Wideband Compressed-Domain Cramér-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 couples beam squint and wavefront curvature, and existing single-frequency compressed covariance models are severely biased as a result. To the best of our knowledge, no compressed-domain Cramér-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 two terms: a dominant data-diversity term, exactly 10 log10(K_s) dB, where K_s denotes the number of independent subcarrier observations, and we prove that for a centred array the full-array range bound is invariant to beam squint, so the full-array wideband gain equals the data-diversity term to within 3x10^-4 dB. Under hybrid compression, however, this invariance breaks: the residual is a combiner-dependent fluctuation of either sign rather than a propagation-geometry effect, with mean +0.157 dB and standard deviation 0.767 dB over 385 realizations at N_RF = 16, B = 400 MHz, and its spread shrinks toward zero as the number of RF chains grows. At 28 GHz with B = 400 MHz, data diversity contributes +27.1 dB and 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 therefore the dominant requirement, and the residual is a property of the analog front end rather than of the propagation geometry.

8 pages (incl. IEEE notice), 5 figures. Accepted for publication in GLOBECOM 2026 - 2026 IEEE Global Communications Conference. Supersedes v3. v4 adds required IEEE copyright notice post-acceptance; corrects Fig. 3 reference distance (EBRD, not r_RD/8) per Hussain et al., IEEE TWC 2025