CAP transmission are identified. The most significant are the peak to average power ratio, which is higher than in one or two dimensions and noise correlation at the output of a 3-D equalizer. It is found that the latter problem severely degrades bit error rates achieved but can be efficiently mitigated using noise whitening equalization. Finally, 1-D, 2-D, and 3-D CAP are compared experimentally in a step-index polymer optical fiber link.