| Summary: | From Shanon's theory, we know that information capacity is a logarithmic function of signal-to-noise ratio (SNR) but a linear function of the number of dimensions. By increasing the number of dimensions <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>, we can dramatically improve the spectral efficiency. At the same time, in <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>-dimensional space <formula formulatype="inline"> <tex Notation="TeX">$(D\ >\ 2)$</tex></formula>, for the same average symbol energy, we can increase the Euclidean distance between signal constellation points compared with the conventional in-phase (I)/quadrature (Q) 2-D signal space. The 4-D space, with two phase coordinates per polarization, has already been intensively studied. To satisfy the ever-increasing bandwidth demands, in this paper, we propose the <formula formulatype="inline"><tex Notation="TeX">$D$</tex> </formula>-dimensional signaling <formula formulatype="inline"><tex Notation="TeX">$(D\ >\ 4)$</tex></formula> by employing all available degrees of freedom for transmission over a single carrier including amplitude, phase, polarization, and orbital angular momentum (OAM). The proposed modulation scheme can be called hybrid <formula formulatype="inline"><tex Notation="TeX">$D$</tex></formula>-dimensional modulation as it employs all available degrees of freedom. The proposed hybrid 8-D coded-modulation scheme outperforms its 4-D counterpart by 3.97 dB at a bit error rate (BER) of <formula formulatype="inline"><tex Notation="TeX">$10^{-8}$</tex></formula> while outperforming its corresponding polarization-division-multiplexed (PDM) iterative polar quantization (IPQ)-based counterpart by even a larger margin of 6.41 dB (at the same BER). The improvement of the proposed scheme for two amplitude levels per dimension and <formula formulatype="inline"><tex Notation="TeX">$D = 8$</tex></formula> over conventional PDM 64-quadrature amplitude modulation (QAM) is indeed a striking 8.28 dB at a BER of <formula formulatype="inline"><tex Notation="TeX"> $2 \times 10^{-8}$</tex></formula>.
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