1. Introduction

Amplitude and phase shift keying (APSK) format is one example of the advanced modulation scheme to improve the spectral efficiency, and it has been investigated theoretically and experimentally [1–5]. As this format utilizes both the amplitude and the phase of the signal light, it is obvious that the phase information is degraded when the corresponding amplitude information is the space. Therefore, the APSK format has the trade-off between the performances of the amplitude shift keying (ASK) signal and the phase shift keying (PSK) signal through the extinction ratio of the ASK signal. In order to overcome this issue, a method to utilize inverse return-to-zero (inverse RZ) waveform had been proposed, but the generation of the inverse RZ waveform requires complicated transmitter [6].

Recently, the authors had proposed a zero-nulling method to improve the performance of the APSK format [7]. In this method, the phase information transmitted by the ASK space signal is intentionally nulled, and the phase information is only transmitted by the ASK mark signal. Then, it could be possible to improve the PSK performance regardless to the extinction ratio of the ASK, and it was theoretically confirmed through numerical simulations [7]. One demerit of this method is a reduction of the total capacity. As a matter of fact, the capacity of the PSK signal becomes a half assuming ASK signal mark ratio of 1/2, and the total capacity per one signal wavelength becomes 75% compared to the original APSK format.

In this paper, we have compared the transmission performance of the original APSK format and the zero-nulling APSK format with the same channel capacity. The original format had the bit-rate of 7.5Gbit/s for both the ASK signal and the PSK signal, while the zero-nulling format had the bit-rate of 10Gbit/s and 5Gbit/s for the ASK signal and the PSK signal, respectively. The results showed that even when the extinction ratio of the original APSK format was optimized, the zero-nulling APSK format outperformed the original APSK format for the long-haul transmission.

2. Simulation model and zero-nulling APSK format

Figure 1 shows a schematic diagram of the simulation model to evaluate the transmission performance of the APSK format. The undersea system like transmission line [8,9] was assumed in this simulation model. The numerical simulator solved coupled nonlinear Schrödinger equations using the split-step Fourier method [10].

 

Fig. 1. A schematic diagram of the simulation model.

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There were 16 optical transmitters, and the signal wavelengths of these transmitters ranged from 1545.5nm to 1554.5nm with 0.6nm channel separation [9]. The symbol rates were 7.5G symbol/s and 10G symbol/s for original APSK format and zero-nulling APSK format, respectively. The modulation pattern was 2⁹ De Brujin sequence for both cases. There were 256 bits delay between the pattern for the ASK signal and that for the PSK signal. The ASK signal had a return to zero (RZ) raised-cosine waveform. There was no wavelength selective function in the multiplexer. At the input of the transmission line, the modulation patterns of the transmitters were randomized in time scale.

The optical fiber transmission line comprised two types of the optical fibers. The first one was the non zero dispersion shifted fiber (NZDSF), and the second one was the conventional 1.3µm zero dispersion single mode fiber (SMF). The parameters of these fibers are summarized in Table 1. Undersea system like dispersion management [8] was adopted by combining these two fibers, and ten fiber spans composed one dispersion block. In each dispersion block, the first to the fifth and the seventh to the tenth spans were the NZDSF, while the sixth span was the SMF. The repeater span length was 60km. Fig. 2 shows the dispersion map for the signal wavelengths at 1545.5nm, 1549.7nm, and 1554.5nm. The total output power of the repeater was +9dBm, and the noise figure was 6dB. The wavelength dependent gain of the repeater was ignored in the simulation.

Table 1. Parameters of the transmission fiber at 1550nm

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Fig. 2. Dispersion map used for the simulation.

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The demultiplexer at the receiving end had a Gaussian profile, and the bandwidth of it was 0.2nm. The cumulative chromatic dispersion for each channel after the transmission was compensated after the demultiplexer, and the residual chromatic dispersion after the dispersion compensation was 100ps/nm for all the channels. The ASK signal was detected directly, and the performance of it was evaluated by the Q-factor using electrical levels of the mark and the space. For the PSK signal detection, difference of the optical phase was directly calculated from the optical field [11]. The difference of the phase was defined as the phase difference between two sampling points separated by one bit period, and it was arranged within the range between −π/2 to 3π/2 to obtain an eye-like diagram of the phase. The performance was evaluated by the Q-factor obtained from the rails of 0 phase and π phase same as the method described in reference [11].

For the zero-nulling APSK format, the information of the PSK signal transmitted by the space level of the ASK signal was intentionally ignored, and the PSK information was only transmitted by the mark level of the ASK signal. Fig. 3 shows the difference between the original APSK format and the zero-nulling APSK format schematically [7]. As seen in the figure, the information capacity of the zero-nulling APSK format becomes 75% of that of the original APSK format, assuming the mark ratio of the ASK signal is 50%.

 

Fig. 3. A schematic to explain the difference between the original and the zeronulling APSK.

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Fig. 4. Transmission performance of the APSK format.

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3. Results and discussions

Figure 4 shows the transmission performance of the original and the zero-nulling APSK formats as a function of the transmission distance. Open symbols show the ASK signal performance, and the closed symbols show the PSK performance. Each point denotes an averaged value over 16 WDM channels. The extinction ratio of the ASK signal of the original APSK format was varied between 5 and 6dB, while it was fixed at 13dB for the zero-nulling APSK format.

As seen in Fig. 4, the performance of the zero-nulling APSK format outperformed that of the original APSK format for any distance regardless to the extinction ratio of the ASK signal. As the total capacity of both the original APSK format and the zero-nulling APSK format was identical, these results clearly show the effectiveness of the zero-nulling APSK format. Comparing the ASK signal performance and the PSK signal performance of the original APSK format, there was a certain gap between two performances. The optimum extinction ratio for the original APSK format could achieve a comparable performance for both the ASK and the PSK signals. From Fig. 4, it seemed that the optimum extinction ratio depended on the transmission distance. Then, the extinction ratio was varied to obtain an optimum value. Figure 5 shows the results. Numbers in parentheses show the extinction ratio of the original APSK format.

As seen in Fig. 5, even when the extinction ratio of the original APSK format was optimized along the transmission distance, the zero-nulling APSK format demonstrated better performance. The results proved the superior performance of the zero-nulling APSK format for the long-haul transmission system.

One more issue of the zero-nulling APSK format is an implementation of the receiver. As there is no phase information in the ASK space signal, it is impossible to adopt a conventional delay demodulation scheme for the PSK signal detection. Even though, it should be possible to adopt an intra-dyne detection and a digital signal processing [12] to realize the zero-nulling APSK receiver. An experimental demonstration of the zero-nulling APSK format will be realized by using this technology.

 

Fig. 5. Transmission performance of the APSK format with optimized extinction ratio.

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4. Conclusions

We have conducted numerical simulations to compare the transmission performance of the original APSK format and the zero-nulling APSK format with the same channel capacity. Even when the extinction ratio of the original APSK format was optimized as a function of the transmission distance, the zero-nulling APSK format outperformed the original APSK format. The results proved the effectiveness of the zero-nulling APSK format for the long-haul optical fiber transmission system.