Polarization-switched QPSK Research Articles

Comparative analysis of inter-channel nonlinear distortions from PM-QPSK and PS-QPSK interferers

Polarization-Switched QPSK (PS-QPSK) can offer a higher tolerance to fiber nonlinearities than Polarization Multiplexed QPSK (PM-QPSK), albeit with 25% loss of spectral efficiency. While improved performance has been shown experimentally, a thorough study of inter-channel nonlinearities in these systems has not been performed. Here we numerically study two separate manifestations of cross phase modulation (XPM) generated by these two formats; XPM-induced phase noise (XPM-PN) and XPM-induced polarization crosstalk (XPM-PC). We find that in both dispersion-compensated (DC) and dispersion uncompensated (DUC) systems, greater XPM-PN is generated by PS-QPSK interferers, whereas greater XPM-PC is generated by PM-QPSK interferers. While the combined effect of these distortions provides similar penalties in either system, this finding may help inform the design of efficient nonlinear equalizers.

Stacked modulation formats enabling highest-sensitivity optical free-space links.

A new modulation scheme with a sensitivity of 2.3 photons per bit at a bit-error ratio (BER) of 10(-3) is discussed theoretically and demonstrated experimentally. We achieve a limiting sensitivity of 2.3 photons per bit (3.7 dB photons per bit) by stacking the modulation formats 64PPM, 4FSK and polarization-switched (PS) QPSK. This modulation stack encodes 11 bit per symbol (PPM: 6 bit, FSK: 2 bit, PS-PQSK: 3 bit). We also replaced 4FSK by 2ODFM (2-channel multiplex) for comparison. With 64PPM-2OFDM-PS-QPSK a total of 12 bit are encoded (PPM: 6 bit, 2 OFDM channels with PS-QPSK: 2 × 3 bit). Both modulation stacks show a similar limiting sensitivity and are probably the highest sensitivities so far reported for a BER of 10(-3), Our theoretical considerations are supported by simulations and experiments.

Four-dimensional Rotations in Coherent Optical Communications

To model electromagnetic wave propagation for coherent communications without polarization dependent losses, the unitary 2 ×2 Jones transfer matrix formalism is typically used. In this study, we propose an alternative formalism to describe such transformations based on rotations in four-dimensional (4d) Euclidean space. This formalism is usually more attractive from a communication theoretical perspective, since decisions and symbol errors can be related to geometric concepts such as Euclidean distances between points and decision boundaries. Since 4d rotations is a richer description than the conventional Jones calculus, having six rather than four degrees of freedom (DOF), we propose an extension of the Jones calculus to handle all six DOF. In addition, we show that the two extra DOF in the 4d description represents transformations that are nonphysical for propagating photons, since they does not obey the fundamental quantum mechanical boson commutation relations. Finally, we exemplify on how the nonphysical rotations can change the polarization-phase degeneracy of well-known constellations such as single-polarization QPSK, polarization-multiplexed (PM-)QPSK and polarization-switched (PS-) QPSK. For example, we show how PM-QPSK, which is well known to consist of four polarization states each having four-fold phase degeneracy, can be represented as eight states of polarizations, each with binary phase degeneracy.

Application of a Novel Modulation Scheme of PS-RZ-QPSK Signal in High-Speed Optical Transmission System

Modulation principle of dual-polarization quadratu-re phase shift keying signal and polarization-switched QPSK signal are demonstrated and advantages of PS-QPSK are proved in theoretically. A novel modulation scheme of PS-RZ-QPSK signal is proposed in this paper. The scheme reduces transmitter cost by less use of Mach-Zehnder modulator, but also presents similar performance as traditional structure for PS-RZ-QPSK. The simulate result indicates PS-RZ-QPSK can achieve a better transmission performance than DP-RZ-QPSK at the same bit rate (84Gb/s) and baud rate (28GBd), and proves showing the feasibility of novel modulation scheme.

On the Energy Efficiency of Modulation Formats for Optical Communications

An information theoretic framework for performance evaluation of high-dimensional modulation formats in an optical communication link is proposed. The spectral and energy efficiency of different candidates for future coherent optical communications are analyzed to explore the advantages of exploiting different degrees of freedom for symbol coding, construction, and transmission. Our analysis demonstrates the advantage of fully utilizing both polarization states from the spectral and energy efficiency perspective. In particular, at the same spectral efficiencies of 2.5 and 2.8 b/s/Hz, dual polarization quadrature phase shift keying (DP-QPSK) has, respectively, 0.8 and 1.6 dB energy efficiency advantage over polarization switched QPSK (PS-QPSK).

Transmission of PM-QPSK and PS-QPSK with different fiber span lengths

We perform experimental and numerical investigations of the transmission reach of polarization-switched QPSK (PS-QPSK) and polarization-multiplexed QPSK (PM-QPSK) for three different fiber span lengths: 83, 111 and 136 km. In the experimental comparison we investigate the performance of PS-QPSK at 20 Gbaud and PM-QPSK at the same bit rate (60 Gbit/s) and at the same symbol rate, both the single channel case and a WDM system with 9 channels on a 50 GHz grid. We show that PS-QPSK gives significant benefits in transmission reach for all span lengths. Compared to PM-QPSK, use of PS-QPSK increases the reach with more than 41% for the same symbol rate and 21% for the same bit rate. In the numerical simulations we use the same data rates as in the experiment. The simulation results agree well with the experimental findings, but the transmission reach is longer due to the absence of various non-ideal effects and higher back-to-back sensitivity. Apart from using data coded in the absolute phase in the simulations, we also investigate differentially coded PS-QPSK for the first time and compare with PM-QPSK with differential coding. The power efficiency advantage of PS-QPSK then increases with approximately 0.3 dB at a bit error rate of 10⁻³, resulting in a further relative transmission reach improvement over PM-QPSK. Both the experimental and the numerical results indicate that PS-QPSK has slightly higher tolerance to inter-channel nonlinear crosstalk than PM-QPSK.

Demonstration of Record Sensitivities in Optically Preamplified Receivers by Combining PDM-QPSK and M-Ary Pulse-Position Modulation

We present the principle, implementation, and performance of a recently introduced high-sensitivity modulation format based on the combined use of polarization-division-multiplexed quadrature phase-shift keying (PDM-QPSK, or PQ) and m-ary pulse-position modulation (m-PPM). This novel modulation format, termed PQ-mPPM, offers high receiver sensitivity in optically preamplified receivers. We study the sensitivity of the PQ-mPPM format both analytically and experimentally, and compare it to common modulation formats such as PDM-QPSK, m-PPM, differential phase-shift keying, and polarization-switched QPSK. The bandwidth expansion factor of this format is also discussed. A record sensitivity of 3.5 photons per bit at BER = 10-3 is experimentally demonstrated at 2.5 Gb/s with a novel pilot-assisted digital coherent-detection scheme, outperforming PDM-QPSK by about 3 dB.

Ultra-long-haul transmission of 7×429 Gbit/s PS-QPSK and PDM-BPSK

We investigated ultra-long-haul transmission of polarization-switched QPSK (PS-QPSK) and polarization-division-multiplexed BPSK (PDM-BPSK) at 42.9 Gbit/s experimentally as well as by means of computer simulations. PDM-BPSK allowed transmission distances in excess of 14,040 km to be achieved, compared to 13,640 km for PS-QPSK. However, PS-QPSK offers a significant reduction in receiver complexity due to the lower symbol-rate.

Generation and long-haul transmission of polarization-switched QPSK at 429 Gb/s

We demonstrate, for the first time, the generation and transmission of polarization-switched QPSK (PS-QPSK) signals at 42.9 Gb/s. Long-haul transmission of PS-QPSK is experimentally investigated in a recirculating loop and compared with transmission of dual-polarization QPSK (DP-QPSK) at 42.9 Gb/s per channel. A reduction in the required OSNR of 0.7 dB was found at a BER of 3.8 x 10(-3), resulting in an increase in maximum reach of more than 30% for a WDM system operating on a 50 GHz frequency grid. The maximum reach of 13640 km for WDM PS-QPSK is, to the best of our knowledge, the longest distance reported for 40 Gb/s WDM transmission, over an uncompensated link, with standard fiber and amplification.

Comparison of polarization-switched QPSK and polarization-multiplexed QPSK at 30 Gbit/s

We present the first experimental results for polarization-switched QPSK (PS-QPSK) and make a comparison with polarization-multiplexed QPSK. Our measurements confirm the predicted sensitivity advantage of PS-QPSK. We have also studied the single channel performance after transmission over 300 km and support the results with numerical simulations. It is shown that the two modulation formats have similar nonlinear tolerance and that optical dispersion compensation outperforms compensation with digital signal processing in the single channel case. Finally, we propose a novel transmitter for PS-QPSK based on an IQ modulator and two amplitude modulators driven in a push-pull configuration.

Modified constant modulus algorithm for polarization-switched QPSK

By using a generalized cost function, a modified constant modulus algorithm (CMA) that allows polarization demultiplexing and equalization of polarization-switched QPSK is found. An implementation that allows easy switching between the conventional and the modified CMA is described. Using numerical simulations, the suggested algorithm is shown to have similar performance for polarization-switched QPSK as CMA has for polarization-multiplexed QPSK.

Performance evaluation of coherent WDM PS-QPSK (HEXA) accounting for non-linear fiber propagation effects

Coherent-detection (CoD) permits to fully exploit the four-dimensional (4D) signal space consisting of the in-phase and quadrature components of the two fiber polarizations. A well-known and successful format exploiting such 4D space is Polarization-multiplexed QPSK (PM-QPSK). Recently, new signal constellations specifically designed and optimized in 4D space have been proposed, among which polarization-switched QPSK (PS-QPSK), consisting of a 8-point constellation at the vertices of a 4D polychoron called hexadecachoron. We call it HEXA because of its geometrical features and to avoid acronym mix-up with PM-QPSK, as well as with other similar acronyms. In this paper we investigate the performance of HEXA in direct comparison with PM-QPSK, addressing non-linear propagation over realistic links made up of 20 spans of either standard single mode fiber (SSMF) or non-zero dispersion-shifted fiber (NZDSF). We show that HEXA not only confirms its theoretical sensitivity advantage over PM-QPSK in back-to-back, but also shows a greater resilience to non-linear effects, allowing for substantially increased span loss margins. As a consequence, HEXA appears as an interesting option for dual-format transceivers capable to switch on-the-fly between PM-QPSK and HEXA when channel propagation degrades. It also appears as a possible direct competitor of PM-QPSK, especially over NZDSF fiber and uncompensated links.