Harnessing Wavefront Curvature and Spatial Correlation in Noncoherent MIMO Communications

Noncoherent communication systems have regained interest due to the growing demand for high-mobility and low-latency applications. Most existing studies using large antenna arrays rely on the far-field approximation, which assumes locally plane wavefronts. This assumption becomes inaccurate at higher frequencies and shorter ranges, where wavefront curvature plays a significant role and antenna arrays may operate in the radiative near field. In this letter, we adopt a model for the channel spatial correlation matrix that remains valid in both near and far field scenarios. Using this model, we demonstrate that noncoherent systems can leverage the benefits of wavefront spherical curvature, even beyond the Fraunhofer distance, revealing that the classical far-field approximation may significantly underestimate system performance. Moreover, we show that large antenna arrays enable the multiplexing of various users and facilitate near-optimal noncoherent detection with low computational complexity.

Conditional Dependence via U-Statistics Pruning

The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information shared by the original pair. A typical issue in this challenging problem is the inversion of ill-conditioned autocorrelation matrices. This paper presents a novel measure of conditional dependence based on the use of incomplete unbiased statistics of degree two, which allows to re-interpret independence as uncorrelatedness on a finite-dimensional feature space. This formulation enables to prune data according to the observations of the confounder itself, thus avoiding matrix inversions altogether. Moreover, the proposed approach is articulated as an extension of the Hilbert-Schmidt independence criterion, which becomes expressible through kernels that operate on 4-tuples of data.

Asymptotic Analysis of Near-Field Coupling in Massive MISO and Massive SIMO Systems

This paper studies the receiver to transmitter antenna coupling in near-field communications with massive arrays. Although most works in the literature consider that it is negligible and approximate it by zero, there is no rigorous analysis on its relevance for practical systems. In this work, we leverage multiport communication theory to obtain conditions for the aforementioned approximation to be valid in MISO and SIMO systems. These conditions are then particularized for arrays with fixed inter-element spacing and arrays with fixed size.

Asymptotic Analysis of Synchronous Signal Processing

This paper extends various theoretical results from stationary data processing to cyclostationary (CS) processes under a unified framework. We first derive their asymptotic eigenbasis, which provides a link between their Fourier and Karhunen-Lo\`eve (KL) expansions, through a unitary transformation dictated by the cyclic spectrum. By exploiting this connection and the optimalities offered by the KL representation, we study the asymptotic performance of smoothing, filtering and prediction of CS processes, without the need for deriving explicit implementations. We obtain minimum mean squared error expressions that depend on the cyclic spectrum and include classical limits based on the power spectral density as particular cases. We conclude this work by applying the results to a practical scenario, in order to quantify the achievable gains of synchronous signal processing.

On the convergence of Block Majorization-Minimization algorithms on the Grassmann Manifold

The Majorization-Minimization (MM) framework is widely used to derive efficient algorithms for specific problems that require the optimization of a cost function (which can be convex or not). It is based on a sequential optimization of a surrogate function over closed convex sets. A natural extension of this framework incorporates ideas of Block Coordinate Descent (BCD) algorithms into the MM framework, also known as block MM. The rationale behind the block extension is to partition the optimization variables into several independent blocks, to obtain a surrogate for each block, and to optimize the surrogate of each block cyclically. The advantage of the block MM is that the construction and successive optimization of the surrogate functions is potentially easier than with the non-block alternative. The purpose of this letter is to exploit the geometrical properties of the Grassmann manifold (a non-convex set) for the purpose of extending classical convergence proofs of the block MM when at least one of the blocks is constrained in this manifold.

Quadratic Detection in Noncoherent Massive SIMO Systems over Correlated Channels

With the goal of enabling ultrareliable and low-latency wireless communications for industrial internet of things (IIoT), this paper studies the use of energy-based modulations in noncoherent massive single input multiple output (SIMO) systems. We consider a one-shot communication over a channel with correlated Rayleigh fading and colored Gaussian noise. We first provide a theoretical analysis on the limitations of non-negative pulse-amplitude modulation (PAM) in systems of this kind, based on maximum likelihood detection. The existence of a fundamental error floor at high signal-to-noise ratio (SNR) regimes is proved for constellations with more than two energy levels, when no (statistical) channel state information is available at the transmitter. In the main body of the paper, we present a design framework for quadratic detectors that generalizes the widely-used energy detector, to better exploit the statistical knowledge of the channel. This allows us to design receivers optimized according to information-theoretic criteria that exhibit lower error rates at moderate and high SNR. We subsequently derive an analytic approximation for the error probability of a general class of quadratic detectors in the large array regime. Finally, we introduce an improved reception scheme based on the combination of quadratic detectors and assess its capabilities numerically.