Precise Near-Field Beam Training with DFT Codebook based on Amplitude-only Measurement

Extremely large antenna arrays (ELAAs) operating in high-frequency bands have spurred the development of near-field communication, driving advancements in beam training and signal processing design. In this work, we present a low-complexity near-field beam training scheme that fully utilizes the conventional discrete Fourier transform (DFT) codebook designed for far-field users. We begin by analyzing the received beam pattern in the near field and derive closed-form expressions for the beam width and central gain. These analytical results enable the definition of an angle-dependent, modified Rayleigh distance, which effectively distinguishes near-field and far-field user regimes. Building on the analysis, we develop a direct and computationally efficient method to estimate user distance, with a complexity of O(1), and further improve its accuracy through a simple refinement. Simulation results demonstrate significant gains in both single- and multi-user settings, with up to 2.38 dB SNR improvement over exhaustive search. To further enhance estimation accuracy, we additionally propose a maximum likelihood estimation (MLE) based refinement method, leveraging the Rician distribution of signal amplitudes and achieving accuracy close to the Cramer--Rao bound (CRB). Simulation shows the single-user and multi-user achievable rates can both approach those obtained with ideal channel state information.

Sparsity-Aware Near-Field Beam Training via Multi-Beam Combination

This paper proposes an adaptive near-field beam training method to enhance performance in multi-user and multipath environments. The approach identifies multiple strongest beams through beam sweeping and linearly combines their received signals - capturing both amplitude and phase - for improved channel estimation. Two codebooks are considered: the conventional DFT codebook and a near-field codebook that samples both angular and distance domains. As the near-field basis functions are generally non-orthogonal and often over-complete, we exploit sparsity in the solution using LASSO-based linear regression, which can also suppress noise. Simulation results show that the near-field codebook reduces feedback overhead by up to 95% compared to the DFT codebook. The proposed LASSO regression method also maintains robustness under varying noise levels, particularly in low SNR regions. Furthermore, an off-grid refinement scheme is introduced to enhance accuracy especially when the codebook sampling is coarse, improving reconstruction accuracy by 69.4%.