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 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.

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.