  The support of artificial intelligence (AI) based decision-making is a key
element in future 6G networks, where the concept of native AI will be
introduced. Moreover, AI is widely employed in different critical applications
such as autonomous driving and medical diagnosis. In such applications, using
AI as black-box models is risky and challenging. Hence, it is crucial to
understand and trust the decisions taken by these models. Tackling this issue
can be achieved by developing explainable AI (XAI) schemes that aim to explain
the logic behind the black-box model behavior, and thus, ensure its efficient
and safe deployment. Recently, we proposed a novel perturbation-based XAI-CHEST
framework that is oriented toward channel estimation in wireless
communications. The core idea of the XAI-CHEST framework is to identify the
relevant model inputs by inducing high noise on the irrelevant ones. This
manuscript provides the detailed theoretical foundations of the XAI-CHEST
framework. In particular, we derive the analytical expressions of the XAI-CHEST
loss functions and the noise threshold fine-tuning optimization problem. Hence
the designed XAI-CHEST delivers a smart input feature selection methodology
that can further improve the overall performance while optimizing the
architecture of the employed model. Simulation results show that the XAI-CHEST
framework provides valid interpretations, where it offers an improved bit error
rate performance while reducing the required computational complexity in
comparison to the classical DL-based channel estimation.
