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The performance of cascaded in-line phase-preserving amplitude regeneration using nonlinear amplifying loop mirrors has been studied in numerical simulations. As an example of a spectrally efficient modulation format with two amplitude states and multiple phase states, the regeneration performance of a star-16QAM format, basically an 8PSK format with two amplitude levels, was evaluated. An increased robustness against amplified spontaneous emission and nonlinear phase noise was observed resulting in a significantly increased transmission distance.
© 2014 Optical Society of America
1. Introduction
To increase the transmission capacity of optical communication systems, employment of spectrally efficient quadrature amplitude modulation (QAM) formats, a combination of multilevel amplitude- and phase-shift keying, has been proposed. On the other side, QAM formats, having a number of densely packed signal states, are rather sensitive to amplitude and phase noise [1]. Particularly amplitude noise does not only diminish the separation of different amplitude states but it can also be converted into nonlinear phase noise due to the Gordon-Mollenauer effect in the transmission fiber [2], which is the major limiting factor for phase-encoded transmission systems operating at 10 Gbaud [3], and due to cross-phase modulation in multichannel transmission [4]. Distortions in the signal phase can be regenerated but usually it is quite complex [5,6]. A simpler way is phase-preserving amplitude regeneration to reduce amplitude fluctuations and, therefore, the origin of nonlinear phase noise [7–9].
It was already shown that modified Sagnac interferometers can be used to reduce amplitude noise in multiple amplitude states simultaneously [9]. Providing noise suppression and signal amplification at the same time, nonlinear amplifying loop mirrors (NALM) are promising candidates to replace conventional in-line amplifiers [10].
Here we consider the performance of a NALM as a phase-preserving in-line amplitude regenerator for a star-16QAM modulation format, which consists of two amplitude and eight phase states, in a transmission line with cascaded regenerators. Having a 16 symbol alphabet, this modulation format provides spectral efficiency four times higher than binary modulation. The state power ratio of 1:2.7, optimal for regenerator performance, was used, which is only slightly larger than the ideal state power ratio of 1:2.5 for such a 2ASK-8PSK format. The ideal ratio can be easy derived from the constellation diagram, assuming complex Gaussian noise and the most compact arrangement of all signal states as it is shown in Fig. 1.
Fig. 1 Setup of a NALM-based regenerator (left) and constellation diagram of a star-16QAM modulation format (right). OBPF – optical bandpass filter.
To evaluate the performance of a regenerator cascade in a transmission line, both amplified spontaneous emission (ASE) and nonlinear phase noise (NPN) were considered. The symbol error rate (SER) was used to compare the results with a conventional transmission line.
2. Regenerator scheme and transmission line
A NALM is a modified fiber Sagnac interferometer with an optical bidirectional amplifier in the fiber loop (Fig. 1). Due to self-phase modulation in a nonlinear fiber, the interference of the counter-propagating signals is power dependent. A coupler with an asymmetric splitting ratio and a bidirectional fiber amplifier, properly placed in the interferometer loop, allow the realization of a power transfer function with multiple flat plateau regions, suitable for phase-preserving amplitude regeneration of multiple amplitude states. Details on the operation principle as well as the optimization for multilevel operation are given in [10].
To simulate a regenerating transmission line, a simplified scheme was used (Fig. 2). In each of the spans, the signal is regenerated first by the NALM and then propagated in the transmission fiber. Assuming that the NALM’s gain and span fiber losses are balanced, a white Gaussian noise can be added to the signal in each span to simulate the effect of amplified spontaneous emission originating from in-line amplification. The average power of the signal was kept constant at the beginning of each span and, therefore, also at the NALM input. As a figure of merit for the amount of ASE added per span, the optical signal-to-noise ratio (OSNR, in 0.1nm bandwidth) at the input of the transmission line (right after the first in-line amplifier) was used. The amount of noise added in each processing node was kept constant (the same noise figure of all in-line amplifiers) and defined by the input OSNR in the first span. So the OSNR is gradually decreasing from span to span. To include nonlinear effects in the transmission fiber, the nonlinear phase shift in each span - a product of the fiber nonlinear coefficient, effective fiber length in a span, and fiber launch average signal power - was varied. The baud rate of the 25%-RZ star-16QAM format was 100 Gbaud. A similar transmission line scheme was used in [11] but in a quasi-linear transmission regime without taking nonlinearity in the transmission fiber into account.
Fig. 2 Transmission line (top) and simulated transmission line schemes (bottom): Tx –star-16QAM transmitter, ASE – injection of amplified spontaneous emission, Rx – coherent receiver.
3. Transfer characteristics and constellation diagrams
The regenerator was optimized for two-level operation with an additional condition of minimal change of the state power ratio of the signal: the power splitting ratio of the NALM coupler was set to 90:10, the directional phase bias to −2 rad, the amplifier gain to 25 dB, dispersion of the highly nonlinear fiber to zero and its total nonlinearity to 5 W−1. Then the 1:2.7 state power ratio of the signal constellation matches best to the plateau power spacing of the regenerator. This value of the state power ratio is quite close to 1:2.5 which would be geometrically optimal for the star-16QAM considered and, if necessary, NALM parameters could be adapted also for the value 1:2.5 by a fine trimming of the coupler splitting ratio and directional phase bias.
Power and phase transfer functions of the regenerator can be seen as the bold lines in Fig. 3 together with the total transfer characteristics of the regenerator cascade after the Nth span. While the NALM transfer characteristics are identical for each span, the total transfer characteristics of a regenerator cascade are changing with every additional span as each regenerator influences slightly the state power ratio. A flat-top staircase-like power transfer function is created already after a few spans, being a product of the transfer functions of all regeneration nodes under the condition of constant average power for each span. The signal state power ratio remains nearly constant in the transmission line.
Fig. 3 Peak power transfer function (left) and power-phase transfer function (right) of regenerator cascade for different span numbers. First (blue) and second (red) plateau centers are marked.
On the other side, the transfer characteristics of the signal phase are just the sum over the respective spans. Hereby, phase undulations in the plateau regions are hardly significant; merely the phase offset between the two amplitude states is constantly growing. A phase shift between the two amplitude levels is not a problem for the regenerator because the amplitude regeneration is not sensitive to the input phase. A compensation of this state ring rotation is easy to realize in practical systems by individual phase recovery for different amplitude levels in the digital signal-processing algorithms at the receiver as it was used also in our simulations.
The transfer characteristic of the regenerator is essential for the signal quality. Its impact on the signal states can be seen in the constellation diagrams in Fig. 4. To get rid of the state ring rotation as mentioned before, the amplitude level decision at the receiver side was done first and afterwards the phase recovery was done for each of the two amplitude levels separately, so that the original shape of the star-16QAM is independent of constant phase offsets between the two amplitude state rings. This operation has no effect on the symbol error rate becauseonly an existing amplitude error will lead to a wrong phase recovery and thus phase errors will be generated only from existing amplitude errors. Already after the first regenerator, a reduction in amplitude noise can be seen. This continuous reduction in amplitude noise is preventing accumulation of nonlinear phase noise in the subsequent spans. In contrast to the reference case, the amount of phase noise is still quite low after five spans. This can be clearly seen by the density of wrongly detected symbols. For the reference signal, the phase distributions have broadened and the phase states of neighboring symbols overlap significantly, causing a number of errors, while only a few errors have been observed for the regenerated signal. After ten iterations, the reference signal is almost completely destroyed while the regenerated signal is still within the forward-error-correction limit of 10−3.
Fig. 4 Constellation diagrams of the star-16QAM after different spans for the reference (top) and regenerative transmission line (bottom) for 23 dB OSNR and 5 rad/span nonlinear phase shift. The receiver decision thresholds are marked with dotted lines and wrong detected symbols are colored in red.
4. System performance
The system performance was evaluated with focus on the symbol error rate (SER) using Monte Carlo simulations. In Fig. 5 the SER is depicted as a function of ASE and NPN. As a figure of merit for NPN, the average nonlinear phase shift in each span was used, keeping the average fiber launch power constant at 10 dBm for the reference and regenerated signal. This figure of merit can also be rearranged in terms of input power for a fixed total nonlinearity in a transmission line. Both points of view are equal and depend only on the system parameters. Please note that influence of NPN on both amplitude levels is different as NPN scales with the state power.
Fig. 5 Symbol error rate as a function of average nonlinear phase shift per span and input OSNR for the reference transmission line (top) and the regenerative transmission line (bottom) after different spans.
As one can see in Fig. 5, in the first few spans, all errors are based on the ASE noise, as the SER hardly changes with the average nonlinear phase shift but only with the input OSNR. After five spans, the limitation by NPN can be seen for the reference case: now the SER is increasing also with an increase of the average nonlinear phase shift. In contrast to that, the performance of the regenerative transmission line stays almost independent of the nonlinear phase shift. At twice the distance (10 spans), the reference signal is almost completely distorted for the evaluated values of input OSNR and NPN. Contrary, in the regenerative system, due to consistent periodic regeneration, the performance is changing only slightly, but some nonlinear distortions can also be seen in this case. For 10 and 12 spans, a sharp edge between almost error-free transmission and completely distorted transmission can be seen in each case at a total, accumulated over the link, average nonlinear phase shift of about 130 rad. The reason of this rapid change with respect to NPN is a change of the noise probability distributions and the residual amplitude noise that cannot be completely removed by the NALM.
The system improvement by regeneration can be expressed also in terms of transmission distance extension. Hereby the maximum transmission distance for the regenerating transmission line at a SER of 10−3, the threshold for forward error correction, was compared to the reference transmission line. The factor, by which the transmission distance can be extended, is shown in Fig. 6. The NALM-based, phase-preserving amplitude regeneration is most efficient to counteract nonlinear phase noise: the best improvement - more than three times the reference transmission distance - is achieved for a high, above 8 rad/span, average nonlinear phase shift per span and input OSNR of about 30 dB. In most of the parameter range studied, the transmission distance is at least doubled. Below an input OSNR of about 22 dB, the transmission performance is too bad already after the first span and no improvement can be obtained by regeneration. This can be also seen in Fig. 5 for both schemes.
Fig. 6 Transmission distance extension as a function of average nonlinear phase shift per span and input OSNR for SER of 1e−3 (threshold of forward error correction).
5. Conclusions
It was shown that cascaded phase-preserving amplitude regeneration using NALM can significantly increase the signal quality in terms of the symbol error rate in a transmission network. The number of transmission spans and thus the transmission distance can at least be doubled. A total accumulated nonlinear phase shift of up to 130 rad can be tolerated. Alternatively, cascaded regenerating transmission lines can manage a higher amount of noise and, therefore, be operated at a lower signal-to-noise level.
Acknowledgment
The authors gratefully acknowledge funding by the Fraunhofer Society and the Max-Planck-Society in the framework of the MultiReg project as well as funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German Research Foundation (DFG) in the framework of the German excellence initiative.
References and links
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