Transmission of Waveforms Determined by 7 Eigenvalues with PSK-Modulated Spectral Amplitudes

2-ns waveforms with 7 eigenvalues and their QPSK-modulated spectral amplitudes were optimized by taking constraints of link, transmitter, and receiver into account. In experiment these signals were transmitted with a BER of 3.2E-3 over 1440-km of NZ-DSF fiber spans. Introduction In recent years the modulation of the nonlinear spectrum or detection in this nonlinear domain has been re-discovered and refined for transmission over the fiber in the nonlinear regime. Such schemes are called nonlinear frequency division multiplexing (NFDM) 1,2 . Following the argumentation of Wahls 3 , nonlinear Fourier transform (NFT) based modulation and/or detection is motivated by (1) replacing multi step digital back-propagation (DBP) by a less complex one step NFT scheme, by (2) exploiting the quasi linear propagation behaviour of the nonlinear spectrum for operation beyond the nonlinear threshold, or by (3) using detection schemes working on the nonlinear spectrum rather than on the time domain signal. So far, only limited work has been done on lab implementation of these schemes. Recently, the discrete part of the nonlinear spectrum was modulated by on/off keying of up to 4 eigenvalues 4 or by independently QPSK modulated spectral amplitudes of a 2 eigenvalue soliton 5 . Modulation in the continuous part of the nonlinear spectrum was also demonstrated 6 . In this paper, we present the design of pulses with a high count of 7 eigenvalues and QPSK modulation of spectral amplitudes. The eigenvalues are not all located on the imaginary axis as it was the case in the papers before. For the first time, we demonstrate generation, transmission, and detection of such 7eigenvalue signals in experiment. NFDM Signal Design Our goal was to design a set of finite eigenvalues (carriers), , where the information bits are modulated over spectral amplitudes, independently, provided that the following conditions are fulfilled: (i) Distance between eigenvalues is large enough for reliable detection in Rx in the presence of ASE noise, and numerical limitation of current NFT algorithms. (ii) The largest pulsewidth (duration) of all pulses becomes minimum (highest transmission rate) (iii) The largest bandwidth (BW) of all pulses becomes minimum in Tx and Rx (highest spectral efficiency) (iv) No inter-symbol interference (ISI) between adjacent pulses during the transmission (v) Pick-toaverage power ratio (PAPR) stays in a practical range. It is not yet fully clear how to satisfy all these constraints in general, while these conditions are strongly coupled. We relax the condition (iii) to a given BW limit. We limit the BW in Tx to 12.5 GHz, and BW in Rx to 20 GHz assuming the fiber link length is less than 2000 km, including some BW margin for more precise waveform generation and detection. We define BW (pulse-width, respectively) as the frequency (time) interval holding 99% of pulse energy. We choose a set of 7 eigenvalues as shown in Table 1. The spectral amplitude of each eigenvalue, , has QPSK constellation,