The Kramers-Kronig (KK) receiver is capable of retrieving the phase information of optical single-sideband (SSB) signal from the optical intensity when the optical signal satisfies the minimum phase condition. Thus, it is possible to direct-detect the optical SSB signal without suffering from the signal-signal beat interference and linear transmission impairments. However, due to the spectral broadening induced by nonlinear operations in the conventional KK algorithm, it is necessary to employ the digital upsampling at the beginning of the digital signal processing (DSP). The increased number of samples at the DSP would hinder the real-time implementation of this attractive receiver. Hence, we propose a new DSP algorithm for KK receiver operable at 2 samples per symbol. We adopt a couple of mathematical approximations to avoid the use of nonlinear operations such as logarithm and exponential functions. By using the proposed algorithm, we demonstrate the transmission of 112-Gb/s SSB orthogonal frequency-division-multiplexed signal over an 80-km fiber link. The results show that the proposed algorithm operating at 2 samples per symbol exhibits similar performance to the conventional KK one operating at 6 samples per symbol. We also present the error analysis of the proposed algorithm for KK receiver in comparison with the conventional one.

The Kramers-Kronig (KK) receiver has recently drawn a great deal of attention due to its capability of retrieving the phase information from the directly-detected intensity waveforms. However, a technical challenge associated with the implementation of this attractive receiver is the high sampling rate of digital signal processing (DSP). Since nonlinear operations (such as logarithm and exponential functions) included in the conventional KK algorithm broaden the signal spectrum significantly, digital upsampling is required at the beginning of DSP. To solve this problem, we have recently proposed and demonstrated a new KK algorithm operable without the digital upsampling. In this upsampling-free algorithm, we removed the exponential function by expressing the complex signal in the Cartesian form (i.e., real plus imaginary) and replaced the logarithm function with its mathematical approximation. In this paper, we present the detailed comparison between the conventional and upsampling-free KK algorithms through numerical simulations. We investigate the performance of the KK receivers when we employ orthogonal frequency-division multiplexing (OFDM) and Nyquist subcarrier multiplexing (SCM) signals formatted in 16-quadrature amplitude modulation (16-QAM) and 64-QAM. Also investigated in this paper is the performance limitation of the upsampling-free KK algorithm. We propose the schematic diagrams of hardware implementation for the two KK algorithms, and study their complexity as well as their power consumption. The results show that the upsampling-free KK algorithm reduces the complexity and power consumption by a factor of 7 to 10, in comparison with the conventional algorithm at the expense of small sensitivity penalties. For example, the sensitivity difference between the two algorithms is shown to be <1 dB for the 16-QAM formatted signals.

High-altitude airborne platforms inter-connected by free-space optical communications (FSOCs) have recently emerged as a promising solution for establishing wireless networks for rural and remote areas. The performance of FSOC system is severely degraded by the angle-of-arrival (AoA) fluctuation and pointing error. The precise alignment between the optical transmitter and receiver can be achieved by using the pointing, acquisition, and tracking (PAT), but it should work within the tight constraints of airborne platforms on size, weight, and power. It is also highly desirable that the PAT operates rapidly (e.g., without iteration for optimization) since the airborne platforms can be on the fast move. We propose a rapid and computation power-efficient adaptive beam control technique, where the beam sizes are adjusted without iterations at both the transmitter and receiver using non-mechanical variable-focus lenses, to mitigate the deleterious effects of AoA fluctuation and pointing error simultaneously. For this purpose, we provide the closed-form expressions about the optimum beam sizes at the transmitter and receiver for the outage probability. We carry out Monte Carlo simulations to validate the accuracy of our theoretical derivations. We show that the airborne FSOC system using the adaptive beam control technique outperforms the system having fixed beam sizes over wide ranges of AoA fluctuation and pointing error.

The probabilistic constellation shaping (PCS) technology has recently gained a great deal of attention for coherent optical communication systems since it allows us to approach the Shannon capacity limit by varying the symbol distribution adaptively to the signal-to-noise ratio (SNR). However, there is a lack of literature on how to apply this technology to intensity modulation (IM)/direct detection (DD) systems. In this paper, we propose and demonstrate an efficient way to apply the PCS technology for IM/DD systems. In the mapping of forward error correction-encoded bits onto the pulse amplitude modulation (PAM) symbols, we assign the uniformly distributed bits to the least significant bit of binary reflected Gray coding. Then, we have a pairwise distribution of symbol amplitude, where two adjacent symbols have the same probability. Although this distribution deviates from the optimum distribution (such as Maxwell-Boltzmann distribution), we show that the SNR penalty caused by this discrepancy is negligible. We evaluate the performance of the proposed scheme through simulation by measuring the achievable rate and frame error ratios after inverse distribution matcher. The results show that the proposed scheme provides a shaping gain larger than the time-division hybrid modulation. We also carry out the experimental demonstration of the proposed scheme using a 10-Gbaud PAM-8 signal. By using the proposed scheme, we improve the receiver sensitivity by 0.9 dB when compared with the uniformly distributed PAM-8 signal.

In this paper, we study two adaptive beam control techniques, where the beam divergence angle is adjusted at the transmitter to (i) maximize link availability or (ii) minimize transmitter power while maintaining target link availability. For this purpose, we provide closed-form expressions about the link availability and optimum beam divergence angle under the effect of generalized two-dimensional Gaussian distribution of the alignment error between the transmitter and receiver. These simple and closed-form expressions reduce the computational complexity for performance optimization. Thus, they can be used to (i) reduce the power consumption required for adaptive beam control and (ii) facilitate the fast operation of the control techniques. The results show that the adaptive beam control techniques can improve system performance under various scenarios.

Volterra nonlinear equalizers (VNLEs) are known to be effective in compensating for nonlinear distortions. However, the major drawback of these equalizers is the huge implementation and computation complexity. In this paper, we propose and demonstrate low-complexity quadratic VNLEs specifically designed for directly modulated laser (DML)-based intensity-modulation/direct-detection (DD) systems. We first derive an analytical expression of the quadratic Volterra model for DML/DD system and then identify the nonlinear distortion terms mainly contributing to the system performance. We show that the interplay between the DML's adiabatic frequency chirp and fiber chromatic dispersion produces the quadratic beating between the signal and the sum of time-sampled signals, which, in turn, makes the coefficients of some beating terms in Volterra series similar. Based on these findings, we reduce the number of coefficients to be determined in the quadratic VNLEs by grouping those beating terms. The performance of the proposed VNLEs is evaluated experimentally on a 56-Gb/s 4-ary pulse amplitude modulation link implemented by using a 1.55-μm DML. We measure the bit-error ratio performance of various equalizers including feedforward equalizer, polynomial nonlinear equalizer, diagonally-pruned (DP) VNLE, and proposed quadratic VNLE, and compare them in terms of receiver sensitivity and implementation complexity. The results show that the proposed VNLE outperforms the DP-VNLE although the implementation complexity of the two equalizers is similar. Also presented in this paper is an algorithm for optimizing the parameter required in the proposed VNLE.