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Nyquist signals with low roll-off factors pose a challenge for non-data-aided blind symbol rate estimation problems in long-haul applications. We adopted the nonlinear least squares (NLS) approach to estimate the symbol rate of low roll-off factor signals. This method tolerates chromatic dispersion and additive Gaussian noise. In addition, this method can operate below two samples per symbol, thus enabling low-power-consumption receivers. Simulation and experimental results show that the mean squared error is below $10^{-4}$ with only 3000 samples needed for polarization-division-multiplexed (PDM) quadrature phase-shift keying (QPSK) or quadrature amplitude modulation (QAM) systems with a roll-off factor below 0.1 for an optical signal-to-noise ratio greater than 12 dB. Compared with the maximum likelihood estimation (MLE) method, our proposed method has a more robust performance under low roll-off factor signals and in low-sampling-rate scenarios. The mean squared error remains the same for a nominal symbol rate (i.e., the ratio of the symbol rate to the sampling rate, also widely known as oversampling rate) ranging from 0.1 to 0.9.

This paper proposes a novel and efficient low-complexity chromatic dispersion equalizer (CDE) based on finite impulse response (FIR) filter architecture for polarization-multiplexed coherent optical communication systems. The FIR filter coefficients are optimized by weights to reduce the energy leakage caused by the truncation effect, and then quantization is used uniformly to reduce the number of real number additions and real number multiplications by utilizing the diversity of the quantized coefficients. Using Optisystem 15 to build a coherent optical communication system for simulation and experimental demonstration, the results show that after the filter coefficients are optimized by weights. Compared with the time-domain chromatic dispersion equalizer (TD-CDE), the proposed design has a lower bit error rate (BER) and better equalization effect. When the transmission distance is 4000 km and the system quantization stages M = 16, the multiplication operation and addition operations reduce computing resources by 99% and 43%, and the BER only increases by 5%. Compared with frequency-domain chromatic dispersion equalizer (FD-CDE), widely used in long-distance communication, the multiplication operation reduces computing resources by 30%. The proposed method provides a new idea for high-performance CDE in long-distance coherent optical communication systems.

Chromatic dispersion equalization (CDE) in coherent optical communication systems is extremely critical for subsequent digital signal processing (such as frequency offset estimation and carrier phase recovery). Various methods mentioned in the published literature are not satisfactory when the signal bandwidth is limited. This paper proposes a way of using singular value decomposition least square (SVDLS) to obtain the optimal tap weight of the CDE filter and a method to introduce the adaptive mutation particle swarm optimizer (AMPSO) algorithm into the CDE. We show that the two proposed approaches are based on the best approximation of the frequency domain response of the designed and ideal CDE filter. Compared with the traditional CDE method, which needs to be implemented in the full frequency band, the two methods can be implemented in the narrow frequency band. The simulation shows that the effective bandwidth of the baseband signal is limited by squared-root-raised-cosine (SRRC) pulse shaping with a roll-off factor of 0.25 in different modulation formats (DP-QPSK, DP-16 QAM, DP-64 QAM) when the number of taps of the filter is 131, which is 37.5% less than the full frequency band. The designed filter is superior to the existing filter in terms of filtering effect and implementation complexity.

As optical performance monitoring (OPM) requires accurate and robust solutions to tackle the increasing dynamic and complicated optical network architectures, we experimentally demonstrate an end-to-end optical signal-to-noise (OSNR) estimation method based on the convolutional neural network (CNN), named OptInception. The design principles of the proposed scheme are specified. The idea behind the combination of the Inception module and finite impulse response (FIR) filter is elaborated as well. We experimentally evaluate the mean absolute error (MAE) and root-mean-squared error (RMSE) of the OSNR monitored in PDM-QPSK and PDM-16QAM signals under various symbol rates. The results suggest that the MAE reaches as low as 0.125 dB and RMSE is 0.246 dB in general. OptInception is also proved to be insensitive to the symbol rate, modulation format, and chromatic dispersion. The investigation of kernels in CNN indicates that the proposed scheme helps convolutional layers learn much more than a lowpass filter or bandpass filter. Finally, a comparison in performance and complexity presents the advantages of OptInception.

Symbol rate and chromatic dispersion (CD) are very important for optical performance monitoring. The CD, however, hinders the symbol rate detection. In this paper, we proposed a joint estimation of symbol rate and chromatic dispersion. We show that, when the signal conjugates and multiplies with the delayed replica, the spectral line can be restored. The proposed method provides a fast and simple solution for joint estimation as traditional tentative CD scanning is time consuming. The simulation shows that the root-mean-squared error (RMSE) for CD was 39.5 ps/nm and the symbol rate was 2.4 MHz. For the squared-root-raised-cosine (SRRC) pulse shape with a roll-off factor of 0.1, the experimental results show that 25,000 input samples were needed for an error-free estimation. The RMSE is 105.6 ps/nm and 63.5 kHz for CD and symbol rate, respectively.