PAPR Reduction Techniques for Coherent Optical OFDM Transmission Bernhard Goebel, Graduate Student Member, IEEE, Stephan Hellerbrand, Graduate Student Member, IEEE, Norman Haufe, Norbert Hanik, Member, IEEE Institute for Communications Engineering, Technische Universität München, D-80290 Munich, Germany E-mail: Bernhard.Goebel@tum.de ABSTRACT In coherent optical OFDM systems, the large peak-to-average power ratio (PAPR) gives rise to signal impairments through the nonlinearity of modulator and fiber. We review the most prominent PAPR reduction techniques that have been proposed for mitigating the impairments with regard to their reduction capability, computational complexity and redundancy. Simulation results are presented for Clipping, Selected Mapping, Active Constellation Extension and Trellis Shaping. Keywords: modulation, OFDM, coherent detection, nonlinear fiber effects, PAPR, coding. 1. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) is considered one of the most promising transmission schemes for future 100 Gigabit Ethernet (100 GbE) networks. In combination with coherent detection, it offers virtually unlimited electronic compensation of chromatic dispersion and PMD  as well as record spectral efficiencies -. One major drawback of OFDM signals is their large peak-to-average power ratio (PAPR) which gives rise to distortions caused by nonlinear devices such as A/D converter, external modulator and transmission fiber . Upon transmission along the fiber, the Kerr effect creates distortions through four-wave mixing (FWM) between OFDM subcarriers; the strength of these FWM products depends on the signal’s PAPR . Various PAPR reduction techniques have been proposed in a wireless communications context  and for optical OFDM systems , -. In Section 2, we review the most important PAPR reduction methods for coherent optical OFDM systems with respect to their performance, complexity and introduced redundancy. Section 3 presents numerical simulation results, and Section 4 concludes the paper. 2. PAPR REDUCTION TECHNIQUES FOR OPTICAL OFDM SYSTEMS In OFDM, a high-data-rate bit stream is demultiplexed into N lower-rate streams which modulate N equally spaced subcarriers. The data symbols [X0, X1,…,XN-1], which may be taken e.g. from a QPSK or 16-QAM signal constellation, form a complex OFDM symbol (or data block) of length NT as x(t ) = 1
⋅ e j 2πΔft , 0 ≤ t ≤ NT ,
where Δf = 1 / NT is the subcarrier spacing . For a sufficiently large N, the real and imaginary part of x(t) follow a Gaussian distribution and the signal power has a central chi-square distribution with two degrees of freedom , so that very large power peaks occur with nonzero probability. When the PAPR is calculated from samples of the continuous signal (1), sampling at a rate of at least four times the Nyquist rate is recommendable to fully capture peaks located in between samples , . PAPR reduction methods can be broadly classified into two categories. In one group of methods, the signal is manipulated in a way such that peaks are removed; clipping, active constellation extension (ACE) and precoding are examples for this approach. In contrast, selected mapping (SLM) and trellis shaping (TS) are schemes which add redundancy to the signal, thereby creating a degree of freedom to reshape the signal or to replace OFDM symbols with a particularly large PAPR. In general, PAPR reduction methods are difficult to compare. For a rough comparison, it is common to use the (complementary) cumulative distribution function (CCDF) of the PAPR depicted in Fig. 1 (right). The aim of PAPR reduction schemes is to shift the CCDF curve as much to the left as possible. However, the complexity, redundancy and the actual benefit of a method cannot be judged from its CCDF alone. 2.1 Clipping, Active Constellation Extension and Precoding Clipping all amplitudes that exceed...
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