IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 5, MARCH 1, 2014 497 Channel Equalization Using Independent Component Analysis in PDM-CO-OFDM Xiang Li, Student Member, IEEE, Wen-De Zhong, Senior Member, IEEE, Arokiaswami Alphones, Senior Member, IEEE , and Changyuan Yu, Member, IEEE Abstract— We propose a channel equalization method without training symbols (TSs) based on the independent component analysis (ICA) for polarization-division-multiplexing coherent-optical orthogonal-frequency-division-multiplexing (PDM-CO-OFDM) transmission systems. Compared with the conventional TS-based channel equalization method, the proposed method with 80 collected OFDM symbols shows a better transmission performance in the case of QPSK modulation format, and almost the same performance in the case of 16-quadrature amplitude modulation (QAM) format. In addition, we propose a new channel frequency response initialization method to solve the permutation indeterminacy and complex uncertain scaling problems in ICA-based channel equalization. The proposed initialization method shows faster convergence speed than the conventional random initialization method in the channel equalization process. Finally, we examine the number of OFDM symbols required for the proposed ICA-based channel equalization. This study shows that 40 and 80 OFDM symbols are sufficient for the QPSK and 16-QAM formats, respectively. Since the proposed ICA-based channel equalization method is free of TSs, the spectral efficiency of the PDM-CO-OFDM systems can be improved considerably. Index Terms— Orthogonal-frequency-division-multiplexing (OFDM), independent component analysis (ICA), channel equalization. I. I NTRODUCTION W ITH the increasing interest in digital signal processing (DSP) for optical fiber transmission, coherent-optical orthogonal-frequency-division-multiplexing (CO-OFDM) has emerged as a promising modulation format for future optical networks [1]. Polarization division multiplexing CO-OFDM (PDM-CO-OFDM) has been experimentally demonstrated at 1 Tb/s over 600 km transmission [2]. However, compared with single-carrier (SC) transmission system, PDM-CO-OFDM requires periodic training symbols (TSs) at the transmitter side in both polarizations for channel estimation before equal- ization, which increases the system redundancy and reduces the spectral efficiency [3]. Blind channel de-multiplexing for PDM-CO-OFDM was proposed in [4] based on Stokes space, Manuscript received August 14, 2013; revised December 22, 2013; accepted January 10, 2014. Date of publication January 16, 2014; date of current version February 5, 2014. X. Li, W.-D. Zhong, and A. Alphones are with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798 (e-mail: xli14@e.ntu.edu.sg; ealphones@ntu.edu.sg; ewdzhong@ntu.edu.sg). C. Yu is with the Electrical and Computer Engineering Department, National University of Singapore, Singapore 117576, and also with the Agency for Sci- ence, Technology and Research, Institute for Infocomm Research, Singapore 138632 (e-mail: eleyc@nus.edu.sg). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LPT.2014.2300507 where the PDM matrix is assumed to be unitary. However, the following channel estimation and equalization for fiber dispersion are still based on TSs. Independent component analysis (ICA) has been used for polarization de-multiplexing and channel equalization in coherent SC systems with multi-tap ICA algorithms [5]–[8]. In this letter, we propose a new blind channel equalization method based on ICA in PDM-CO-OFDM transmission sys- tems without inserting TSs for channel estimation. We first derive the ICA model for PDM-CO-OFDM and show that only one-tap ICA equalization is required for each OFDM subcarrier in PDM-CO-OFDM systems. We then compare the performance of channel equalizers based on ICA and TSs in a PDM-CO-OFDM transmission system for both QPSK and 16-QAM modulation formats. The bit error rate (BER) performance of the proposed ICA based channel equalizer with 80 collected OFDM symbols is found to be better than that of TSs based channel equalizer in the case of QPSK transmission and similar in the 16-QAM case. Moreover, we propose a new channel frequency response initialization method to solve the permutation indeterminacy and complex uncertain scaling problems in ICA based signal processing methods [9]. Com- pared with conventional random initialization method in ICA [9], the proposed method can also increase the convergence speed in channel equalization process. Finally, the number of OFDM symbols required for the proposed ICA-based channel equalization is examined. It is found that 40 and 80 OFDM symbols are sufficient for QPSK and 16-QAM modulation formats, respectively. It should be noted that the proposed ICA based channel equalization method eliminates the need for TSs and hence the spectral efficiency of PDM-CO-OFDM systems can be improved considerably. Notation:(·) T (·) H will represent transpose and Hermitian operators. Bold face letters denote vectors and matrices. II. PRINCIPLE The PDM-CO-OFDM can be described by a 2 × 2 MIMO OFDM model in frequency domain as [1]  R i x R i y  =  H i xx H i xy H i yx H i yy  T i x T i y  (1) where T i p ( p = x , y ) is the transmitted data with subcarrier index i in polarization p; R i q (q = x , y ) is the received data with subcarrier index i in polarization q ; H i pq is the i -th subcarrier channel frequency response from polarization state q to polarization state p. The noise term is ignored for 1041-1135 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.