Ana María Cárdenas Soto

Evaluation and compensation of interchannel interference effects in a 16-QAM Nyquist-WDM system with LMS equalization

Nyquist-WDM systems have been proposed as a promising solution in multicarrier transmissions to be a technology which could face the elastic networks challenges. In the spectrum, Nyquist-WDM requires an ideal rectangle, characteristic that is impossible in practice. With a channel spacing near or equal to baud rate, the roll-off factor of the pulse shaping filter has influence in the channel spreading, generating spectral overlapping between adjacent channels. This phenomenon is called Interchannel Interference (ICI). This research evaluates the impact of the ICI effects in a 5 × 32 Gbaud Nyquist-WDM system, with 16-QAM modulation. The impact of the Roll-off and channel spacing value is analyzed for distances up to 5 km. Error Vector Magnitude in constellation and bit error rate are estimated according to channel spacing penalty, roll-off factor, and transmission distance variation. ICI effects minimization using LMS algorithm in the digital coherent receiver is proposed. LMS adapts the coefficients of the adaptive filter making equalization by a training sequence, superchannels signals are received in independent coherent receivers in a joint equalization among channels. The performance of the systems is improved with LMS equalization, reducing the log(BER) from -1 to -11 for 5 km in a channel spacing equal to the symbol rate, and from ~2 to ~20 for a channel spacing penalty of 1.5 GHz, with roll-off factor Nyquist filter of 0.15, which is feasible in practice in the pulse shaping filter at the transmitter.

Adaptive nonsymmetrical demodulation based on machine learning to mitigate time-varying impairments

We proposed and experimentally demonstrated a machine learning-based nonsymmetrical demodulation technique for a DSP-enabled receiver, with the aim of enabling time-varying nonlinear mitigation. Experimental results showed that nonsymmetrical demodulation can reduce the SER by up to 0.7 decades, when assuming time frames consisting of 10 k symbols and fiber transmission of 250 km. The proposed technique is transparent to the specific source of nonlinearity, which makes it simple yet robust. This machine learning method may also allow simplification of the standard demodulation blocks in particular the equalizer. Employing short time windows for demodulation further enables inline optical monitoring, which is a valuable diagnostic tool for future terabit optical communication systems.

Digital pre-distortion in QAM formats based on adaptive complex multipliers

We propose and numerically validate a method to redistribute QAM symbols on the constellation diagram aiming to minimize channel transmission impairment effects. The pre-distortion method is based on the design of digital complex multipliers and it is tested by simulation in a Radioover-Fiber (RoF) system. Assuming different channel responses, ten types of redistributed formats are generated by applying the proposed digital pre-distortion method of data-symbols in the constellation diagram on classical 8-QAM and 16-QAM formats. The robustness of the redistributed modulation formats is evaluated in comparison with classical m-QAM formats in terms of the bit-error-rate (BER), for a transmission distance of 40 and 80 km over uncompensated single-mode fiber links at 1 and 10 Gb/s respectively. It is shown that 8-QAM Offset-π /4 at 80 km with a bit rate of 10 Gb/s attains a gain in log(BER) of 2.3 decades, and improves the reach up to 94.5 km when compared to classical 8-QAM. On the other hand, 16-QAM Offset-π/4 at 40 km achieves a gain of 1.7 decades improving the reach up to 50 km for the same error level having the classical 16-QAM as reference. With these results the future work will enable a methodology to design robust constellations against linear impairments of optical channel.

Enhanced intercarrier interference mitigation based on encoded bit-sequence distribution inside optical superchannels

Abstract. In the context of gridless optical multicarrier systems, we propose a method for intercarrier interference (ICI) mitigation which allows bit error correction in scenarios of nonspectral flatness between the subcarriers composing the multicarrier system and sub-Nyquist carrier spacing. We propose a hybrid ICI mitigation technique which exploits the advantages of signal equalization at both levels: the physical level for any digital and analog pulse shaping, and the bit-data level and its ability to incorporate advanced correcting codes. The concatenation of these two complementary techniques consists of a nondata-aided equalizer applied to each optical subcarrier, and a hard-decision forward error correction applied to the sequence of bits distributed along the optical subcarriers regardless of prior subchannel quality assessment as performed in orthogonal frequency-division multiplexing modulations for the implementation of the bit-loading technique. The impact of the ICI is systematically evaluated in terms of bit-error-rate as a function of the carrier frequency spacing and the roll-off factor of the digital pulse-shaping filter for a simulated 3×32-Gbaud single-polarization quadrature phase shift keying Nyquist-wavelength division multiplexing system. After the ICI mitigation, a back-to-back error-free decoding was obtained for sub-Nyquist carrier spacings of 28.5 and 30 GHz and roll-off values of 0.1 and 0.4, respectively.

Linear carrier predistortion for inter-carrier interference mitigation in multicarrier-RF systems

Linear carrier pre-distortion specifically designed to rearrange the spatial distribution of data-symbols in the constellation diagram is proposed for Intercarrier Interference Mitigation in an electrical multicarrier (MC) system. The linear carrier pre-distortion is achieved by convolving a pre-designed transfer function with each radiofrequency carrier previous by means of a redistribution of the QPSK data-symbols over IQ plane for each carrier composing the MC signal before the up-conversion to RF. At the receiver, an adaptive linear equalizer (Least Mean Squared) re-constructs the QPSK constellations for each radiofrequency carrier after signal demodulation. Our proposal is numerically validated by simulation in a 3 × 0.5 Gbaud Nyquist PSK multicarrier system. For BPSK, the inter-carrier overlapping percentage (IOP) takes values from 90% down to 75%, this enables a reduction of 15% in carrier spacing, and a symbol error rate (SER) gain of 1.2 dB for a Nyquist separation of 0.75. Whereas for QPSK, the reduction achieved is 15%, and the SER gain is 1.8 dB for a Nyquist separation of 0.85 (Being ideal a carrier spacing equal to 100% as carrier bandwidth). We believe that the proposed linear carrier pre-distortion technique enables further investigations on signal constellation re-distributions allowing controlled inter-carrier interference in the context of next broadband generation technologies.

Demodulation of m-ary non-symmetrical constellations using clustering techniques in optical communication systems

In this paper, clustering techniques such as k-means and Fuzzy c-means (FCM) are applied for phase recovery and demodulation of m-ary non-symmetrical constellations, distorted by linear and nonlinear impairments in optical fiber transmission systems. The effect of distortions on data-symbols corresponds to an emulation of electro-optical conversion plus system components impairments, and other phenomenal arisen during optical propagation. These distortions can be observed in a constellation diagram as data-symbol forming irregular elliptical shapes with angular-rotations taking as a reference the ideal positions of the data-symbols in classical modulation. By numerical simulation, the results show that the k-means algorithm according to index values using Silhouette coefficient, find the centroids and estimate the symbols that belong to that cluster in a lower computational time, improving among 2.12 and 3.19 times with respect to FCM. The system performance for the bit error rate (BER) is increased by using the k-means algorithm in 0.44 decades for BPSK, 0.34 decades using QPSK, 0.38 decades for 8-QAM, and 0.36 decades for 16-QAM. For FCM, lower improvements comparing to k-means in m-PSK, but attain gains of 0.20 and 0.33 decades for 8-QAM and 16-QAM, respectively. Although these improvements are conservatives, the whole set of constellations exhibit a better performance than conventional demodulation method for OSNR levels higher than 15 dB. We believe that clustering techniques are promissory for phase-recovery and signal demodulation in non-symmetrical m-ary modulation schemes under irregular decision boundaries.

Mitigation of linear inter-channel interference for sub-Nyquist spacing in optical multicarrier systems

Nyquist optical multicarrier transmission based on gridless wavelength division multiplexing (WDM) technology suffers by inter-channel interference (ICI) due to carrier overlapping. Even though the unpredictable effect of the ICI has been treated as a non-linear noise, temporal correlations of data symbols may partially allow ICI mitigation by linear equalization techniques. In this research, we systematically evaluate and mitigate the impact of the ICI for sub-Nyquist carrier spacing in a multicarrier system by applying a linear equalization technique. System characterization is presented in terms of bit-error-rate (BER) estimation as a function of carrier frequency spacing variations, the roll-off factor of the digital Nyquist pulse-shaping filter, and transmission distance scenarios. The mitigation of the ICI effects is carried out by the linear constant modulus algorithm (CMA) equalizer after compensating fiber linear impairments and before the sampling process at the digital coherent receiver, in a 3 × 32 Gbaud single-polarization Nyquist quadrature phase shift keying (QPSK) multicarier system. The CMA updates the coefficients of an adaptive digital filter based on a blind estimation technique to minimize the error function defined by the constant modulus of QPSK signals. System performance is improved after the linear equalization, reaching optical transmission distance without amplification of up to 130 km assuming a 15% FEC limit. Furthermore, the linear equalization allows a sub-Nyquist spacing of 30.5 GHz assuming a 15% FEC limit. Moreover, the adopted equalization technique relaxes the computational cost of the digital filtering, enabling roll-off factor values of up to 0.3 for 120 km transmission assuming 9% FEC limit.

Characterization and compensation of induced non-linear phase offset in multicarrier optical systems based on clustering techniques

Multicarrier optical systems are expected to allow data transmission above 100 Gbps in the next generation long-haul optical networks with a minimum spectral separation between carriers to increase spectral efficiency. Nevertheless, closely separation between optical carriers cause Interchannel interference (ICI) due to the inherent non-linear effects associated to optical fiber such as self-phase modulation (SPM) and cross-phase modulation (XPM). Both SPM and XPM induce a phase shifting in transmitted frequency multiplexed signals. This phase shifting can be observed as a rotated constellation diagram of phase-modulated signals and it degrades system performance by increasing the Bit-Error-Rate (BER). In this paper, a phase offset estimation and compensation using k-means clustering algorithm is validated by simulation in a multicarrier optical system. The optical carriers are modulated in PSK and 16-QAM formats at 32 Gbaud and signal transmission is simulated over standard single-mode fiber (SSMF). System performance is analyzed as a function of frequency carrier spacing and transmission distances. After Phase correction a decrease of the BER is achieved, demonstrating the feasibility and robustness of the proposed clustering technique to compensate induced nonlinear constellations rotations in future multicarrier optical networks.

Spectrum Balancing algorithms comparison for ADSL downstream

ADSL is the most popularized access technology worldwide. Because its deployed over the conventional twisted pair telephone network. All DSL systems present a higher effect of crosstalk, which limits its performance considerably. Several research and industry groups have worked on improving DSLs systems performance to exploit the existent copper loop plant, as a previous step of the implementation of full-optical solutions in the access network. In this paper, we present a brief description of ADSL and the system model of DSL technologies that implement a DMT modulation scheme. We also mention the three most important Spectrum Balancing algorithms, which is a kind of methods that improves systems performance finding optimal power spectral density allocations. These algorithms are subject to comparison by a simulation scenario of two ADSL systems. Finally, the results of data rates and power spectral densities are analyzed in order to compare the performance of each algorithm.