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

Abstract

Wideband orthogonal frequency-division multiplexing (OFDM) over near-field extremely large-scale MIMO (XL-MIMO) arrays introduces a coupled beam-squint and wavefront-curvature effect that renders single-frequency compressed covariance models severely biased. To the best of our knowledge, no compressed-domain Cramer-Rao bound (CRB) has been reported for this regime under hybrid analog-digital architectures; existing wideband near-field bounds assume full-array observation. We derive the wideband compressed-domain CRB and decompose its Fisher information gain into a dominant data-diversity term scaling as 10 log10(Ks) dB, where Ks denotes the number of independent subcarrier observations, and a secondary geometric-diversity term from frequency-dependent Fresnel curvature. At 28 GHz with bandwidth B = 400 MHz, the total CRB improvement reaches +27.8 dB, comprising +27.1 dB from data diversity and +0.7 dB from geometric diversity; hybrid compression contributes an additional 12.6 dB gap relative to the full-array bound at N_RF = 16 RF chains. Frequency-aware covariance modeling is the dominant requirement; geometric diversity is a secondary but growing benefit as fractional bandwidth approaches 6G regimes.