Atomic-Norm Beamspace Parameter Estimation for Single-BS MIMO–OFDM Positioning

Abstract

Millimeter-wave single-base-station positioning with analog beamforming requires estimating multipath delays and departure/arrival angles from beam–frequency measurements, i.e., compressed observations of the underlying wideband MIMO–OFDM channel. In beamformed settings, the analog precoding/combining operator alters the standard Fourier/Vandermonde structure exploited by classical atomic line-spectral methods, making direct gridless recovery nontrivial. We address this problem by developing a beamspace specialization of coordinate-descent atomic soft-thresholding (CD-AST) that operates directly in the measurement domain through a pushed-forward atomic set induced by the beamforming operator. This yields two estimators: BEAST, a fully coupled 5-D off-grid estimator for joint delay–angle recovery, and EAST, a reduced-complexity delay-first variant that combines one-shot subspace-based delay estimation with per-slice 4-D atomic refinement. Simulations for 400-MHz mmWave MIMO–OFDM with practical beam training show that BEAST achieves delay and angular estimation accuracy close to the corresponding Cram ́er–Rao bounds and avoids the delay-resolution floor exhibited by subspace and matched-filter baselines, while EAST achieves a favorable accuracy–complexity trade-off by replacing repeated delay searches with one-shot subspace estimation. At 10 dBm total transmit power, BEAST attains centimeter-level positioning accuracy close to the position error bound, while EAST achieves comparable centimeter-level accuracy with reduced runtime.