Gunnar Jacobsen

Chromatic dispersion compensation in coherent transmission system using digital filters

We present a comparative analysis of three popular digital filters for chromatic dispersion compensation: a time-domain least mean square adaptive filter, a time-domain fiber dispersion finite impulse response filter, and a frequency-domain blind look-up filter. The filters are applied to equalize the chromatic dispersion in a 112-Gbit/s non-return-to-zero polarization division multiplexed quadrature phase shift keying transmission system. The characteristics of these filters are compared by evaluating their applicability for different fiber lengths, their usability for dispersion perturbations, and their computational complexity. In addition, the phase noise tolerance of these filters is also analyzed.

Impact of phase noise in weakly coherent systems: a new and accurate approach

Coherent optical systems for future broadband local loops may use lasers with significant phase noise, manifest as broad linewidths. This phase noise can be accommodated if the receiver is correctly designed, i.e. if nonsynchronous (envelope or square-law) IF demodulation is used and sufficient IF bandwidth is provided. It is difficult to analyze the performance of a coherent optical receiver when the signals are corrupted by phase noise. The central theoretical problem arising from filtering a signal with phase noise is defined in a particular form which permits the derivation of the forward or Fokker-Planck partial differential equation for probability density of the output voltage of the receiver. The results are used to discuss the IF bandwidth required for optical heterodyne receivers for amplitude-shift-keying (ASK) signals. >

Analytical estimation of phase noise influence in coherent transmission system with digital dispersion equalization

We present a novel investigation on the enhancement of phase noise in coherent optical transmission system due to electronic chromatic dispersion compensation. Two types of equalizers, including a time domain fiber dispersion finite impulse response (FD-FIR) filter and a frequency domain blind look-up (BLU) filter are applied to mitigate the chromatic dispersion in a 112-Gbit/s polarization division multiplexed quadrature phase shift keying (PDM-QPSK) transmission system. The bit-error-rate (BER) floor in phase estimation using an optimized one-tap normalized least-mean-square (NLMS) filter, and considering the equalization enhanced phase noise (EEPN) is evaluated analytically including the correlation effects. The numerical simulations are implemented and compared with the performance of differential QPSK demodulation system.

The effect of laser linewidth on coherent optical receivers with nonsynchronous demodulation

Recent theoretical analysis of the effect of using lasers with significant linewidths in coherent optical fiber transmission systems has shown how the design of the optical receiver, particularly the IF stage, affects the sensitivity. This paper reviews this theory for two classes of coherent systems-those making a differential phase measurement, and those not using phase information-where the requirements on laser linewidth are not stringent. We discuss the factors that affect the performance of systems with significant laser phase noise. Wherever possible, we compare the theoretical results with published system experiments. We show that our theory fits the experimental data well and indicates why experimental results have fallen short of the theoretical limits.

Tuned front-end design for heterodyne optical receivers

A theoretical analysis of the noise performance of optical receivers with front-end tuning, suitable for wideband coherent systems, is presented. An algorithm for choosing the values of the tuning components in the front end so as to minimize the thermal noise output power has been developed. This theory is applied to the well-known simple parallel and serial tuning configurations and also to three more advanced designs. It is shown that any tuning is better than none in the wide-bandwidth designs considered and that the more advanced designs yield up to 12-dB reduction in thermal noise power. Two of the designs can be implemented with discrete components and should yield shot-noise-limited detection with 50-100 mu W of local oscillator power in receivers with 5-GHz bandwidth. The practical problem of equalizing the front-end response is considered, and it is shown that good performance can be expected using realizable components. >

Multichannel CPFSK coherent optical communications systems

A detailed theoretical analysis of multichannel coherent CPFSK communications systems is presented. The analysis accounts for the crosstalk between adjacent channels, the intersymbol interference and correlation between noise samples stemming from the limited IF bandwidth the non-Gaussian statistics of the noise at the decision gate, and the impact of the laser phase noise. It is found that the IF bandwidth needed to avoid intersymbol interference is 2.2 bit rates for a modulation index m=1; it is larger for other modulation index values. For m=1, receiver sensitivity is within 1 dB of the shot noise limit, and the electrical domain channel spacing can be as small as 2.05 bit rates with 1-dB sensitivity penalty. The foregoing conclusions are valid for a negligibly narrow linewidth; the degradation due to phase noise is shown to be modest as long as the linewidth does not exceed 1% of the bit rate if m=1. Larger linewidth can be tolerated if the modulation index is larger than unity. >

Receiver implemented RF pilot tone phase noise mitigation in coherent optical nPSK and nQAM systems.

In this paper, a novel method for extracting an RF pilot carrier signal in the coherent receiver is presented. The RF carrier is used to mitigate the phase noise influence in n-level PSK and QAM systems. The performance is compared to the use of an (ideal) optically transmitted RF pilot tone. As expected an electronically generated RF carrier provides less efficient phase noise mitigation than the optical RF. However, the electronically generated RF carrier still improves the phase noise tolerance by about one order of magnitude in bit error rate (BER) compared to using no RF pilot tone. It is also found, as a novel study result, that equalization enhanced phase noise--which appears as correlated pure phase noise, amplitude noise and time jitter-cannot be efficiently mitigated by the use of an (optically or electrically generated) RF pilot tone.

Multichannel system design using optical preamplifiers and accounting for the effects of phase noise, amplifier noise, and receiver noise

A rigorous and accurate model for multichannel direct detection systems where optical preamplification is used is presented. The model accounts for the influence of an optical bandlimiting filter as well as of a polarization filter. Effects of laser phase noise, of spontaneous emission noise from the amplifier, and of shot noise and thermal noise in the receiver front end are accounted for. The predicted phase noise penalty for a single channel configuration is found. For multichannel system design, it is found that a system with many optical channels and no phase noise should have a channel separation of 9.4 bit rates to have less than 1-dB worst-case crosstalk penalty. For a linewidth of 27% of the bit rate in each channel the required spacing increases to 25 bit rates or more. >

EEPN and CD study for coherent optical nPSK and nQAM systems with RF pilot based phase noise compensation

A radio frequency (RF) carrier can be used to mitigate the phase noise impact in n-level PSK and QAM systems. The systems performance is influenced by the use of an RF pilot carrier to accomplish phase noise compensation through complex multiplication in combination with discrete filters to compensate for the chromatic dispersion (CD). We perform a detailed study comparing two filters for the CD compensation namely the fixed frequency domain equalizer (FDE) filter and the adaptive least-mean-square (LMS) filter. The study provides important novel physical insight into the equalization enhanced phase noise (EEPN) influence on the system bit-error-rate (BER) versus optical signal-to-noise-ratio (OSNR) performance. Important results of the analysis are that the FDE filter position relative to the RF carrier phase noise compensation module provides a possibility for choosing whether the EEPN from the Tx or the LO laser influences the system quality. The LMS filter works very inefficiently when placed prior to the RF phase noise compensation stage of the Rx whereas it works much more efficiently and gives almost the same performance as the FDE filter when placed after the RF phase noise compensation stage.

Study of EEPN mitigation using modified RF pilot and Viterbi-Viterbi based phase noise compensation

We propose--as a modification of the optical (RF) pilot scheme--a balanced phase modulation between two polarizations of the optical signal in order to generate correlated equalization enhanced phase noise (EEPN) contributions in the two polarizations. The method is applicable for n-level PSK system. The EEPN can be compensated, the carrier phase extracted and the nPSK signal regenerated by complex conjugation and multiplication in the receiver. The method is tested by system simulations in a single channel QPSK system at 56 Gb/s system rate. It is found that the conjugation and multiplication scheme in the Rx can mitigate the EEPN to within ½ orders of magnitude. Results are compared to using the Viterbi-Viterbi algorithm to mitigate the EEPN. The latter method improves the sensitivity more than two orders of magnitude. Important novel insight into the statistical properties of EEPN is identified and discussed in the paper.