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.