Advanced Topics in Complex Optical Modulations: Hilbert Transforms, Single Side Band, and Twin-SSB Modulations

Optical modulation is the process used to up-convert the energy of the information content from the baseband up to the optical domain required for optical fiber transmission purposes. Unfortunately, the optical spectrum satisfies the conjugate symmetry property, leading to a double spectral occupancy with respect to the single electrical baseband spectrum. Is there any artifact capable to bring the same spectral bandwidth of the baseband signal up to the modulated optical spectrum? The answer to this question is well-known in communication engineering, and it relies to the analytic signals and Hilbert transforms. The aim of this chapter is to give the reader a mathematical insight of the relationships existing between Fourier transforms and Hilbert transforms of real signals and how to combine those properties to achieve a single-side-band modulation useful in high spectral efficient optical communications. The feasibility of the optical single-side-band spectrum depends on the modulation format. Specifically, single carrier ASK modulation can be easily converted into SSB-ASK doubling the spectral efficiency. Unfortunately, because of the inherent analytic signal requirement embedded into the Hilbert transforms and the consequent single-side-band spectrum generation, quadrature amplitude modulations cannot support SSB format. A valid alternative to QAM signals is represented by the Twin-SSB signals. This applies to every modulation order. As we will see in detail in this chapter, both tributaries of the Twin-SSB can be brought either upon the same carrier phase or upon quadrature phases, but any case each tributary occupies a single side band of the assigned optical phase. Unfortunately, the complementary side band is used by the Hilbert transform spectrum to cancel out the reference tributary side band, and it cannot be used to bring the quadrature tributary.