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-achieving input distribution of non-coherent Rayleigh fading channels with average- and peak-power constraints is known to be discrete with a finite number of points. We sharpen this result by deriving upper and lower bounds on the number of amplitude levels. The upper bounds are based on two techniques from complex analysis: counting the number of maxima of a function that characterizes the Karush-Kuhn-Tucker conditions and an oscillation theorem. The latter provides a stronger bound but applies only if the average power constraint is inactive.

This work considers a binomial noise channel. The paper can be roughly divided into two parts. The first part is concerned with the properties of the capacity-achieving distribution. In particular, for the binomial channel, it is not known if the capacity-achieving distribution is unique since the output space is finite (i.e., supported on integers 0, …, n) and the input space is infinite (i.e., supported on the interval [0, 1 D, and there are multiple distributions that induce the same output distribution. This paper shows that the capacity-achieving input distribution is unique by appealing to the total positivity property of the binomial kernel. In addition, we provide upper and lower bounds on the cardinality of the support of the capacity-achieving distribution. Specifically, an upper bound of order n/2 is shown, which improves on the previous upper bound of order$n$due to Witsenhausen. Moreover, a lower bound of order yin is shown. Finally, additional results about the locations and probability values of the support points are established.

This work investigates the error performance of detection schemes based on the minimum Pearson distance in the context of additive white Gaussian noise channels with unknown and unbounded offset, constant throughout each channel use. We derive a lower bound on the word error rate under modified Pearson (MP) detection. Additionally, we introduce a new and low-complexity detection strategy, namely the Simplified Pearson (SP) detector. We analyze and compare the error performance of the SP detector with that of the MP detector.

This work studies non-coherent Rayleigh fading channels subject to average- and peak-power constraints. Several properties of the optimal input distribution are derived based on the Karush-Kuhn- Tucker conditions. In particular, the capacity-achieving distribution is characterized in the small peak and average power regimes, upper and lower bounds on the optimal input probabilities are presented, insights about the locations of the support points are provided, and bounds on the channel capacity are established.

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.

This paper studies secrecy-capacity of an n-dimensional Gaussian wiretap channel under the peak-power constraint. This work determines the largest peak-power constraint ${\overline {\text{R}} _n}$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the low amplitude regime. The asymptotic of ${\overline {\text{R}} _n}$ 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 for computation. Furthermore, several numerical examples are provided, such as the example of the secrecy-capacity achieving distribution outside of the low amplitude regime.

Upper bounds on the capacity of vector Gaussian channels affected by fading are derived under peak amplitude constraints at the input. The focus is on constraint regions that can be decomposed in a Cartesian product of sub-regions. This constraint models a transmitter configuration employing a number of power amplifiers less than or equal to the total number of transmitting antennas. In general, the power amplifiers feed distinct subsets of the transmitting antennas and partition the input in independent subspaces. Two upper bounds are derived: The first one is suitable for high signal-to-noise ratio (SNR) values and, as we prove, it is tight in this regime; The second upper bound is accurate at low SNR. Furthermore, the derived upper bounds are applied to the relevant case of amplitude constraints induced by employing a distinct power amplifier for each transmitting antenna.

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.

We evaluate capacity bounds for multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) fading channels subject to input amplitude constraints. We focus on two practical cases, in which the transmitter: (i) employs a single antenna amplifier, which induces a constraint on the norm of the input vector, and (ii) it employs multiple amplifiers, one per antenna, which leads to independent constraints on the amplitude of each input vector entry. For both cases, we evaluate the asymptotic capacity gap between upper and lower bounds at high signal-to-noise ratio.

An upper bound on the capacity of multiple-input multiple-output (MIMO) additive white Gaussian noise fading channels is derived under peak amplitude constraints. The tightness of the bound is investigated at high signal-to-noise ratio (SNR), for any arbitrary convex amplitude constraint region. Moreover, a numerical simulation of the bound for fading MIMO channels is analyzed, at any SNR level, for a practical transmitter configuration employing a single power amplifier for all transmitting antennas.