Wideband Near-Field Channel Estimation Under Hybrid Compression: Cross-Subcarrier KL Covariance Fitting With OFDM Fresnel Model

Abstract

We consider wideband channel estimation for extremely large-scale multiple-input multiple-output (XL-MIMO) arrays under hybrid analog-digital compression, in which a uniform linear array (ULA) is observed through far fewer radio-frequency (RF) chains than antennas. At a carrier frequency of 28 GHz with bandwidths reaching several hundred MHz, the standard narrowband polar-domain channel model fails: the near-field Fresnel curvature becomes subcarrier-dependent, and the compressed observation destroys the per-subcarrier spatial covariance structure that narrowband methods exploit. We propose the Wideband Cross-subcarrier Kullback--Leibler (WB-CL-KL) estimator, which jointly estimates angle and range directly from the compressed sample covariance, without full-array reconstruction, by fitting a structured Fresnel covariance model across orthogonal frequency-division multiplexing (OFDM) subcarriers via a cross-subcarrier Kullback--Leibler (KL) divergence criterion. We also derive the wideband compressed-domain Cramér--Rao bound (CRB) -- the performance lower bound for this hybrid architecture -- from the Slepian--Bangs formula, and decompose its gain over the narrowband bound into a data-diversity component of +27.093 dB and a geometric-diversity component of +0.701 dB, totalling +27.793 dB at B = 400 MHz (Propositions 1 and 2). In the single-path line-of-sight regime, WB-CL-KL attains a range root-mean-square error of 19.8 mm against a 19.9 mm bound at signal-to-noise ratio (SNR) = 10 dB, a ratio of 0.996. Under the 3GPP Urban Micro (UMi) path-loss and shadow-fading SNR distribution, it achieves a bound ratio of 0.959 at the median deployment SNR of 9.6 dB, indicating near-CRB operation at the representative deployment point, where the compressed-domain bound is evaluated at the scene-median geometry.