Conditioning-Centric Design of RIS-Assisted Uplink Channel Estimation under Heterogeneous Propagation

Reconfigurable intelligent surfaces (RIS) allow programmable wireless propagation but add intrinsic problems in the estimation of the uplink channel because of high-dimensional cascaded channels, limited pilot budgets, heterogeneous propagation, and realistic hardware limitations. This work identifies numerical conditioning of the pilot-induced sensing matrix as a dominant system-level determinant of estimation performance. We show that the singular value distribution directly governs NMSE scaling, heavy-tailed error behavior, and worst-region reliability, beyond conventional SNR-driven analysis. In order to operationalize this insight, we develop a conditioning-centric, estimator-agnostic framework comprising conditioning-aware RIS phase scheduling and conditioning-adaptive pilot budget selection. Comprehensive simulations in heterogeneous and mismatch cases indicate that there is a close-to-monotonic dependence between log 10κ A and mean NMSE. The proposed design consistently improves worst-region performance and reduces error variance across operating regimes. Further, assessment with one-bit phase resolution (b=1) indicates that, despite severe quantization constraints, conditioning-aware scheduling preserves performance improvements with respect to baseline. Multi-antenna scalability analysis using a block-structured sensing model ensures that these gains persist with higher system dimensionality. The resulting accuracy-overhead and fairness-accuracy trade-offs show that conditioning-based sensing design offers a scalable and robust route to channel estimation when there are realistic system constraints.