Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on Information Theor

Constellation Optimization in the Presence of Strong Phase Noise

In this paper, we address the problem of optimizing signal constellations for strong phase noise. The problem is investigated by considering three optimization formulations, which provide an analytical framework for constellation design. In the first formulation, we seek to design constellations that minimize the symbol error probability (SEP) for an approximate ML detector in the presence of phase noise. In the second formulation, we optimize constellations in terms of mutual information (MI) for the effective discrete channel consisting of phase noise, additive white Gaussian noise, and the approximate ML detector. To this end, we derive the MI of this discrete channel. Finally, we optimize constellations in terms of the MI for the phase noise channel. We give two analytical characterizations of the MI of this channel, which are shown to be accurate for a wide range of signal-to-noise ratios and phase noise variances. For each formulation, we present a detailed analysis of the optimal constellations and their performance in the presence of strong phase noise. We show that the optimal constellations significantly outperform conventional constellations and those proposed in the literature in terms of SEP, error floors, and MI.Comment: 10 page, 10 figures, Accepted to IEEE Trans. Commu

Signal Design and Machine Learning Assisted Nonlinearity Compensation for Coherent Optical Fibre Communication Links

This thesis investigates low-complexity digital signal processing (DSP) for signal design and nonlinearity compensation strategies to improve the performance of single-mode optical fibre links over different distance scales. The performance of a novel ML-assisted inverse regular perturbation technique that mitigates fibre nonlinearities was investigated numerically with a dual-polarization 64 quadrature amplitude modulation (QAM) link over 800 km distance. The model outperformed the heuristically-optimised digital backpropagation approach with <5 steps per span and mitigated the gain expansion issue, which limits the accuracy of an untrained model when the balance between the nonlinear and linear components becomes considerable. For short reach links, the phase noise due to low-cost, high-linewidth lasers is a more significant channel impairment. A novel constellation optimisation algorithm was, therefore, proposed to design modulation formats that are robust against both additive white Gaussian noise (AWGN) and the residual laser phase noise (i.e., after carrier phase estimation). Subsequently, these constellations were numerically validated in the context of a 400ZR standard system, and achieved up to 1.2 dB gains in comparison with the modulation formats which were optimised only for the AWGN channel. The thesis concludes by examining a joint strategy to modulate and demodulate signals in a partially-coherent AWGN (PCAWGN) channel. With a low-complexity PCAWGN demapper, 8- to 64-ary modulation formats were designed and validated through numerical simulations. The bit-wise achievable information rates (AIR) and post forward error correction (FEC) bit error rates (BER) of the designed constellations were numerically validated with: the theoretically optimum, Euclidean (conventional), and low-complexity PCAWGN demappers. The resulting constellations demonstrated post-FEC BER shaping gains of up to 2.59 dB and 2.19 dB versus uniform 64 QAM and 64-ary constellations shaped for the purely AWGN channel model, respectively. The described geometric shaping strategies can be used to either relax linewidth and/or carrier phase estimator requirements, or to increase signal-to-noise ratio (SNR) tolerance of a system in the presence of residual phase noise

Analog Network Coding for Multi-User Spread-Spectrum Communication Systems

This work presents another look at an analog network coding scheme for multi-user spread-spectrum communication systems. Our proposed system combines coding and cooperation between a relay and users to boost the throughput and to exploit interference. To this end, each pair of users, $\mathcal{A}$ and $\mathcal{B}$, that communicate with each other via a relay $\mathcal{R}$ shares the same spreading code. The relay has two roles, it synchronizes network transmissions and it broadcasts the combined signals received from users. From user $\mathcal{B}$'s point of view, the signal is decoded, and then, the data transmitted by user $\mathcal{A}$ is recovered by subtracting user $\mathcal{B}$'s own data. We derive the analytical performance of this system for an additive white Gaussian noise channel with the presence of multi-user interference, and we confirm its accuracy by simulation.Comment: 6 pages, 2 figures, to appear at IEEE WCNC'1

Tight Upper and Lower Bounds to the Information Rate of the Phase Noise Channel

Numerical upper and lower bounds to the information rate transferred through the additive white Gaussian noise channel affected by discrete-time multiplicative autoregressive moving-average (ARMA) phase noise are proposed in the paper. The state space of the ARMA model being multidimensional, the problem cannot be approached by the conventional trellis-based methods that assume a first-order model for phase noise and quantization of the phase space, because the number of state of the trellis would be enormous. The proposed lower and upper bounds are based on particle filtering and Kalman filtering. Simulation results show that the upper and lower bounds are so close to each other that we can claim of having numerically computed the actual information rate of the multiplicative ARMA phase noise channel, at least in the cases studied in the paper. Moreover, the lower bound, which is virtually capacity-achieving, is obtained by demodulation of the incoming signal based on a Kalman filter aided by past data. Thus we can claim of having found the virtually optimal demodulator for the multiplicative phase noise channel, at least for the cases considered in the paper.Comment: 5 pages, 2 figures. Accepted for presentation at ISIT 201

Impact of 4D channel distribution on the achievable rates in coherent optical communication experiments

We experimentally investigate mutual information and generalized mutual information for coherent optical transmission systems. The impact of the assumed channel distribution on the achievable rate is investigated for distributions in up to four dimensions. Single channel and wavelength division multiplexing (WDM) transmission over transmission links with and without inline dispersion compensation are studied. We show that for conventional WDM systems without inline dispersion compensation, a circularly symmetric complex Gaussian distribution is a good approximation of the channel. For other channels, such as with inline dispersion compensation, this is no longer true and gains in the achievable information rate are obtained by considering more sophisticated four-dimensional (4D) distributions. We also show that for nonlinear channels, gains in the achievable information rate can also be achieved by estimating the mean values of the received constellation in four dimensions. The highest gain for such channels is seen for a 4D correlated Gaussian distribution

Demodulation and Detection Schemes for a Memoryless Optical WDM Channel

It is well known that matched filtering and sampling (MFS) demodulation together with minimum Euclidean distance (MD) detection constitute the optimal receiver for the additive white Gaussian noise channel. However, for a general nonlinear transmission medium, MFS does not provide sufficient statistics, and therefore is suboptimal. Nonetheless, this receiver is widely used in optical systems, where the Kerr nonlinearity is the dominant impairment at high powers. In this paper, we consider a suite of receivers for a two-user channel subject to a type of nonlinear interference that occurs in wavelength-division-multiplexed channels. The asymptotes of the symbol error rate (SER) of the considered receivers at high powers are derived or bounded analytically. Moreover, Monte-Carlo simulations are conducted to evaluate the SER for all the receivers. Our results show that receivers that are based on MFS cannot achieve arbitrary low SERs, whereas the SER goes to zero as the power grows for the optimal receiver. Furthermore, we devise a heuristic demodulator, which together with the MD detector yields a receiver that is simpler than the optimal one and can achieve arbitrary low SERs. The SER performance of the proposed receivers is also evaluated for some single-span fiber-optical channels via split-step Fourier simulations

A space communications study Final report, 15 Sep. 1966 - 15 Sep. 1967

Investigation of signal to noise ratios and signal transmission efficiency for space communication system

On the Capacity of the Wiener Phase-Noise Channel: Bounds and Capacity Achieving Distributions

In this paper, the capacity of the additive white Gaussian noise (AWGN) channel, affected by time-varying Wiener phase noise is investigated. Tight upper and lower bounds on the capacity of this channel are developed. The upper bound is obtained by using the duality approach, and considering a specific distribution over the output of the channel. In order to lower-bound the capacity, first a family of capacity-achieving input distributions is found by solving a functional optimization of the channel mutual information. Then, lower bounds on the capacity are obtained by drawing samples from the proposed distributions through Monte-Carlo simulations. The proposed capacity-achieving input distributions are circularly symmetric, non-Gaussian, and the input amplitudes are correlated over time. The evaluated capacity bounds are tight for a wide range of signal-to-noise-ratio (SNR) values, and thus they can be used to quantify the capacity. Specifically, the bounds follow the well-known AWGN capacity curve at low SNR, while at high SNR, they coincide with the high-SNR capacity result available in the literature for the phase-noise channel.Comment: IEEE Transactions on Communications, 201