Learning Regularization Structure for Biosignal Template Estimation

Estimating event-locked templates from bio-signal recordings via regularized least-squares requires choosing both the regularization structure and its magnitude, choices that are typically made heuristically. We develop a data-driven framework based on Stein's Unbiased Risk Estimate (SURE) that jointly optimizes both. By parameterizing the regularization operator as a convolution kernel, our method learns the penalty structure directly from the data, combining smoothness enforcement with ridge-like shrinkage in a way that cannot be achieved by scaling a fixed difference operator. While standard SURE assumes white noise, biosignal noise exhibits temporal autocorrelation. We therefore extend SURE to colored noise by replacing its scalar trace term with a structured correction based on the noise covariance matrix. For AR(1) noise, this correction requires only two parameters, the noise variance and the lag-1 autocorrelation, both estimable from pre-event baselines. Cross-modality validation on auditory event-related potentials, P300 brain--computer interface data, and ECG morphology demonstrates consistent gains compared to alternative methods, all at $K=5$ events per class - the regime most relevant for rapid calibration and personalization.

Multi-User Diversity Scaling in Heavy-Tailed Fading

Classical multi-user diversity theory predicts that throughput over Rayleigh fading channels grows as $\log_2\!\log_2 K$. In this work, we demonstrate a fundamental shift in this scaling law under heavy-tailed composite fading. Specifically, under Fisher--Snedecor $\mathcal{F}$ composite fading, the channel power acquires a regularly varying upper tail, shifting extreme-value statistics from the Gumbel to the Fréchet domain. We prove that the maximum SINR among $K$ users scales polynomially as $K^{1/m_s}$, where $m_s$ is the shadowing severity parameter, leading to an ergodic capacity scaling of $\frac{1}{m_s}\log_2 K$. Crucially, this scaling persists in interference-limited Poisson networks, where aggregate co-channel interference alters the scaling constant but not the exponent. This polynomial gain is most relevant in severe-to-moderate shadowing ($m_s \le 3$), as encountered in body-area networks, vehicular/industrial IoT, and dense indoor environments, where Fréchet asymptotics overtake industry-standard lognormal models at practical user counts. Finally, we establish the conditions necessary to harvest this gain (showing that proportional-fair scheduling under quasi-static shadowing reverts to Gumbel scaling) and validate all analytical findings through Monte Carlo simulations, including MIMO random beamforming.

Adaptive Derivative Estimation via Stein's Unbiased Risk

Estimating derivatives from noisy sampled data is fundamental to control, human--computer interaction, and biomedical engineering. Causal FIR derivative filters offer a natural approach for this challenge, yet their performance depend on their length. While short filters amplify noise, long filters introduce smoothing bias. We present SURDE (SURE Derivative Estimator), which addresses this tradeoff at each time step by evaluating a data-driven cost derived from Stein's Unbiased Risk Estimator (SURE) across a bank of candidate lengths and soft-combining their outputs via exponential weighting. We prove a minimax-optimal oracle inequality for the soft-combined estimator and use it to derive the optimal weighting temperature in closed form. Thus, the only tuning parameter for SURDE is the noise variance. Via numerical simulations we show that SURDE consistently outperforms alternative adaptive methods (the Intersection of Confidence Intervals (ICI) rule and the Adaptive Windowing Velocity Estimator (AWVE)) for first-derivative estimation. We further show that \surede{} is robust to noise-variance misspecification (9\% degradation over a $4\times$ range), and that it is superior to ICI and AWVE also over real data scenarios (the EuRoC MAV dataset). SURDE is causal, computationally light, and requires only a rough estimate of the noise variance.