Keying

Abstract: We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

Abstract: Orthogonal frequency-division multiplexing (OFDM) modulation is a promising technique for achieving the high bit rates required for a wireless multimedia service. Without channel estimation and tracking, OFDM systems have to use differential phase-shift keying (DPSK), which has a 3-dB signal-to-noise ratio (SNR) loss compared with coherent phase-shift keying (PSK). To improve the performance of OFDM systems by using coherent PSK, we investigate robust channel estimation for OFDM systems. We derive a minimum mean-square-error (MMSE) channel estimator, which makes full use of the time- and frequency-domain correlations of the frequency response of time-varying dispersive fading channels. Since the channel statistics are usually unknown, we also analyze the mismatch of the estimator-to-channel statistics and propose a robust channel estimator that is insensitive to the channel statistics. The robust channel estimator can significantly improve the performance of OFDM systems in a rapid dispersive fading channel.

Abstract: Differential-phase-shift keying (DPSK) has recently been used to reach record distances in long-haul lightwave communication systems. This paper will review theoretical, as well as implementation, aspects of DPSK, and discuss experimental results.

Abstract: We present a framework for differential modulation with multiple antennas across a continuously fading channel, where neither the transmitter nor the receiver knows the fading coefficients. The framework can be seen as a natural extension of standard differential phase-shift keying commonly used in single-antenna unknown-channel systems. We show how our differential framework links the unknown-channel system with a known-channel system, and we develop performance design criteria. As a special ease, we introduce a class of diagonal signals where only one antenna is active at any time, and demonstrate how these signals may be used to achieve full transmitter diversity and low probability of error.

Abstract: Orthogonal frequency division multiplexing (OFDM) modulation is a promising technique for achieving the high-bit-rates required for a wireless multimedia service. Without channel estimation and tracking, OFDM systems have to use differential phase-shift keying (DPSK), which has a 3 dB signal-to-noise ratio (SNR) loss compared with coherent phase-shift keying (PSK). To improve the performance of OFDM systems by using coherent PSK, we investigate robust channel estimation for OFDM systems. We derive a minimum mean-square-error (MSE) channel estimator, which makes full use of the time- and frequency-domain correlations of the frequency response of time-varying dispersive fading channels. Since the channel statistics are usually unknown, we also analyze the mismatch of the estimator to channel statistics and propose a robust channel estimator that is insensitive to the channel statistics. The robust channel estimator can significantly improve the performance of OFDM systems in a rapid dispersive fading channel.