# Orthogonal frequency-division multiplexing for optical communications

## Abstract/Contents

- Abstract
- The drive towards higher spectral efficiency and maximum power efficiency in optical systems has generated renewed interest in the optimization of optical transceivers. In this work, we study the different optical applications: Wide Area Networks (WANs), Metropolitan Area Networks (MANs), Local Area Networks (LANs) and Personal Area Networks (PANs). In WANs or long-haul systems, orthogonal frequency-division multiplexing (OFDM) can compensate for linear distortions, such as group-velocity dispersion (GVD) and polarization-mode dispersion (PMD), provided the cyclic prefix is sufficiently long. Typically, GVD is dominant, as it requires a longer cyclic prefix. Assuming coherent detection, we show how to analytically compute the minimum number of subcarriers and cyclic prefix length required to achieve a specified power penalty, trading off power penalties from the cyclic prefix and from residual inter-symbol interference (ISI) and inter-carrier interference (ICI). We derive an analytical expression for the power penalty from residual ISI and ICI. We also show that when nonlinear effects are present in the fiber, single-carrier with digital equalization outperforms OFDM for various dispersion maps. We also study the impairments of electrical to optical conversion when using Mach-Zehnder (MZ) modulators. OFDM has a high peak-to-average ratio (PAR), which can result in low optical power efficiency when modulated through a Mach-Zehnder (MZ) modulator. In addition, the nonlinear characteristic of the MZ can cause significant distortion on the OFDM signal, leading to in-band intermodulation products between subcarriers. We show that a quadrature MZ with digital pre-distortion and hard clipping is able to overcome the previous impairments. We consider quantization noise and compute the minimum number of bits required in the digital-to-analog converter (D/A). Finally, we discuss a dual-drive MZ as a simpler alternative for the OFDM modulator, but our results show that it requires a higher oversampling ratio to achieve the same performance as the quadrature MZ. In MANs, we discuss the use OFDM for combating GVD effects in amplified direct-detection (DD) systems using single-mode fiber. We review known direct-detection OFDM techniques, including asymmetrically clipped optical OFDM (ACO-OFDM), DC-clipped OFDM (DC-OFDM) and single-sideband OFDM (SSB-OFDM), and derive a linearized channel model for each technique. We present an iterative procedure to achieve optimum power allocation for each OFDM technique, since there is no closed-form solution for amplified DD systems. For each technique, we minimize the optical power required to transmit at a given bit rate and normalized GVD by iteratively adjusting the bias and optimizing the power allocation among the subcarriers. We verify that SSB-OFDM has the best optical power efficiency among the different OFDM techniques. We compare these OFDM techniques to on-off keying (OOK) with maximum-likelihood sequence detection (MLSD) and show that SSB-OFDM can achieve the same optical power efficiency as OOK with MLSD, but at the cost of requiring twice the electrical bandwidth and also a complex quadrature modulator. We compare the computational complexity of the different techniques and show that SSB-OFDM requires fewer operations per bit than OOK with MLSD. In LANs, we compare the performance of several OFDM schemes to that of OOK in combating modal dispersion in multimode fiber links. We review known OFDM techniques using intensity modulation with direct detection (IM/DD), including DC-OFDM, ACO-OFDM and pulse-amplitude modulated discrete multitone (PAM-DMT). We describe an iterative procedure to achieve optimal power allocation for DC-OFDM, and compare analytically the performance of ACO-OFDM and PAM-DMT. We also consider unipolar M-ary pulse-amplitude modulation (M-PAM) with minimum mean-square error decision-feedback equalization (MMSE-DFE). For each technique, we quantify the optical power required to transmit at a given bit rate in a variety of multimode fibers. For a given symbol rate, we find that unipolar M-PAM with MMSE-DFE has a better power performance than all OFDM formats. Furthermore, we observe that the difference in performance between M-PAM and OFDM increases as the spectral efficiency increases. We also find that at a spectral efficiency of 1 bit/symbol, OOK performs better than ACO-OFDM using a symbol rate twice that of OOK. At higher spectral efficiencies, M-PAM performs only slightly better than ACO-OFDM using twice the symbol rate, but requires less electrical bandwidth and can employ analog-to-digital converters at a speed only 81% of that required for ACO-OFDM. In PANs, we evaluate the performance of the three IM/DD OFDM schemes in combating multipath distortion in indoor optical wireless links, comparing them to unipolar M-PAM with MMSE-DFE. For each modulation method, we quantify the received electrical SNR required at a given bit rate on a given channel, considering an ensemble of 170 indoor wireless channels. When using the same symbol rate for all modulation methods, M-PAM with MMSE-DFE has better performance than any OFDM format over a range of spectral efficiencies, with the advantage of M-PAM increasing at high spectral efficiency. ACO-OFDM and PAM-DMT have practically identical performance at any spectral efficiency. They are the best OFDM formats at low spectral efficiency, whereas DC-OFDM is best at high spectral efficiency. When ACO-OFDM or PAM-DMT are allowed to use twice the symbol rate of M-PAM, these OFDM formats have better performance than M-PAM. When channel state information is unavailable at the transmitter, however, M-PAM significantly outperforms all OFDM formats. When using the same symbol rate for all modulation methods, M-PAM requires approximately three times more computational complexity per processor than all OFDM formats and 63% faster analog-to-digital converters, assuming oversampling ratios of 1.23 and 2 for ACO-OFDM and M-PAM, respectively. When OFDM uses twice the symbol rate of M-PAM, OFDM requires 23% faster analog-to-digital converters than M-PAM but OFDM requires approximately 40% less computational complexity than M-PAM per processor.

## Description

Type of resource | text |
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Form | electronic; electronic resource; remote |

Extent | 1 online resource. |

Publication date | 2011 |

Issuance | monographic |

Language | English |

## Creators/Contributors

Associated with | Fernandes Barros, Daniel Jose | |
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Associated with | Stanford University, Department of Electrical Engineering | |

Primary advisor | Kahn, Joseph | |

Thesis advisor | Kahn, Joseph | |

Thesis advisor | Gill, John T III | |

Thesis advisor | Widrow, Bernard, 1929- | |

Advisor | Gill, John T III | |

Advisor | Widrow, Bernard, 1929- |

## Subjects

Genre | Theses |
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## Bibliographic information

Statement of responsibility | Daniel Jose Fernandes Barros. |
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Note | Submitted to the Department of Electrical Engineering. |

Thesis | Thesis (Ph.D.)--Stanford University, 2011. |

Location | electronic resource |

## Access conditions

- Copyright
- © 2011 by Daniel Jose Fernandes Barros
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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