Sparse Array Enable Wideband Beamforming for Near-Field Multiuser Communications

In this paper, we investigate a near-field wideband multiuser communication system based on the symmetric nested array (SNA), which is formed by nesting a dense subarray within a uniformly sparse subarray. We begin by characterizing the near-field beam pattern of the SNA channel steering vector, showing that, with the same number of antennas, the SNA significantly enhances spatial resolution in contrast to dense array (DA) and exhibits lower side lobes than uniform sparse array (USA) of the same aperture. Additionally, we reveal the near-field beam splitting effect in a wideband channel model. By leveraging the geometric architecture of the dense middle and sparse sides of the SNA, we propose a novel digital and hybrid beamforming (DHB) scheme designed to maximize the achievable sum rate in wideband multiuser systems. However, the formulated problem is challenging to solve due to the non-convexity of constraints and the objective function, with intricately coupled variables. To address this, a two-layer penalty-based optimization method is introduced to decouple the original problem into three sub-problems and then iteratively solve them until convergence. The sub-problem for the digital beamformers is solved using the semidefinite relaxation algorithm. The optimal analog beamformers and true-time delayers (TTDs) are derived in closed-form expressions and solved via a low-complexity one-dimensional search by applying the block coordinate descent method. Simulation results validate the effectiveness of the proposed algorithm and demonstrate the superior performance of the proposed DHB scheme, particularly for densely located users.