Compressive Beam-Pattern-Aware Near-field Beam Training via Total Variation Denoising

TL;DR

This work addresses near-field beam training for extremely large ULAs/UPAs in 6G, where steering depends on both angle and range, producing plateau-like energy in 2D DFT beamspace. It shows that a separable Fresnel model yields a factorized beam pattern with axis-wise lobe widths, making the 2D sparsity cluster into compact plateaus. To exploit this structure without designing polar-domain codebooks, the authors propose a low-overhead three-stage pipeline: Stage I uses LASSO to detect a coarse support, Stage II dilates the 2D mask to cover the full plateau, and Stage III refines magnitudes with magnitude-based 2D TV denoising on the masked region. Simulations for a $N_y\times N_z=128\times16$ UPA at $28$ GHz show that LASSO+TV outperforms plain LASSO and L2 baselines in NMSE and beamforming gain across SNRs and pilot budgets, delivering robust near-field channel recovery and improved effective SNR by approximately 2–3 dB in the tested scenarios.

Abstract

Extremely large antenna arrays envisioned for 6G incurs near-field effect, where steering vector depends on angles and range simultaneously. Polar-domain near-field codebooks can focus energy accurately but incur extra two-dimensional sweeping overhead; compressed-sensing (CS) approaches with Gaussian-masked DFT sensing offer a lower-overhead alternative. This letter revisits near-field beam training using conventional DFT codebooks. Unlike far-field responses that concentrate energy on a few isolated DFT beams, near-field responses produce contiguous, plateau-like energy segments with sharp transitions in the DFT beamspace. Pure LASSO denoising, therefore, tends to over-shrink magnitudes and fragment plateaus. We propose a beam-pattern-preserving beam training scheme for multiple-path scenarios that combines LASSO with a lightweight denoising pipeline: LASSO to suppress small-amplitude noise, followed by total variation (TV) to maintain plateau levels and edge sharpness. The two proximal steps require no near-field codebook design. Simulations with Gaussian pilots show consistent NMSE and cosine-similarity gains over least squares and LASSO at the same pilot budget.

Figures (6)

• Figure 1: Diagram of the near-field communication system featuring a UPA.
• Figure 2: Normalized DFT--beamspace magnitude on a $(128\times 128)$ UPA at $f_c=28~\mathrm{GHz}$.
• Figure 3: 1D cuts of the normalized gain and the 6-dB lobe widths.
• Figure 4: DFT beamspace magnitude on a UPA near-field channel.
• Figure 5: Simulation results for the SNR sweeping.