Case-based reasoning (CBR) is a promising approach for integrating explainability into artificial intelligence (AI) systems used in the medical domain. However, physiological signals recorded as time series pose challenges due to complex temporal structures, large case bases, and inter-individual variability. We address these limitations by introducing a twin explainable CBR (XCBR) system, combining an XGBoost classifier with an interpretable CBR component. To improve retrieval efficiency, we propose PURS (Prototype-based Unsupervised Retrieval with Self-similarity matrices), which computes self-similarity matrices and applies agglomerative clustering to generate a compact, representative prototype case base. Additionally, our twin system provides visual explanations through supportive and contrastive cases. We test our approach on radar-based sleep data from healthy participants for automatic sleep-wake recognition (SWR), a clinically relevant task where explainability is crucial. Our results demonstrate that PURS substantially reduces the computational cost of retrieval while preserving classification accuracy, enabling efficient and interpretable decision support for clinical use.