Robust Channel Estimation for RIS-Aided Communication Systems Under Unknown Mutual Coupling

At sub-half-wavelength element spacing, mutual coupling degrades RIS channel estimation by several decibels when ignored, yet the passive surface cannot sense its own response and existing coupling-aware estimators require the scattering matrix a priori. This letter proposes a sparse channel estimator that remains accurate when the coupling is entirely unknown: translation invariance, reciprocity, and a single mirror plane confine the scattering matrix of a uniform planar array to a block-Toeplitz form with (r+1)2-1 coefficients over a coupling radius r, reducing the joint problem to a few unknowns recoverable from a pilot budget far below the array size. On a 64-element RIS with 12 pilots, the estimator operates within 1.5 dB of a genie granted the exact scattering matrix, whereas a coupling-blind estimator saturates at an error floor more than 12 dB higher at high SNR. Under coupling coefficients reported for a fabricated prototype, which include interactions beyond the assumed model, the estimator retains a 4.6 dB advantage over the coupling-blind baseline.