Distributionally Robust Receive Combining

TL;DR

This paper introduces a distributionally robust framework for receive combining in wireless communication, addressing uncertainties like channel variations and noise, and unifies linear and nonlinear estimators within a machine learning perspective.

Contribution

It proposes a novel distributionally robust receive combining framework that handles various uncertainties without requiring channel estimation, unifies existing methods, and extends to kernel and neural network-based estimators.

Findings

The framework includes existing combiners as special cases.

Kernelized diagonal loading improves robustness in nonlinear estimation.

Ridge and kernel ridge regression are shown to be distributionally robust.

Abstract

This article investigates signal estimation in wireless transmission (i.e., receive combining) from the perspective of statistical machine learning, where the transmit signals may be from an integrated sensing and communication system; that is, 1) signals may be not only discrete constellation points but also arbitrary complex values; 2) signals may be spatially correlated. Particular attention is paid to handling various uncertainties such as the uncertainty of the transmit signal covariance, the uncertainty of the channel matrix, the uncertainty of the channel noise covariance, the existence of channel impulse noises, the non-ideality of the power amplifiers, and the limited sample size of pilots. To proceed, a distributionally robust receive combining framework that is insensitive to the above uncertainties is proposed, which reveals that channel estimation is not a necessary operation. For optimal linear estimation, the proposed framework includes several existing combiners as special cases such as diagonal loading and eigenvalue thresholding. For optimal nonlinear estimation, estimators are limited in reproducing kernel Hilbert spaces and neural network function spaces, and corresponding uncertainty-aware solutions (e.g., kernelized diagonal loading) are derived. In addition, we prove that the ridge and kernel ridge regression methods in machine learning are distributionally robust against diagonal perturbation in feature covariance.