Distributionally Robust Receive Combining
Shixiong Wang, Wei Dai, Geoffrey Ye Li
TL;DR
The paper tackles robust signal estimation in wireless receive combining under distributional uncertainty and ISAC-like signaling. It introduces a distributionally robust framework that covers both linear and nonlinear estimators, showing channel-estimation is not strictly necessary and linking ridge and kernel ridge methods to robustness. Through moment-based and Wasserstein/F-norm uncertainty sets, it derives closed-form robust linear beamformers and kernel/RKHS/NN-based nonlinear estimators, with multi-frame extensions for dynamic channels. Experiments demonstrate robustness gains from diagonal loading and nonlinear methods under limited pilots and impulse noise, while noting tradeoffs between kernel/NN expressiveness and computational burden. The work provides a principled foundation for robust, data-driven receive combining in next-generation wireless systems.
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.