We present a model for Rx ISI effects using a new and completely general and rigorous dynamic Rx model for-mulation aiming at 10–40 Gbit/s WDM system design applications. The signal shaping part of an electrical fil-ter is modelled in the optical domain using the filter impulse response to modify the signal vector and the covariance matrix. In this way inter-symbol-interference (ISI) effects from any type of electrical filter – specified by the filter impulse response – can be described. The formulation leads to a Hermitian form of the covariance matrix, thus allowing a straightforward analytical formu-lation of the moment generating function (MGF) which in turn specifies the bit-error-ratio (BER). Numerical ex-amples for a 10 Gbit/s pre-amplified Rx shows that the ISI leads to (up to) several dBʼs degradation in sensitivity. Thus it is imperative to account for the Rx ISI effect in rigorous and accurate form in any general WDM trans-mission model.
We present a comparative study of the influence of dispersion induced phase noise for CO-OFDM systems using Tx channel multiplexing and Rx matched filter (analogue hardware based); and digital FFT multiplexing/ IFFT demultiplexing techniques (software based). An RF carrier pilot tone is used to mitigate the phase noise influence. From the analysis, it appears that the phase noise influence for the two OFDM implementations is very similar. The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (ICI) and this, in turns, leads to a BER specification. Numerical results focus on a CO-OFDM system with 1 GS/s QPSK channel modulation. Worst case BER results are evaluated and compared to the BER of a QPSK system with the same capacity as the OFDM implementation. Results are evaluated as a function of transmission distance, and for the QPSK system the influence of equalization enhanced phase noise (EEPN) is included. For both types of systems, the phase noise variance increases significantly with increasing transmission distance. An important and novel observation is that the two types of systems have very closely the same BER as a function of transmission distance for the same capacity. For the high capacity QPSK implementation, the increase in BER is due to EEPN, whereas for the OFDM approach it is due to the dispersion caused walk-off of the RF pilot tone relative to the OFDM signal channels. For a total capacity of 400 Gbit/s, the transmission distance to have the BER < 10-4 is less than 277 km. For an RF pilot located in the center of the OFDM band in a CO-OFDM implementation with n-level PSK channel modulation the current results suggest that the walk-off effect is equivalent to the EEPN impact in a single channel n-level PSK system with the same capacity. This observation is important for future design of coherent long-range systems since it shows that there is a free choice between CO-OFDM and a high capacity nPSK implementation at least as long as the phase noise influence is concerned.
We present a comparative study of the influence of dispersion induced phase noise for n-level PSK systems. From the analysis, we conclude that the phase noise influence for classical homodyne/heterodyne PSK systems is entirely determined by the modulation complexity (expressed in terms of constellation diagram) and the analogue demodulation format. On the other hand, the use of digital signal processing (DSP) in homodyne/intradyne systems renders a fiber length dependence originating from the generation of equalization enhanced phase noise. For future high capacity systems, high constellations must be used in order to lower the symbol rate to practically manageable speeds, and this fact puts severe requirements to the signal and local oscillator (LO) linewidths. Our results for the bit-error-rate (BER) floor caused by the phase noise influence in the case of QPSK, 16PSK and 64PSK systems outline tolerance limitations for the LO performance: 5 MHz linewidth (at 3-dB level) for 100 Gbit/s QPSK; 1 MHz for 400 Gbit/s QPSK; 0.1 MHz for 400 Gbit/s 16PSK and 1 Tbit/s 64PSK systems. This defines design constrains for the phase noiseimpact in distributed-feed-back (DFB) or distributed-Bragg-reflector (DBR) semiconductor lasers, that would allow moving the system capacity from 100 Gbit/s system capacity to 400 Gbit/s in 3 years (1 Tbit/s in 5 years). It is imperative at the same time to increase the analogue to digital conversion (ADC) speed such that the single quadrature symbol rate goes from today's 25 GS/s to 100 GS/s (using two samples per symbol).
We present a study of the influence of dispersion induced phase noise for CO-OFDM systems using FFT multiplexing/IFFT demultiplexing techniques (software based). The software based system provides a method for a rigorous evaluation of the phase noise variance caused by Common Phase Error (CPE) and Inter-Carrier Interference (ICI) including - for the first time to our knowledge - in explicit form the effect of equalization enhanced phase noise (EEPN). This, in turns, leads to an analytic BER specification. Numerical results focus on a CO-OFDM system with 10-25 GS/s QPSK channel modulation. A worst case constellation configuration is identified for the phase noise influence and the resulting BER is compared to the BER of a conventional single channel QPSK system with the same capacity as the CO-OFDM implementation. Results are evaluated as a function of transmission distance. For both types of systems, the phase noise variance increases significantly with increasing transmission distance. For a total capacity of 400 (1000) Gbit/s, the transmission distance to have the BER < 10-2 for the worst case CO-OFDM design is less than 800 and 460 km, respectively, whereas for a single channel QPSK system it is less than 1400 and 560 km.
Coherent optical systems have relatively high laser phase noise, which affects the performance of forward error correction (FEC) codes. In this paper, we propose a method for selecting Bose-Chaudhuri-Hocquenghem (BCH) codes for coherent systems with star-shaped constellations and M-ary differential quadrature amplitude modulation (DQAM). Our method supports constellations of any order M which is a power of 2, and includes differential M-ary phase shift keying as a special case. Our approach is straightforward, requiring only short pre-FEC simulations to parameterize a statistical model, based on which we select codes analytically. It is applicable to pre-FEC bit error rates (BERs) of around 10-3. We evaluate the accuracy of our approach using numerical simulations. For a target post-FEC BER of 10-5, codes selected with our method yield BERs within 2× target. Lastly, we extend our method to systems with interleaving, which enables us to use codes with lower overhead.
In this paper, we analyze the sensitivities of coherent optical receivers and microwave receivers. We derive theoretical limits of signal-to-noise ratio and bit error rate. By applying a generic approach to a broad range of receivers, we can compare their performance directly. Other publications have considered some of these receivers. However, their diverse nature obscures the big picture. Using our results as a unifying platform, previous publications can be compared and discrepancies between them identified.