Covariance-Domain Near-Field Channel Estimation under Hybrid Compression: USW/Fresnel Model, Curvature Learning, and KL Covariance Fitting
arXiv:2603.28918v1 Announce Type: new Abstract: Near-field propagation in extremely large aperture arrays requires joint angle-range estimation. In hybrid architectures, only $N_\mathrm{RF}\ll M$ compressed snapshots are available per slot, making the $N_\mathrm{RF}\times N_\mathrm{RF}$ compressed sample covariance the natural sufficient statistic. We propose the Curvature-Learning KL (CL-KL) estimator, which grids only the angle dimension and \emph{learns the per-angle inverse range} directly from the compressed covariance via KL divergence minimisation. CL-KL uses a $Q_\theta$-element dictionary instead of the $Q_\theta Q_r$ atoms of 2-D polar gridding, eliminating the range-dimension dictionary coherence that plagues polar codebooks in the strong near-field regime, and operates entirely
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Abstract:Near-field propagation in extremely large aperture arrays requires joint angle-range estimation. In hybrid architectures, only $N_\mathrm{RF}\ll M$ compressed snapshots are available per slot, making the $N_\mathrm{RF}\times N_\mathrm{RF}$ compressed sample covariance the natural sufficient statistic. We propose the Curvature-Learning KL (CL-KL) estimator, which grids only the angle dimension and \emph{learns the per-angle inverse range} directly from the compressed covariance via KL divergence minimisation. CL-KL uses a $Q_\theta$-element dictionary instead of the $Q_\theta Q_r$ atoms of 2-D polar gridding, eliminating the range-dimension dictionary coherence that plagues polar codebooks in the strong near-field regime, and operates entirely on the compressed covariance for full compatibility with hybrid front-ends. At $N_\mathrm{MC}=400$ ($f_c=28$
GHz, $M=64$, $N_\mathrm{RF}=8$, $N=64$, $d=3$, $r\in[0.05,1.0],r_\mathrm{RD}$), CL-KL achieves the lowest channel NMSE among all six evaluated methods -- including four full-array baselines using $64\times$ more data -- at $\mathrm{SNR}\in{-5,0,+5,+10}$ms for the compressed-domain peer P-SOMP), CL-KL's dominant cost is the $N_\mathrm{RF}{\times}N_\mathrm{RF}$ inversion rather than $M$: measured runtime stays near 70dB. Running in approximately 70ms per trial (vs.\ 5ms across $M\in{32,64,128,256}$, making it aperture-scalable for XL-MIMO deployments. CL-KL is further validated against a derived compressed-domain Cramér-Rao bound and confirmed robust to non-Gaussian (QPSK) source distributions, with a maximum NMSE gap below 0.6dB.
Comments: 13 pages,9 figures. Submitted to IEEE Transactions on Wireless Communications, March 2026. Code and data: this https URL
Subjects:
Signal Processing (eess.SP); Information Theory (cs.IT)
Cite as: arXiv:2603.28918 [eess.SP]
(or arXiv:2603.28918v1 [eess.SP] for this version)
https://doi.org/10.48550/arXiv.2603.28918
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Rıfat Volkan Şenyuva [view email] [v1] Mon, 30 Mar 2026 18:49:45 UTC (301 KB)
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