High-dimensional modulation for coherent optical communications systems

Abstract

In this paper, we examine the performance of several modulation formats in more than four dimensions for coherent optical communications systems. We compare two high-dimensional modulation design methodologies based on spherical cutting of lattices and block coding of a 'base constellation' of binary phase shift keying (BPSK) on each dimension. The performances of modulation formats generated with these methodologies is analyzed in the asymptotic signal-to-noise ratio regime and for an additive white Gaussian noise (AWGN) channel. We then study the application of both types of high-dimensional modulation formats to standard single-mode fiber (SSMF) transmission systems. For modulation with spectral efficiencies comparable to dual-polarization (DP-) BPSK, polarization-switched quaternary phase shift keying (PS-QPSK) and DP-QPSK, we demonstrate SNR gains of up to 3 dB, 0.9 dB and 1 dB respectively, at a BER of 10(-3).

High-Dimensional Modulation for Optical Fiber Communications

“…In our previous research [11,[13][14][15][16][17], we have used the term "high-dimensional modulation" to refer to any modulation format with more than four dimensions. It should be noted however, that this terminology is not universal, and "multidimensional" is often used elsewhere in the literature -although this is also often used to describe 4-D modulation, which is relatively conventional in optical communications.…”

“…Geometric based constellation design has previously been described in the wireless literature [9,18], and more recently applied to optical communications [13,15,17]. The use of geometric objects such as lattices enables the relatively easy design of constellations with arbitrary numbers of points, with good performance in the high SNR regime.…”

“…BPSK per dimension), it is possible to easily design constellations in many dimensions [10,11,13,17]. Since these constellations have a natural labeling, they do not require labeling optimization even with many constellation points.…”

“…In [20], the (8,4,4) bi-orthogonal code (as initially proposed in [10], and further examined in [17]) is used with a mapping specifically chosen to have a zero mean degree of polarization over a pair of consecutive time-slots. While the initial results from seem promising, it is not clear that this this methodology can easily be used to design other modulation formats.…”

Throughput Gains From Adaptive Transceivers in Nonlinear Elastic Optical Networks

“…To maximize the data transmitted over a given light path the transceivers can use basic modulation format adaptation [2], 4D modulation schemes [3], time division hybrid formats [4], OFDM subcarrier modulation adaptation [5], probabilistic shaping [6], [7] and FEC overhead (OH) adaptation [8]- [11]. The adaptation of the optical launch power [12], [13] and mitigation of nonlinear interference using, for example digital back propagation (DBP) [14], [15], can improve the properties of the light path.…”