Alan Pak Tao Lau

Coherent detection in optical fiber systems

The drive for higher performance in optical fiber systems has renewed interest in coherent detection. We review detection methods, including noncoherent, differentially coherent, and coherent detection, as well as a hybrid method. We compare modulation methods encoding information in various degrees of freedom (DOF). Polarization-multiplexed quadrature-amplitude modulation maximizes spectral efficiency and power efficiency, by utilizing all four available DOF, the two field quadratures in the two polarizations. Dual-polarization homodyne or heterodyne downconversion are linear processes that can fully recover the received signal field in these four DOF. When downconverted signals are sampled at the Nyquist rate, compensation of transmission impairments can be performed using digital signal processing (DSP). Linear impairments, including chromatic dispersion and polarization-mode dispersion, can be compensated quasi-exactly using finite impulse response filters. Some nonlinear impairments, such as intra-channel four-wave mixing and nonlinear phase noise, can be compensated partially. Carrier phase recovery can be performed using feedforward methods, even when phase-locked loops may fail due to delay constraints. DSP-based compensation enables a receiver to adapt to time-varying impairments, and facilitates use of advanced forward-error-correction codes. We discuss both single- and multi-carrier system implementations. For a given modulation format, using coherent detection, they offer fundamentally the same spectral efficiency and power efficiency, but may differ in practice, because of different impairments and implementation details. With anticipated advances in analog-to-digital converters and integrated circuit technology, DSP-based coherent receivers at bit rates up to 100 Gbit/s should become practical within the next few years.

Signal Design and Detection in Presence of Nonlinear Phase Noise

In optical fiber transmission systems using inline amplifiers, the interaction of a signal and amplifier noise through the Kerr effect leads to nonlinear phase noise that can impair the detection of phase-modulated signals. We present analytical expressions for the maximum-likelihood (ML) decision boundaries and symbol-error rate (SER) for phase-shift keying and differential phase-shift keying systems with coherent and differentially coherent detection, respectively. The ML decision boundaries are in the form thetas(r) = c2r2 + c1r + c0, where thetas and r are the phase and the amplitude of the received signal, respectively. Using the expressions for the SER, we show that the impact of phase error from carrier synchronization is small, particularly for transoceanic links. For modulation formats such as 16-quadrature amplitude modulation, we propose various transmitter and receiver phase rotation strategies such that the ML detection is well approximated by using straight-line decision boundaries. The problem of signal constellation design for optimal SER performance is also studied for a system with four signal points.

Joint Power Minimization in Wireless Relay Channels

Energy-constrained multihop wireless links are considered, where the total power consumption is minimized under given requirements on the end-to-end bit error rate (BER). As multihop transmissions are known to be able to save transmission energy in a wireless environment, we study the optimal power scheduling schemes over intermediate hops when the source- relays-destination link can be modeled as cascaded binary symmetric channels. The problem is formulated with an end- to-end BER constraint, and the resulting power consumption is compared with that of the individual link requirement strategy where each hop assigns power under a per-link BER constraint. Results show that the proposed joint power scheduling strategy can achieve a maximum power reduction factor of M in an M-hop route.

Coherent detection in optical fiber systems: erratum

We correct a table showing the signal-to-noise ratio obtained in coherent detection. We also clarify a table showing the bandwidth requirements for homodyne and heterodyne downconverters. Otherwise, our previous results and conclusions are unchanged.

Experimental Comparison of Adaptive Optics Algorithms in 10-Gb/s Multimode Fiber Systems

<para> We experimentally compare various adaptive algorithms that use a spatial light modulator (SLM) to compensate modal dispersion in 50-<formula formulatype=inline> <tex Notation=TeX>

On the Statistics of Intrachannel Four-Wave Mixing in Phase-Modulated Optical Communication Systems

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Joint power minimization in wireless relay channels

</tex></formula>m graded-index multimode fibers. We show that continuous-phase sequential coordinate ascent (CPSCA) gives better bit-error-ratio performance than 2- or 4-phase sequential coordinate ascent, in concordance with simulations in <citerefgrp><citeref refid=ref10/> </citerefgrp>. We then evaluate the bandwidth characteristics of CPSCA, and show that a single SLM is able to simultaneously compensate the modal dispersion in up to 9 wavelength-division-multiplexed 10-Gb/s channels, spaced by 50 GHz, over a total bandwidth of 450 GHz. We also show that CPSCA is able to compensate for modal dispersion in fibers up to 2.2 km long, even in the presence of midspan connector offsets up to 4 <formula formulatype=inline><tex Notation=TeX>

16-QAM Signal Design and Detection in Presence of Nonlinear Phase Noise

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Design of inline amplifier gains and spacings to minimize the phase noise in optical transmission systems

</tex></formula>m (simulated in experiment by offset splices). A known non-adaptive launching technique using a fusion-spliced single-mode-to-multimode patchcord is shown to fail under these conditions. </para>

Power Profile Optimization in Phase-Modulated Systems in Presence of Nonlinear Phase Noise

We have analytically derived the correlation functions of intrachannel four-wave mixing (IFWM)-induced phase and amplitude noises in phase-modulated optical communication systems. The phase and amplitude noises are correlated with each other for binary phase-shift keying (PSK) systems but uncorrelated for M-ary PSK systems with M > 2. We have also derived analytical approximations to the probability distribution of IFWM-induced phase noise for PSK and differential PSK systems. Furthermore, we have studied the performance of an optimal linear phase-noise predictor derived from the IFWM-induced phase-noise autocorrelation function. This yields a performance improvement of 1.8 dB when IFWM-induced phase noise is the dominant impairment, and an improvement of 0.8 to 1.2 dB in the presence of amplified spontaneous emission noise and nonlinear phase noise in typical terrestrial links.