Covariance-Domain Near-Field Channel Estimation under Hybrid Compression: USW/Fresnel Model, Curvature Learning, and KL Covariance Fitting

TL;DR

This paper introduces the CL-KL estimator for near-field channel estimation in hybrid array systems, leveraging covariance domain learning to improve accuracy and scalability in large MIMO deployments.

Contribution

The paper proposes a novel covariance-domain estimator that learns inverse range directly, avoiding coherence issues and enabling efficient, aperture-scalable near-field channel estimation.

Findings

CL-KL achieves the lowest NMSE among evaluated methods at various SNRs.

CL-KL operates in approximately 70 ms per trial, scalable with array size.

Validated against Cramér-Rao bound and robust to non-Gaussian sources.

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 $\mathrm{SNR}\in\{-5,0,+5,+10\}$~dB. Running in approximately 70~ms per trial (vs.\ 5~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 70~ms 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 Cram\'er-Rao bound and confirmed robust to non-Gaussian (QPSK) source distributions, with a maximum NMSE gap below 0.6~dB.