This paper studies the secrecy capacity of an n-dimensional Gaussian wiretap channel under a peak power constraint. This work determines the largest peak power constraint ${\overline{\mathsf{R}}}_n$, such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the low-amplitude regime. The asymptotic value of ${\overline{\mathsf{R}}}_n$ as n goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy capacity is also characterized in a form amenable to computation. Several numerical examples are provided, such as the example of the secrecy-capacity-achieving distribution beyond the low-amplitude regime. Furthermore, for the scalar case $(n=1)$, we show that the secrecy-capacity-achieving input distribution is discrete with finitely many points at most at the order of $\frac{{\mathsf{R}}^2}{{\sigma }_1^2}$, where ${\sigma }_1^2$ is the variance of the Gaussian noise over the legitimate channel.

An upper bound on the capacity of multiple-input multiple-output (MIMO) Gaussian fading channels is derived under peak amplitude constraints. The upper bound is obtained borrowing concepts from convex geometry and it extends to MIMO channels notable results from the geometric analysis on the capacity of scalar Gaussian channels. Relying on a sphere packing argument and on the renowned Steiner’s formula, the proposed upper bound depends on the intrinsic volumes of the constraint region, i.e., functionals defining a measure of the geometric features of a convex body. The tightness of the bound is investigated at high signal-to-noise ratio (SNR) for any arbitrary convex amplitude constraint region, for any channel matrix realization, and any dimension of the MIMO system. In addition, two variants of the upper bound are proposed: one is useful to ensure the feasibility in the evaluation of the bound and the other to improve the bound’s performance in the low SNR regime. Finally, the upper bound is specialized for two practical transmitter configurations, either employing a single power amplifier for all transmitting antennas or a power amplifier for each antenna.

The capacity-achieving input distribution of noncoherent Rayleigh fading channels is known to be discrete, and this result is refined in several ways. First, a detailed analysis is provided for bounded peak-power constraints. Second, scenarios for which binary inputs are optimal are characterized by analyzing the interplay between average-and peak-power constraints, including conditions under which the average-power constraint remains active or inactive. Third, cardinality bounds on the support of the capacity-achieving distribution are provided using methods from complex analysis, such as the oscillation theorem. Fourth, bounds on the location of the support points are provided. Fifth, new methods are derived to bound the probability masses of the optimal input distribution, along with techniques to connect the support-point locations and probabilities. Several other results are provided, such as capacity bounds.

The effectiveness of Volterra equalization (VE) is analyzed to improve the performance of a metropolitan area network (MAN), characterized by directly-modulated (DM) vertical-cavity surface-emitting laser (VCSEL) sources combined with coherent detection, in order to target both high capacity and hundreds of km reaches. VE, which is a well-known nonlinear equalization technique, is used to cope not only with the distortion introduced by the real implementation of direct discrete multi-tone (DMT) modulation of the VCSEL, but also with the nonlinear impairments. A suitable experimentation, in case of 25-GHz spaced dense wavelength division multiplexed (DWDM) propagation, allows to validate a simulation tool, developed to provide a systematic analysis of the supported capacity per VCSEL, with and without VE. Simulations permit to analyze the effects of VE for different channel spacings (25, 50 and 100 GHz) and for different standard single-mode fiber (SSMF) lengths (up to 200 km), focusing on the evolution of the capacity per channel in case of different launch powers and optical signal-to-noise ratios. The dependence of the VE effectiveness is evaluated also in terms of spectral behavior. VE allows to achieve up to 13%-capacity increase, assuring 50 Gb/s rate per polarization per VCSEL, in case of DWDM transmission and after 200-km propagation, as targeted by the considered MAN applications.

Low-complexity detection schemes are studied for additive white Gaussian noise channels with an unknown and unbounded offset constant over each memory read. Detectors based on the Pearson distance are analyzed, and a new lower bound on the word error rate of Modified Pearson (MP) detection is derived. Three novel detectors are proposed: the Simplified Pearson (SP), the Ultra-Simplified Pearson (USP), and the Adjusted-Threshold (AT) detectors. The USP and AT detectors are designed to be robust against destructive readings. The proposed schemes are particularly suited for memory systems employing ramp-reading architectures. The analysis demonstrates that the proposed detectors achieve competitive error-rate performance with significantly reduced complexity compared to MP detection.

The capacity of multiple-input multiple-output additive white Gaussian noise channels is investigated under peak amplitude constraints on the norm of the input vector. New insights on the capacity-achieving input distribution are presented. Furthermore, it is provided an iterative algorithm to numerically evaluate both the information capacity and the optimal input distribution of such channel.