GP Bandit-Assisted Two-Stage Sparse Phase Retrieval for Amplitude-Only Near-Field Beam Training

Abstract: The transition to Extremely Large Antenna Arrays (ELAA) in 6G introduces significant near-field effects, necessitating robust near-field beam training strategies in multi-path environments. Because signal phases are frequently compromised by hardware impairments such as phase noise and frequency offsets, amplitude-only channel recovery is a critical alternative to coherent beam training. However, existing near-field amplitude-based training methods often assume simplistic line-of-sight conditions. Conversely, far-field phase retrieval (PR) methods lack the sensing flexibility required to optimize training efficiency and are fundamentally limited by plane-wave models, making them ill-suited for near-field propagation. We propose a two-stage sparse PR framework for amplitude-only near-field beam training in multipath channels. Stage I performs adaptive support discovery on the standard 2D DFT beamspace by exploiting a physics-guided prior induced by near-field beam patterns. Stage II then refines the channel estimate by restricting sensing and sparse PR to the learned subspace. Numerical results show that the proposed adaptive pipeline consistently outperforms non-adaptive baselines, improving beamforming gain by over 70% at low SNR.