Moshe Nazarathy 1 , Jacob Khurgin 2 , Rakefet Weidenfeld 1 , Yehuda Meiman 3 , Pak Cho 3 Reinhold Noe 4 and Isaac Shpantzer 3 1: Electrical Engineering Department, Technion, Israel Institute of Technology, Haifa 32000, Israel nazarat@ ee.technion.ac.il.+972-4-829-3917, fax: +972-4-8360-981 2: Department of Electrical & Computer Engineering, Johns Hopkins University, Baltimore, MD, USA. 3: Celight Inc., Silver Spring, MD, USA. 4:Optical Communication and High-Frequency Engineering, Univ. Paderborn, Germany Abstract: We develop a novel all-analytic model of FWM generation over dispersive multi- span coherent OFDM long-haul links, leading to a new phased-array effect. The nonlinear FWM impairment may be mitigated by destructive interference of intermodulation products. © 2008 Optical Society of America OCIS codes: (060.1660) Coherent Communication; (060.5060) Phase Modulation. 1. Introduction and overview Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) is emerging as a key optical trans- mission technique [1-4], resilient to Chromatic Dispersion (CD) and PMD, due to the long symbol length of the in- dividual data tributaries carried over a multitude of low-rate orthogonal sub-channels. The residual CD may be fur- ther suppressed by digital Dispersion Compensation (DC) in the frequency domain. The remaining main factor limit- ing performance is then the Four-Wave-Mixing (FWM) impairment. Lowery [2] provided an analytic estimate of FWM generation, assuming a dispersion-free system. We point out that although the dispersive phase mismatch walkoff between adjacent subcarriers is negligible, the overall effect of CD on FWM over the full frequency band may be appreciable for a high-speed OFDM system occupying an extended bandwidth of tens of GHz (the dispersive walkoff is large between carriers well separated in the band). It follows that by neglecting CD, [2] merely provided a loose upper bound on the impact of the FWM impairment. An understanding of the interaction between CD and FWM, including possible interactions among multiple spans, is critical to CO-OFDM system analysis and design. This paper develops for the first time a rigorous analytic model of BER performance of long-haul CO-OFDM sys- tems, evaluating the Q-factors for QPSK transmission over the sub-carriers in terms of compact closed-form expres- sions averaging the contributions of all triplets of intermodulation products (IPs), properly accounting for the reduc- tion in the efficiency of FWM generation due to CD-induced phase-mismatch. A new consequence of our analysis is that, unlike predicted in [2] for the CD-free case, the FWM contributions of the individual spans in a multi-span long-haul link do not add up in-phase. Rather, we prove that the individual fiber spans act as antennas in a very long one-dimensional phased-array. Akin to the presence of nulls in the radiation pattern of a phased-array, destructive interference may onset between the FWM contributions of the individual fiber spans, e.g. for the OFDM system de- scribed in this paper, we attain ~16.5 dB of FWM reduction, averaged over all IPs. We developed our analytical model to account for CD+FWM. The model was then applied to analyze the perfor- mance of a state-of-the-art coherent system transmitting a 102.4 Gbps OFDM signal comprising M=128 QPSK sub- channels, each operating at 200 Msym/sec with polarization multiplexing: /sec sec 128 200 2 2 102.4 Msym bit Gbit Ch Pol sym Ch pol       . At the subcarrier separation of 200 v  MHz, the total OFDM Bandwidth is 25.6 B M v   GHz. Previewing our key findings, we first assume that the only mechanism present were the reduction in FWM efficiency over each indi- vidual span due to phase-mismatch. Then such hypothesis would yield a 4 10 BER   over 30 spans, each of 80 span L Km  (assume G.652 standard fiber with sec 17 p nm Km D   , 0.22 / dB Km   , and optical amplifier gain and noise figure span L G e   , 6.5 N F dB  ). Remarkably, once our newly discovered phased-array FWM effect is mod- eled in, the ideal transmission range can be significantly extended from 30 spans (2400 Km) to 82 spans (6560 Km). 2. Analysis of dispersive FWM including the phased-array multi-span effect Our analytic model is rigorous within the framework of the undepleted pumps assumption [5] (which is very accurate given the relatively low level of NonLinear (NL) FWM fluctuations required at 4 10 BER   ). Here the “pumps” are the QPSK-modulated subcarriers. We worked out the FWM generation by two alternative independent methods: The FWM Impairment in Coherent OFDM Compounds on a Phased-Array Basis over Dispersive Multi-Span Links a296_1.pdf CWA4.pdf © 2008 OSA: COTA/ICQI/IPNRA/SL