Leveraging Kronecker Structure for Mutual Coupling-Aware RIS Channel Estimation

In reconfigurable intelligent surface (RIS)-aided massive MIMO systems, the dense integration of elements introduces mutual coupling (MC), destroying the diagonal RIS response and causing a severe dimensionality curse in channel estimation (CE). This renders conventional estimation methods impractical due to prohibitive overhead and complexity. To overcome this, we reveal that the bilinear nature of the cascaded channel can be formulated as a Kronecker-structured (KS) prior, significantly reducing the number of independent parameters to be estimated. By embedding this structural prior into an approximate message passing (AMP) framework, we propose a low-complexity Kronecker-structured AMP (KS-AMP) algorithm to directly recover the overall cascaded channel. Simulation results confirm that KS-AMP delivers high estimation accuracy while drastically reducing pilot overhead and complexity compared to state-of-the-art benchmarks.