A Speculative GLRT-Backed Approach for Adversarial Resilience on Deep Learning-Based Array Processing

Abstract: Classical array processing methods such as the generalized likelihood ratio test (GLRT) provide statistically grounded solutions for signal detection and direction-of-arrival (DoA) estimation, but their high computational cost limits their use in low-latency settings. Deep learning (DL) has recently emerged as an efficient alternative, offering fast inference for array processing tasks. However, DL models lack statistical guarantees and, moreover, are highly susceptible to adversarial perturbations, raising fundamental concerns about their reliability in adversarial wireless environments. To address these challenges, we propose an adversarially resilient speculative array processing framework that consists of a low-latency DL classifier backed by a theoretically-grounded GLRT validator, where DL is used for fast speculative inference and later confirmed with the GLRT. We show that second order statistics of the received array, which the GLRT operates on, are spatially invariant to L-p bounded adversarial perturbations, providing adversarial robustness and theoretically-grounded validation of DL predictions. Empirical evaluations under multiple L-p bounds, perturbation designs, and perturbation magnitudes corroborate our theoretical findings, demonstrating the superior performance of our proposed framework in comparison to multiple state-of-the-art baselines.