Power-Efficient Modulation Schemes

Abstract

Coherent optical fiber communications had a brief period of popularity in the early 1990s, mainly because the optical links of that day were significantly power-limited. Coherent detection provided a possibility of optically amplifying the signal to a power level that, after photodetection, made the thermal noise negligible. Two things, however, caused those coherent systems to be abandoned. The first was the sheer technical difficulties: a coherent receiver requires a local oscillator laser that is to be phase-and polarization-locked to the received signal. This gave rise to significant technical obstacles, and only a few limited and expensive coherent receiver solutions were demonstrated [17,26]. The second was the development of the Erbium-doper fiber amplifier (EDFA) that provided an elegant and practical solution to the problem of the thermal noise. By 1995, the EDFA was a commodity in fiber communication systems, simple on-off keying modulation worked well enough, and coherent communication was forgotten. However, coherent transmission systems got renewed attention around 2005 [12, 34]. This time the motivation was entirely different. A coherent receiver gives access to both the optical phase and amplitude, which provides two important benefits; (i) advanced multilevel modulation formats can be used, that can improve the spectral efficiency; and (ii) electronic distortion mitigation can be used, as the optical field is directly mapped to the electrical signal. Moreover, the practical problems with the coherent detection could now be solved by performing the phase-and polarization tracking by fast digital signal processing. This enabled a third significant

Optimizing Constellations for Single-Subcarrier Intensity-Modulated Optical Systems

“…Overall, modulation formats optimized for P o perform well in average-power limited systems. In [54], a similar conclusion was reached for the case of coherent optical systems.…”

Generalized Pulse-Position Modulation for Optical Power-Efficient Communication

“…This deficiency is even more prominent for the most power-efficient 4d constellations with m ≥ 22 and 2d constellations with m ≥ 5 (not included in the figure). The reason is that these constellations have a small "PPM distance" due to a constellation point near the origin [9]. …”

Multidimensional Optimized Optical Modulation Formats

“…i.e., the continuous-time average energy is proportional to the discrete-time average energy E. Unfortunately, there exists no analogous relation between the continuoustime and discrete-time peak energies. Constellation designs based on E max tend nevertheless to be relatively good also in terms of the continuous-time peak energy, but not necessarily optimal [31].…”

“…Modulation optimization for some specific nonlinear and non-Gaussian channel models will be summarized in 2.3.2. In the limit of high SNR, the formats with the lowest symbol error rate (SER) can be found from optimized packings of solid spheres [27,31,33]. For a constant dimensionality and number of spheres, such packing optimization can be done by either minimizing the average distance of the spheres from the origin (the average second moment E) or by minimizing the maximum distance (the maximum symbol energy E max ).…”

“…Both cases will be discussed below, in section 2.3.1. The balls and their relevance were discussed in [31] and will be briefly touched upon in section 2.3.2.…”