1. Introduction

Digital coherent receivers have long been of interest in the field of optical communications, most recently due to their high power sensitivity, frequency selectivity and ability to capture the full optical field. Passive optical networks (PON), as loss limited systems, require high sensitivity receivers in order to increase capacity and reach, making coherent detection an attractive option for next generation commercial systems [1].

While coherent receivers offer intrinsic sensitivity gains over direct detection receivers, it has been proposed that the sensitivity of a coherent receiver can be best utilized by modulating all four dimensions of the optical field (in-phase and quadrature phase components of two orthogonal polarizations). One such modulation format, PS-QPSK, was singled out as having an inherent theoretical sensitivity gain over all other frequency-domain modulation formats [2], and this has been verified experimentally in terms of optical signal-to-noise ratio [3–5] and received optical power [6].

When a wavelength division multiplexed PON (WDM-PON) is combined with coherent detection, there are significant benefits to employing more spectrally efficient modulation formats in which each symbol carries multiple bits of information. For a given data rate, such formats allow the electrical bandwidth requirements of the components to be reduced and, if the overall bandwidth is limited, allows a greater number of users to be serviced; both of which are attractive features for a WDM-PON. PDM-8QAM offers a six fold reduction in the optical and electrical bandwidth compared with binary on-off keying since each symbol carries six bits of information; a key metric for spectrally efficient modulation formats. PDM-8QAM is also investigated here to provide an insight into the trade-off between capacity and power sensitivity.

We note that the receiver sensitivity in [6] could be improved by preamplifying the received signal and local oscillator (LO), as suggested for the optical line terminal (OLT) in [7]. This technique maximizes the LO-signal beat amplitude and, therefore, reduces the noise associated with digitizing weak analogue electrical signals at the receiver, while also overcoming the limits of photodiodes with quantum efficiency less than unity. It was previously shown that optical preamplification allows receiver sensitivity to approach the shot noise limit [8]. Therefore, we extend this work to further approach the theoretical sensitivity limit of the formats; PDM-BPSK, PDM-QPSK, PS-QPSK and PDM-8QAM. We assume the use of hard decision forward error correction (FEC) with a coding overhead of 25% and a BER limit of 1.3 × 10⁻² [9].

2. Generation of the reference modulation formats

This investigation required the generation of four distinct modulation formats, three of which (PDM-QPSK, PS-QPSK, PDM-8QAM) are based on the generation of single-polarization QPSK. The experimental transmitter configurations for all four modulation formats are shown in Fig. 1(a–d). The QSPK signal which forms the first stage shown in Fig. 1(b–d) was obtained by passing 1550 nm CW light from a 100 kHz linewidth external cavity laser (ECL) through a triple Mach-Zehnder modulator (MZM) (denoted ‘IQ’ in Fig. 1). The applied data pattern was a pseudo-random bit sequence (PRBS) of length 2¹⁵ – 1, decorrelated by half a pattern length between the in-phase and quadrature components of each QPSK symbol. The symbol rate required for each format is shown within each subfigure. The BPSK signal was generated in a similar manner, except that the two data inputs of the triple MZM were driven with data and inverse data to encode only a single bit per symbol. In the case of 8QAM, Fig. 1(d), the third bit of information was modulated using a second triple MZM in series and driving only one modulator input. The second input was terminated, and the bias and phase set such that the original QPSK signal was mapped to an inner QPSK constellation.

 

Fig. 1 Experimental transmitter configurations for generating (a) PDM-BPSK, (b) PS-QSPK, (c) PDM-QPSK and (d) PDM-8QAM. Shown adjacent to each configuration is the recovered constellation at a received power corresponding to a BER of 3 × 10⁻³. The receiver configuration is shown in (e). In this configuration, the two EDFAs shown amplify the signal and the LO. In practice, the LO preamplifier could be removed if the LO laser had sufficient output power. In the case where no preamplification is considered, the EDFA shown as boxed is removed.

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For all polarization division multiplexed formats, Fig. 1(a,c,d), polarization multiplexing was emulated by passing the modulated signal through an optical 3 dB splitter into two arms of a polarization multiplexing stage; one arm incorporating additional fiber (corresponding to a 2.4 ns delay) and the other a variable optical delay line for synchronising the symbols in each polarization. Polarization controllers (PC) were used to set orthogonal polarizations before recombination using a polarization beam combiner (PBC).

Similarly, polarization-switching was achieved for PS-QPSK, Fig. 1(b), by equally splitting the signal into two arms of a polarization multiplexing stage. However, each arm included a single MZM driven such that one arm would be in the transmit state when the other was extinguished. By driving symbol synchronously before recombination with a PBC, one bit per symbol was encoded on which of two orthogonal polarization states contained the signal.

The received power was set using a variable optical attenuator (VOA) prior to the receiver, with a calibrated optical spectrum analyser (OSA) used to monitor the optical power. The coherent optical receiver, Fig. 1(e), consisted of a polarization beam splitter (PBS) followed by a 90 degree optical hybrid for each polarization, where light from a second ECL (100 kHz linewidth) was combined with the signal. A balanced pair of photodiodes followed by an analogue-to-digital converter (ADC) was used to measure the signal from each optical hybrid output. The signal was sampled at 2 samples/symbol and processed offline using digital signal processing (DSP). To increase the amplitude of the beat between signal and LO, erbium doped fiber amplifiers (EDFA) were used after the signal (where indicated) and after the LO.

It was necessary that the DSP varied slightly between the formats, but the main DSP blocks were those described for PDM-QPSK in [10]. Otherwise, only the equaliser and phase recovery varied. PDM-QPSK required constant modulus equalization, PDM-BPSK required joint equalization and phase recovery [11], PDM-8QAM required radially directed equalization [12] and PS-QPSK used polarization directed equalization [13]. PDM-QPSK used 4^th power Viterbi and Viterbi phase estimation [14] while PDM-8QAM used a radially directed version of the 4^th power Viterbi and Viterbi phase estimation [12] and PS-QPSK used polarization directed 4^th power phase estimation [3]. In the case of PDM-8QAM, maximum likelihood hard decisions were made by using a k-means clustering algorithm [15].

3. Experimental results and discussion

Using the methods outlined in section 2, we were able to experimentally obtain relations between power sensitivity and BER for PDM-BPSK, PS-QPSK, PDM-QPSK and PDM-8QAM. These results are compared with theory and shown in Fig. 2. The theoretical power sensitivity curves were obtained using the noise sensitivity formulae for each modulation format [2, 16] and evaluating these using the formula for shot noise limited sensitivity, as in [8].

 

Fig. 2 Sensitivity of different modulation formats at a datarate of 12.5 Gbit/s using the configuration shown in Fig. 1. Shown in (a) are the theoretical shot noise sensitivity limits (QPSK and BPSK have the same sensitivity limit). The experimental data points are shown (b) with receiver preamplification and (c) without receiver preamplification. The horizontal black line indicates the 1.3 × 10⁻² FEC limit.

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It is clear from Fig. 2 that PS-QPSK maintains a sensitivity advantage over all of the reference formats, as expected from theory. Indeed, the sensitivity of PS-QPSK at the FEC limit is −52.7 dBm (4.2 photons/bit). The sensitivities of all modulation formats are compared in Table 1. Without further analysis, we can conclude that PS-QPSK offers the best power sensitivity of these modulation formats. However, the intrinsic sensitivity gains of PS-QPSK are almost negated in the high BER region. While PS-QPSK could be employed in a PON to improve system margin, it is likely that the 33% increased bandwidth requirements of PS-QPSK would not justify the 0.4 dB increase in sensitivity over PDM-QPSK.

Table 1. Sensitivity and Maximum Information Rate of Test Formats at 12.5 Gbit/s

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To reduce the latency and power consumption of DSP, it can be desirable to use a lower coding overhead for FEC. The FEC assumed from [9] is also specified when using a 7% overhead as having a target BER of 1.3 × 10⁻³. Assuming these parameters, the sensitivity of PS-QPSK is −50.3 dBm (7.0 photons/bit). In this region, the discrepancy between PDM-QPSK and PDM-BPSK can be attributed to differences in the implementation penalty of the transmitted signals due to different transmitter configurations. Theory suggests that this advantage is not intrinsic.

In the high power limit, the theoretical BER curves suggest that PS-QPSK should approach a sensitivity advantage over PDM-QPSK and PDM-BPSK of 1.76 dB, however, this advantage diminishes with increasing BER. In fact, the sensitivity penalty relative to PS-QPSK is reduced in the high BER region for all the modulation formats considered here. Importantly, this trend is independent of the encoded bit/symbol of the modulation format.

Shown in Fig. 3 are the information bit/symbol limits (bit/symbol after FEC decoding) for each of the modulation formats against their sensitivities (see Fig. 2) at the two FEC limits (1.3×10⁻² and 1.3×10⁻³). In terms of capacity limits, PS-QPSK is, counter-intuitively, more sensitive than PDM-BPSK, even though its bandwidth requirements are 33% lower. Therefore, it is logical to prefer PS-QPSK over PDM-BPSK in loss-limited scenarios.

 

Fig. 3 Theoretical (open markers) and experimental (filled markers) sensitivities for the modulation formats under test. To highlight the trend, theoretical values for higher order QAM are also shown. The sensitivity for each format at a target BER of 1.3 × 10⁻³ is shown in (a), where a 7% overhead is assumed for FEC. The sensitivity at a target BER of 1.3 × 10⁻² is shown in (b), where a 25% overhead is assumed for FEC.

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However, PS-QPSK encodes 25% less information per symbol compared with PDM-QPSK, and so the capacity limit of PS-QPSK is also 25% lower than for PDM-QPSK. There is then a trade-off between sensitivity and optical and electrical bandwidth requirements. Fig. 3 indicates that, when using strong FEC, PDM-QPSK would have the lowest bandwidth requirements of the two formats while being only 0.4 dB less sensitive than PS-QPSK. Conversely, the sensitivity penalty when using weaker FEC is 0.8 dB relative to PS-QPSK.

For the spectrally efficient format PDM-8QAM, assuming the 1.3 × 10⁻³ FEC limit, Fig. 3(a), the sensitivity penalty relative to PDM-QPSK is 3.2 dB. At the 1.3 × 10⁻² FEC limit, Fig. 3(b), PDM-QPSK outperforms PDM-8QAM by 2.8 dB. The trend which emerges is that, for the best sensitivity, PS-QPSK is the best option especially with a low target BER. However, when optical or electrical bandwidth are constrained, the choice of format is strongly dependent on FEC.

4. Conclusions

The power sensitivity limits of four modulation formats (PDM-BPSK, PS-QPSK, PDM-QPSK and PDM-8QAM) were experimentally investigated, using an optically preamplified digital coherent receiver. The relative sensitivity of all formats, operating at 12.5 Gbit/s, was found to be in line with theory, with PS-QPSK the most power efficient of the modulation formats. Assuming a 25% coding overhead for FEC with a target BER of 1.3 × 10⁻², PS-QPSK was detected at 10 Gbit/s with a received power of −52.7 dBm (4.2 photons/bit).

It was experimentally verified that formats which encode fewer bit/symbol do not necessarily offer greater sensitivity and that, with a higher BER threshold for FEC, PDM-QPSK, PDM-BPSK and PS-QPSK approach a comparable shot noise limit while PDM-8QAM, a format with a high capacity limit (6 bit/symbol), also begins to approach a similar sensitivity.

We found that the optimum choice of modulation format for a PON was strongly dependent on FEC threshold and target capacity. As FEC overhead decreases (lower target BER), PS-QPSK outperforms the reference formats with asymptotically increasing margin. However, for a high target BER, the bandwidth requirements of the formats becomes the critical factor.