Wideband Compressed-Domain Cramér--Rao Bounds for Near-Field XL-MIMO: Data and Geometric Diversity Decomposition

Wideband orthogonal frequency-division multiplexing (OFDM) over extremely large-scale MIMO (XL-MIMO) arrays in the near-field Fresnel regime suffers from a coupled beam-squint and wavefront-curvature effect that renders single-frequency covariance models severely biased: the per-subcarrier compressed covariance diverges from the center-frequency model by 64\% at $B = 100$~MHz and by 177\% at $B = 400$~MHz. We derive the wideband compressed-domain Cramér--Rao bound (CRB) for hybrid analog--digital architectures and decompose the Fisher information gain into a dominant data-diversity term that scales as $10\log_{10}K_s$~dB and a secondary geometric-diversity term arising from frequency-dependent curvature. At 28~GHz with $M = 256$ antennas, $N_\mathrm{RF} = 16$ RF chains, and $K_s = 512$ subcarriers, wideband processing yields $+27.8$~dB of CRB improvement at $B = 400$~MHz, of which $+0.7$~dB is attributable to geometric diversity.