COMPARATIVE ANALYSIS OF ML AND MAP DETECTORS FOR PAM CONSTELLATIONS IN AWGN CHANNEL

In this paper we perform a comparative performances analysis of “maximum a posteriori” (MAP) and “maximum likelihood” (ML) detectors for one-dimensional constellation in the adaptive white Gaussian noise (AWGN) channel. More precisely, error probabilities per symbol for the aforementioned detectors are compared for the case when the pulse amplitude modulation (PAM) constellation with the equidistant and non-equiprobable constellation points is used as one-dimensional constellation. We perform analysis for different distributions of the constellation point probabilities and different values of the signal-to-noise ratio (SNR). The analysis indicates which detector can be adequate choice for the certain distribution of constellation point probabilities and the SNR. Besides this, for the straightforward performance assessment of the MAP detector we derive a formula for the symbol error probability. Our analysis also points out that the nonuniform distribution of the constellation points probabilities does not necessarily improve the symbol error probability. With the aim to decrease the symbol error probability we propose a method for defining constellation point probabilities. The presented results show that PAM constellation designed by utilizing the method we propose significantly outperforms the conventional PAM constellation in terms to the symbol error probability

Eight-dimensional Polarization-ring-switching Modulation Formats

We propose two 8-dimensional (8D) modulation formats (8D-2048PRS-T1 and 8D-2048PRS-T2) with a spectral efficiency of 5.5 bit/4D-sym, where the 8 dimensions are obtained from two time slots and two polarizations. Both formats provide a higher tolerance to nonlinearity by selecting symbols with nonidentical states of polarization (SOPs) in two time slots. The performance of these novel 8D modulation formats is assessed in terms of the effective signal-to-noise ratio (SNR) and normalized generalized mutual information. 8D-2048PRS-T1 is more suitable for high SNRs, while 8D-2048PRS-T2 is shown to be more tolerant to nonlinearities. A sensitivity improvement of at least 0.25 dB is demonstrated by maximizing normalized generalized mutual information (NGMI). For a long-haul nonlinear optical fiber transmission system, the benefit of mitigating the nonlinearity is demonstrated and a reach increase of 6.7% (560 km) over time-domain hybrid four-dimensional two-amplitude eight-phase shift keying (TDH-4D-2A8PSK) is observed

Constellation Shaping in Optical Communication Systems

Exploiting the full-dimensional capacity of coherent optical communication systems is needed to overcome the increasing bandwidth demands of the future Internet. To achieve capacity, both coding and shaping gains are required, and they are, in principle, independent. Therefore it makes sense to study shaping and how it can be achieved in various dimensions and how various shaping schemes affect the whole performance in real systems. This thesis investigates the performance of constellation shaping methods including geometric shaping (GS) and probabilistic shaping (PS) in coherent fiber-optic systems. To study GS, instead of considering machine learning approaches or optimization of irregular constellations in two dimensions, we have explored multidimensional lattice-based constellations. These constellations provide a regular structure with a fast and low-complexity encoding and decoding. In simulations, we show the possibility of transmitting and detecting constellation with a size of more than 10^{28} points which can be done without a look-up table to store the constellation points. Moreover, improved performance in terms of bit error rate, symbol error rate, and transmission reach are demonstrated over the linear additive white Gaussian noise as well as the nonlinear fiber channel compared to QAM formats.Furthermore, we investigate the performance of PS in two separate scenarios, i.e., transmitter impairments and transmission over hybrid systems with on-off keying channels. In both cases, we find that while PS-QAM outperforms the uniform QAM in the linear regime, uniform QAM can achieve better performance at the optimum power in the presence of transmitter or channel nonlinearities

Multidimensional Optimized Optical Modulation Formats

This chapter overviews the relatively large body of work (experimental and theoretical) on modulation formats for optical coherent links. It first gives basic definitions and performance metrics for modulation formats that are common in the literature. Then, the chapter discusses optimization of modulation formats in coded systems. It distinguishes between three cases, depending on the type of decoder employed, which pose quite different requirements on the choice of modulation format. The three cases are soft-decision decoding, hard-decision decoding, and iterative decoding, which loosely correspond to weak, medium, and strong coding, respectively. The chapter also discusses the realizations of the transmitter and transmission link properties and the receiver algorithms, including DSP and decoding. It further explains how to simply determine the transmitted symbol from the received 4D vector, without resorting to a full search of the Euclidean distances to all points in the whole constellation

Capacity of a Nonlinear Optical Channel with Finite Memory

The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about 10 symbols or more. These results confirm previous results that the GN model is accurate for uncoded transmission. However, when coding is considered, the results obtained using the finite-memory model are very different from those obtained by previous models, even when the channel memory is large. In particular, the peaky behavior of the channel capacity, which has been reported for numerous nonlinear channel models, appears to be an artifact of applying models derived for independent input in a coded (i.e., dependent) scenario

Multidimensional Constellation Shaping for Coherent Optical Communication Systems

To overcome the increasing demands for Internet traffic, exploiting the available degrees of freedom in optical communication systems is necessary. In this thesis, we study how constellation shaping can be achieved in various dimensions and how various shaping schemes affect the whole performance in real systems. This thesis investigates the performance of constellation shaping methods including geometric shaping and probabilistic shaping in coherent fiber-optic systems.To study geometric shaping, we explore multidimensional lattice-based constellations. These constellations provide a regular structure with fast and low-complexity encoding and decoding. We show the possibility of transmitting and detecting constellations with a size of more than 10^{28} points, which can be done without a look-up table to store the constellation points. Moreover, we experimentally realize our proposed multidimensional modulation formats in long-haul optical communication systems.Finally, we investigate the performance of probabilistically shaped quadrature amplitude modulation and compare it with uniform cross quadrature amplitude modulation in the presence of transmitter impairments, and with uniform quadrature amplitude modulation in links where higher-order modulation formats co-propagate with on-off keying wavelength channels