High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform

Abstract

In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

Capacity Lower Bounds of the Noncentral Chi-Channel With Applications to Soliton Amplitude Modulation

“…The asymptotic expression for the output entropy can be written by combining (60), (44), (45) and (53), which yields…”

“…The spectral efficiency of the multiple-eigenvalue encoding schemes is an area actively explored at the moment [29], [42], [43]. Multisoliton transmission has also received increased attention in recent years, see, e.g., [44] and [45] and references therein. Finding the capacity of the multi-eigenvalue-based systems in the presence of in-line noise that breaks integrability still remains an open research problem.…”

Variance normalizing transform for performance improvement in radio-over-fiber systems

“…In a number of other works general communication system designs, including the modulation on the norming constants, were studied [63][64][65][66][67][68][69][70]. Recently in [71], transmission of 6 bits/symbol at 24 Gbps over 1000 km of fibre was demonstrated by experiment using a single eigenvalue and its corresponding norming constant. In general, it can be concluded from all these research that reliable high data rates can be achieved for long distances of fibre link by signalling on DS provided that an optimized system design is opted.…”

“…In [54], spectral efficiency of coherent soliton communication was estimated by optimizing ratio of the pulse width to the bit slot. More recently, the performance of communication system using only a single eigenvalue was studied in [71]. A multi-level modulation format was used for modulating data on norming constant and optimization techniques were exploited which resulted in 6 bits/symbol rate at 24 Gbps over 1000 km.…”

Contour integrals for numerical computation of discrete eigenvalues in the Zakharov–Shabat problem

“…The contour integrals approach does not have this issue. These properties make the contour integrals a viable tool for multi-eigenvalue NFT communication [12][13][14].…”