Multi-Scale Channel Estimation for Transmissive RIS Transceivers via Partial Active Elements

We propose a two-stage channel estimation protocolfor partially active transmissive reconfigurable intelligentsurface (RIS) transceivers. Local estimates of the quasi-staticfeed antenna--RIS channel are reused during RIS--user trainingto reduce repeated pilot overhead. A multi-scale orthogonal matching pursuit (OMP) algorithm reconstructs both full-dimensional channels through coarse-to-fine dictionary searches. Numerical results show that the proposed method outperforms interpolation baselines and approaches conventional OMP accuracy with reduced dictionary-search cost.Training-length evaluation demonstrates diminishing accuracy gains from longer training, supporting a trade-off between reconstruction accuracy and training overhead.